text:
\section{Introduction}

The physics of systems of confined particles has attracted the
interest of researchers from many different areas working on both, theoretical and experimental aspects \cite{wigner_1934,wineland_1987}. One feature of such quantum systems that has recently gained
impulse is the study of entropic measures of entanglement \cite{osenda_2015, garagiola_2016, koscik_2015, lopezrosa_2015,simonovic_2015}. Among the many kind of systems that could be addressed using the physics of the confined systems, in the present work we focus on Wigner molecules, which are the finite-size analogue of Wigner crystals, named after the seminal work of E. Wigner \cite{wigner_1934}. Since the late 80's, when the
first confined linear chains of ions where reported by D. Wineland \cite{wineland_1987}, there has been an increasing capacity to confine, control and manipulate such entities, and has turned the Wigner molecules into a new platform to test the known, and look for new, traits of quantum
mechanics \cite{drewsen_2015}.

Trapped ions are not the only physical systems that allow the
formation of entities like the Wigner molecules (also named Coulomb crystals \cite{drewsen_2015}). The experimental observation of strongly correlated states in quantum dots has attracted considerable interest \cite{cavaliere_2009}. Wigner molecules have also been observed in two-dimensional semiconductor heteroestructures \cite{andrei_1998,piot_2008}, semiconductor quantum dots \cite{kallikaos_2008},
one-dimensional quantum wires \cite{ellenberger_2006,singha_2010,kristinsdottir_2011,meyer_2009}, carbon
nanotubes \cite{deshpande_2008,pecker_2013}, and in crystalline states
for dusty plasma \cite{melzer_2003}. Several theoretical
studies \cite{jauregui_1993,guclu_2008,mendl_2014,gambeta_2014,cavaliere_2014,
cavaliere_2015,cavaliere_2015_2,kylanpaa_2016} have demonstrated that
the physics of these systems with reduced dimensionality usually does not
depend on the shape of the confinement but on its symmetries and
strength (see Ref. \cite{pecak_2016} for an example where shape does have an
influence). In the present work we use a harmonic confinement as a model potential, and represent different physical situations using different interaction potentials. Wigner molecules arise when the interparticle interaction strength is much larger than the kinetic energy. The latter can be related to the temperature of the system \cite{drewsen_2015} and also to the density, or confining energy, of the particles \cite{filinov_2001}. Hence Wigner localization is expected for low density systems or for large
interaction strengths.

The Calogero and Moshinsky models are the most salient examples of
analytically solvable models of confined particles, including the exact
computation of the entanglement entropies
\cite{osenda_2015,garagiola_2016,manzano_2010,dehesa_2012,benavides_2014,
koscik_2010,koscik_2013, koscik_saha_2015}, in this sense it can
also be mentioned the spherium model \cite{toranzo_2015}, and the quasi-solvable
Hook model \cite{taut_1993}. In particular, the Calogero model has been widely
studied in condensed matter physics and has experienced several
revivals \cite{Polychronakos_1993,Polychronakos_2006}, such as the discovery of
an explicit relation of the Calogero model with the fractionary quantum hall
effect \cite{Azuma_1994} and fractional statistics \cite{Murthy_1994}.
{In a previous paper~\cite{garagiola_2016}, we have studied the
behavior of the von Neumann and R\'enyi entropies of the one- and
two-dimensional Calogero model for two particles. By considering anisotropic
confinement in the two-dimensional case we showed that the one-dimensional
regime is reached when the anisotropy of the trap increases, and we also
demonstrated that the R\'enyi entropies present a non analytical behavior in
the neighborhood of those values of the interaction strength parameter for which
the reduced density matrix has finite support.}

Motivated by this, we consider anisotropic harmonic confinement and compute the
exact expression for the occupation numbers or occupancies of the
two-dimensional ground state wave function in the large interaction strength
limit for two particles which interact via different potentials depending on the
distance between the particles. The exact natural orbitals are obtained from the
Schmidt decomposition of the ground state wave function in the same limit and
the occupancies are used to evaluate several quantum information measurements
such as von Neumann and R\'enyi entropies in closed form. {The
method presented here is a generalization of the strategy
developed in Refs.~\cite{koscik_2015,koscik_2010,koscik_2015_2,glasser_2013}.
The two particle one-dimensional systems with Coulomb and inverse powers
interactions are addressed in~\cite{koscik_2015,koscik_2015_2,glasser_2013},
while the
natural orbitals and occupation numbers of elliptically deformed
two-dimensional quantum dots are reported in~\cite{koscik_2010}. Here we
give the analytical expressions of the natural
orbitals, occupation numbers, von Neumann and R\'enyi entropies in the
strong interaction limit for any potential which depends only on the
interparticle distance.}

Our main purpose is to determine the influence of the anisotropy and the type of interparticle interaction
by looking upon the linear, von Neumann, min-entropy, max-entropy
and R\'enyi entropies as entanglement measures. We have a particular interest in which are the differences arising from a short-range interaction with respect to a long range one for which the
emergence of Wigner Molecules has been widely described (see, for example, Refs.
\cite{jauregui_1993,guclu_2008,cavaliere_2014}). With this aim, we study
two interacting potential cases for each interaction range, including one that can be exactly
solved. In the long-range interaction case we consider the inverse power and the
inverse logarithmic potential, and for the short-range interaction we solve the
screened inverse power potential and a Gaussian repulsive interaction. It is important to
emphasize that the inverse power interaction case is used to model quantum dots
\cite{kallikaos_2008} or ion traps \cite{wineland_1987} where the large
interaction regime can be achieved experimentally due to a strong interaction
between the particles or a weak confinement energy scale, for inverse square
power one gets the Calogero model, while the screened Coulomb interaction provides a simple model potential for ions and plasmas \cite{li_2012}.

The paper is organized as follows. The
model is discussed in Section \ref{section_2d2p_sys}. In Section
\ref{section_analytical_derivation}
we show the derivation of the analytical occupancies of two interacting
particles in a two-dimensional anisotropic harmonic trap, while in Section
\ref{section_entropies} we calculate the entropic entanglement measures. We
discuss the results for long- and short-range interaction potentials in Sections
\ref{section_long_range} and \ref{section_short_range} respectively. Finally, a
summary and conclusions are presented in Section
\ref{section_summary_conclusions}.

\section{Confined two-dimensional two-particle systems}
\label{section_2d2p_sys}

The physics of confined particle systems is nowadays very relevant to understand the many recent experiments conducted in cold atom traps or in quantum dots, at least in a qualitative way \cite{andrei_1998, piot_2008, kallikaos_2008, ellenberger_2006, singha_2010, kristinsdottir_2011, meyer_2009}. The models for those systems contain two contributions to the potential energy: one is given by the trap potential and the other by the interaction between the particles. For small dots, containing few electrons the trap potential can be approximated by a harmonic one \cite{cavaliere_2009}, therefore we focus here on two interacting particles in a two-dimensional anisotropic harmonic traps, and implement a method to solve the entanglement spectrum in the large interaction limit for arbitrary interaction potentials. The Hamiltonian for two particles in an anisotropic trap, in atomic units, is

\begin{equation}
\label{H_QD_2D}
H = -\frac{1}{2}\left( \nabla_1^2+\nabla_2^2\right) + \frac{1}{2}\left\lbrace (x_1^2+x_2^2)+\varepsilon^2(y_1^2+y_2^2) \right\rbrace + g V\left( r_{12} ; \left\lbrace \gamma_{i} \right\rbrace \right) \; ,
\end{equation}

\noindent where the frequency of the trap was taken equals to unity, $\varepsilon > 1$ is the anisotropy parameter, $V\left( r_{12} ; \left\lbrace \gamma_{i} \right\rbrace \right)$ denote the interaction potential as a function of the interparticle distance $r_{12}$ and some parameters $\left\lbrace \gamma_{i}
\right\rbrace$, and $g$ is the ratio between the interaction and the confinement
energy scale. By introducing the center of mass $\vec{R} = \frac{1}{2} (\vec{r}_1 + \vec{r}_2)=(X,Y)$ and relative coordinates $\vec{r} = \vec{r}_2-\vec{r}_1=(x,y)$ the Hamiltonian
(\ref{H_QD_2D}) decouple as  $H = H^R + H^r$, where

\begin{eqnarray}
\label{H_cal_2D_mc}
& &H^R = -\frac{1}{4} \nabla_R^2 + \left(X^2+ \varepsilon^2 Y^2\right)\; , \\
\label{H_cal_2D_r}
& &H^r = -\nabla_r^2 + V^{eff}(x,y;\varepsilon,\left\lbrace \gamma_{i} \right\rbrace)\; ,
\end{eqnarray}

\noindent and $V^{eff}$ is the effective potential of the relative Hamiltonian given by

\begin{equation}
\label{Veff}
V^{eff}(x,y;\varepsilon,\left\lbrace \gamma_{i} \right\rbrace)=
\frac{1}{4}\left( x^2+ \varepsilon^2 y^2\right) + g V\left( \sqrt{x^2+y^2} ;
\left\lbrace \gamma_{i} \right\rbrace \right)\; .
\end{equation}

The total wave function is then the product of the center of mass wave function and the relative wave function

\begin{equation}
\label{psi_prod}
\Psi(x,y,X,Y) = \psi^R(X,Y) \psi^r(x,y) \; ,
\end{equation}

\noindent and, consequently, the Schr\"odinger equation separates into two
equations

\begin{eqnarray}
\label{Schr_eq_1}
& &H^R\psi^R(\vec{R}\,) = E^R \psi^R(\vec{R}\,)\; ,\\
\label{Schr_eq_2}
& &H^r\psi^r(\vec{r}\,) = E^r \psi^r(\vec{r}\,)\; .
\end{eqnarray}

The solutions of the center of mass equation (Eq. (\ref{Schr_eq_1})) are the
eigenfunctions of the harmonic oscillator that are invariant under particle
exchange.

The relative Hamiltonian, Eqs.~(\ref{H_cal_2D_r}) and~(\ref{Veff}), must be
analysed on a case-specific basis. However, in
the next section we present a method to obtain the large interaction strength
limit of general potentials that fulfil simple requirements.

\section{Derivation of the analytical occupancies}
\label{section_analytical_derivation}

The relative wave function may be obtained by solving the Schr\"odinger
equation in the large interaction strength regime, $g \gg 1$, by using the
harmonic approximation (HA) \cite{james_1998, balzer_2006}. In the framework of the harmonic
approximation one has to find the minima of the effective potential Eq.
(\ref{Veff}) and then the potential is replaced by its Taylor
expansion up to second order about its minima, which satisfy $\nabla V^{eff}(x,y;\varepsilon,\left\lbrace \gamma_{i} \right\rbrace) = 0 $. If the potential is repulsive, decreases monotonously
and $ V \left( r ; \left\lbrace \gamma_{i} \right\rbrace \right) \to
0 $ for $r\to\infty$, with $\varepsilon > 1$, the minima lie on the $x-$axis
and can be written as

\begin{equation}
\label{min_V_eff}
\vec{r}_{min} =\left(\pm x_0, 0 \right) \;\;\;\; \mbox{with $x_0>0$ given
by}\;\;\;\; \frac{1}{2g}=-\left.\left( \frac{1}{r} \frac{\partial V}{\partial
r}\right)\right\vert_{x_0} \,.
\end{equation}

\noindent It is important to notice that when the particles are confined in an
isotropic trap, \textit{i.e} $\varepsilon=1$, the minima degenerate into a
circle of radius $x_0$.

Within the harmonic approximation, a Hamiltonian of uncoupled oscillators is obtained

\begin{equation}
\label{H_Ha}
H^r_{HA} = -\nabla_r^2 + \frac{1}{2} \left\lbrace \omega_x^2 \left( x- x_0  \right)^2 + \frac{1}{2} \left(\varepsilon^2 -1 \right) y^2 \right\rbrace\; ,
\end{equation}

\noindent with a frequency associated to the $x$-coordinate given by
\begin{equation}
\label{wx_2}
\omega_x^2 = \frac{1}{2} \left( 1 + \frac{\left. \frac{\partial^2 V}{\partial
r^2}\right\vert_{x_0} }{\left. -\frac{1}{r} \frac{\partial V}{\partial
r}\right\vert_{x_0}} \right)\;  ,
\end{equation}

\noindent where the dependence on the parameters $g$ and $\left\lbrace \gamma_{i} \right\rbrace$ is implicit in $x_0=x_0\left(g, \left\lbrace \gamma_{i} \right\rbrace \right) $.

The totally symmetric ground state wave function $\Psi ^{GS} \left( \vec{r}_1,
\vec{r}_2 \right)$ of the harmonic Hamiltonian $H^R + H^{r}_{HA}$ is a product
of Gaussians. The eigenvalues of the one-particle reduced
density matrix $\rho=\textrm{Tr}_2 \left(\left| \Psi^{GS}\right\rangle
\left\langle \Psi^{GS} \right|\right)$ are explicitly obtained (see supporting
information), and are given by

\begin{equation}
\label{auval_2D}
\Lambda_{l,\tilde{l}} = \Lambda_{l}^{x} \, \Lambda_{\tilde{l}}^{y} \;,
\end{equation}

\noindent where

\begin{equation}
\label{auval_2D_x}
\Lambda_{l}^{x}  = \frac{\left(1-\zeta\left( \omega_x\right)  \right)}{2 \left( 1 + e^{-\frac{x_0^2\,\omega_x}{\sqrt{2}}} \right) } \zeta\left( \omega_x\right)^{l} \;\;\;\; \mbox{,}\;\;\;\; \zeta\left( \omega_x\right) = \left( \frac{ \left( 2 \omega_x^2\right) ^{\frac{1}{4}} - 1}{\left( 2 \omega_x^2\right) ^{\frac{1}{4}} + 1}\right)^2 \;,
\end{equation}

\noindent and

\begin{equation}
\label{auval_2D_y}
\Lambda_{\tilde{l}}^{y} = \left(1-\xi(\varepsilon)\right) \xi(\varepsilon)^{\tilde{l}} \;\;\;\; \mbox{,}\;\;\;\; \xi(\varepsilon) = \left( \frac{\left( \varepsilon^2 -1 \right) ^\frac{1}{4} - \sqrt{\varepsilon}}{\left( \varepsilon^2 -1 \right) ^\frac{1}{4} + \sqrt{\varepsilon}}\right)^2 \;.
\end{equation}

\noindent where $l,\tilde{l}=0,1,2,\ldots$. Each eigenvalue, or occupancy,
is doubly degenerate due to the particle exchange symmetry.

The limiting values and behavior of  $\zeta\left(\omega_x\right)$ and $\xi(\varepsilon)$ are needed to compute the entropic quantities. We note then that for $\omega_x>0$, $\zeta\left( \omega_x\right)$
is always below unity and $\zeta\left( \omega_x\right) \to 1$ when $\omega_x
\to \infty$, while for $\varepsilon>1$, $\xi(\varepsilon)$ remains below one
and $\xi(\varepsilon) \to 1$ for $\varepsilon \to 1^+$, then we must be specially careful in the isotropic confinement case (see Eq. (\ref{auval_2D_y})). For large anisotropy parameter
$\varepsilon \gg 1 $ one gets $\xi(\varepsilon) \to 0$ and the occupancies reach
the asymptotic values of the one dimensional model $\Lambda_{l}^{x}$.

\section{Entropies in the large interaction strength limit}
\label{section_entropies}

The entanglement can be measured using different entropic quantities. If
$\{\Lambda_i\}$ is the complete set of eigenvalues, then the
R\'enyi entropies are a family of such entropies defined by

\begin{equation}
\label{def_Renyi}
S^{\alpha} = \frac{1}{1-\alpha} \,\log_2 \mbox{Tr} \, \rho^{\alpha} =
\frac{1}{1-\alpha}\, \log_2 \left( \sum_i \Lambda^{\alpha}_i \right)  \,,
\end{equation}

\noindent which are widely used in many-body or extended systems
\cite{Calabrese2011a,Alba2010}.
Special values of the parameter
$\alpha$ allow to recover other entropies, being the min- and max-entropy good
examples obtained by taking the limits $\alpha\rightarrow \infty$ and
$\alpha\rightarrow 0$, respectively. The min-entropy serves as a lower bound to
the entanglement measures obtained from the whole family of entropies. The
Hartley or
max-entropy, $S^{0}=\log_2 R$, only depends on the Schmidt rank $R$
of the spectrum distribution and is a measure of bipartite entanglement which
serves as a criterion for efficient classical representation of the state
\cite{amico_2014}. The distribution of the entanglement spectrum can be better
understood by computing the R\'enyi entropies for many different values of the
parameter $\alpha$ \cite{garagiola_2016}. The von Neumann entropy is given by

\begin{equation}
\label{def_vN}
S_{vN} = - \mbox{Tr} \left(\rho \log_2 \rho \right) = - \sum_i \Lambda_i \log_2
\Lambda_i \,.
\end{equation}

\noindent The von Neumann entropy has been used to study entanglement in
continuous variables systems and spin models \cite{Alba2010, osenda_2007,
pont_2010}. It can be recovered from the R\'enyi entropies in the
limit $\alpha
\to 1$. Finally, some authors use the linear entropy, defined by

\begin{equation}
\label{def_SL}
S_{L} = 1 - \mbox{Tr} \, \rho^2 = 1 - \sum_i \Lambda^{2}_i \,,
\end{equation}

\noindent since for continuous variable systems the calculation of $\mbox{Tr}
\,
\rho^2$ is reduced to a single integral. Even though, the linear entropy has no
relevant information for the systems studied in the present work, we compute it
for the sake of completeness.

Once we have obtained the occupancies it is possible to calculate the quantum entropies. Since these calculations involve geometric series in
$\zeta\left(\omega_x\right)$ and $\xi(\varepsilon)$, the limiting values must be carefully computed.

Let us start with the R\'enyi entropies defined by Eq. (\ref{def_Renyi}). It is straightforward to show that due to the separability of the wave function,  the R\'enyi entropies in the large interaction strength limit are the sum of the entropy associated to $\psi_x(x_1,x_2)$ and
$\psi_y(y_1,y_2)$, then

\begin{equation}
\label{Renyi_xy}
S^{\alpha} = S^{\alpha}_{x}(\omega_x) + S^{\alpha}_{y}(\varepsilon) \,,
\end{equation}

\noindent where

\begin{equation}
\label{Renyi_2D_x}
S^{\alpha}_{x} \left( \omega_x\right) = \frac{1}{1-\alpha} \log_2 \left(
\frac{(1-\zeta\left( \omega_x\right))^ \alpha}{(1-\zeta\left( \omega_x\right)^\alpha)}
\right) + 1 \,,
\end{equation}

\noindent and

\begin{equation}
\label{Renyi_2D_y}
S^{\alpha}_{y} (\varepsilon) = \frac{1}{1-\alpha} \log_2 \left(
\frac{(1-\xi(\varepsilon))^ \alpha}{(1-\xi(\varepsilon)^\alpha)}
\right) \,.
\end{equation}

Again, due to the separability of the wave function, we can write the two-dimensional von Neumann entropy of Eq. (\ref{def_vN}) as

\begin{equation}
\label{S_VN}
S_{vN} = S_{x}^{1}\left( \omega_x\right) + S_{y}^{1}(\varepsilon) \;,
\end{equation}
\noindent where each one of the terms in the sum has the form of a
one-dimensional von Neumann entropy \cite{koscik_2015}, {\it i.e.}

\begin{equation}
\label{Sx}
S_{x}^{1}\left( \omega_x\right) = - \frac{\log_2\left( \left(1-\zeta\left( \omega_x\right) \right)^{(1-\zeta\left( \omega_x\right))} \zeta\left( \omega_x\right)^{\zeta\left( \omega_x\right)} \right)}{ \left(1-\zeta\left( \omega_x\right)\right)} + 1\;,
\end{equation}

\begin{equation}
\label{Sy}
S_{y}^{1}(\varepsilon) = - \frac{\log_2\left( \left(1-\xi(\varepsilon)\right)^{(1-\xi(\varepsilon))} \xi(\varepsilon)^{\xi(\varepsilon)} \right)}{ \left(1-\xi(\varepsilon)\right)}\;.
\end{equation}

The super-index points that the von Neumann entropy can be obtained as a limiting case of the
R\'enyi entropies when $\alpha\to 1$.

It is worth to notice that from Eq. (\ref{Renyi_2D_x}) and (\ref{Renyi_2D_y})
it is straightforward to show that the min-entropy $S^\infty$, can also be written as a two-term sum:

\begin{equation}
\label{min_entropy}
S^\infty = \lim_{\alpha\to\infty} \left( S^{\alpha}_{x}\left( \omega_x\right) + S^{\alpha}_{y}(\varepsilon) \right)  = \lim_{\alpha\to\infty}  S^{\alpha}_{x}\left( \omega_x\right) + \lim_{\alpha\to\infty} S^{\alpha}_{y}(\varepsilon)= S^{\infty}_{x}\left( \omega_x\right)+S^{\infty}_{y}(\varepsilon) \,.
\end{equation}

The Hartley or max-entropy in the large interaction strength limit can also be calculated as a limiting case with $\alpha\to 0$, $S^{0}=\log_2 R$, and has finite value only when the one-particle reduced density matrix has finite support.

The two-dimensional linear entropy defined by Eq. (\ref{def_SL}) gives

\begin{equation}
\label{le_final}
S_{L} = 1 - \frac{1}{2} \; \frac{1-\zeta\left(
\omega_x\right)}{1+\zeta\left( \omega_x\right)} \;
\frac{1-\xi(\varepsilon)}{1+\xi(\varepsilon)} \;.
\end{equation}

\noindent For the isotropic model $\varepsilon \to 1^{+}$, $\xi(\varepsilon)\to 1$ and the linear entropy goes to one, while for any other value of $\varepsilon$ the linear entropy remains below one.

A comment on the extension of the previous results to dimension $D$ is in
place. They can be extended if one considers $D-1$ anisotropy parameters (see
supporting information). The von Neumann and R\'enyi entropies are the sum of
$D$ terms each one associated to one cartesian coordinate and, as we
demonstrated for the two-dimensional case, the $x$-entropy term depends on the
parameters of the interaction potential through $\omega_x$ and each one of the
remaining terms depend on only one of the $D-1$ anisotropy parameters.

\begin{figure}
\begin{center}
\includegraphics[width=0.3\textwidth]{fig_1a.eps}
\includegraphics[width=0.32\textwidth]{fig_1b.eps}
\end{center}
\caption{\label{f_S_2D_omega}  Both terms of the two-dimensional von Neumann (black dashed), min-entropy (magenta dash-dotted) and R\'enyi entropies with $\alpha = 0.2,\,0.4,\,0.8,\,1.5,\,2$ (red, blue, green, orange and cyan full lines respectively). (a) $S_y$ as a function of the anisotropy parameter $\varepsilon$. (b) One dimensional entropies $S_x$ as a function of the squared frequency, $\omega_x^2$.
}
\end{figure}

The two terms of the two-dimensional von Neumann, min-entropy and R\'enyi entropies
($\alpha = 0.2, \,0.4, \,0.8, \,1.5, \,2$) are depicted in Fig. \ref{f_S_2D_omega}. Let us first discuss the behavior of the entropies with respect to the anisotropy of the trap, and afterwards the influence of the interparticle interaction.

As can be appreciated in Fig. \ref{f_S_2D_omega}(a), for the isotropic model ($\varepsilon \to 1^{+}$) the entropies $S^{\alpha}_y(\varepsilon)$ diverge logarithmically, whilst for any other values
of $\varepsilon$ they remain finite. By calculating the first derivative of Eq. (\ref{Sy}) it is
straightforward to show that

\begin{equation}
\label{vNe_limit}
S_{vN} \sim -\frac{\ln(\varepsilon-1)}{\ln
16}  \;\;\;\; \mbox{for}\;\; \varepsilon \sim  1^{+}\,.
\end{equation}

\noindent This asymptotic leading term is depicted in the figure as a yellow dashed line which makes the logarithmic divergence of the isotropic von Neumann entropy evident. Actually, for $\varepsilon \to 1^{+}$ the von Neumann, min-entropy and the family of R\'enyi entropies present this same behaviour. The figure also shows that for large anisotropy parameter the entropies $S^{\alpha}_{y}(\varepsilon)$ vanish. In other words, for $\varepsilon \gg 1$ the one dimensional problem is recovered and the von Neumann, R\'enyi and min-entropy reach the one dimensional values $S_{x}^{\alpha}(\omega_x)$.

The behavior of the $x$-entropies (denoted by $S^{\alpha}_x(\omega_x)$) as a function of the frequency is shown in Fig. \ref{f_S_2D_omega}(b). The figure shows that the entropies are decreasing functions of the frequency for $0< \omega_x^2 < 1/2$, and increasing functions for $\omega_x^2 > 1/2$.
Actually, the entropies diverge logarithmically for large frequencies and also
for $\omega_x \to 0$, because in these limits one gets that $\zeta(\omega_x) \to 1$.

The entropy of a given system is computed using the frequency $\omega_x$ obtained by the harmonic approximation Eq. (\ref{wx_2}). If it remains finite for large interactions parameters $g \gg 1$, then the von Neumann, min-entropy and the family of R\'enyi entropies are finite for the anisotropic model and diverge
logarithmically for the isotropic model. In the deformed or anisotropic case the
particles crystallize around the two classical minima of the relative
Hamiltonian giving rise to a Wigner molecule, while for the isotropic model
those minima degenerate into a circle, the particles are no
longer localized around discrete minima and this lack of information is
reflected in the divergence of the entanglement entropies. If the obtained frequency
increases monotonously for large interactions, the von Neumann, min-entropy and
the family of R\'enyi entropies diverge logarithmically for any anisotropy
parameter. In this sense, the behaviour of the system is defined by the
one-dimensional entropy $S_{x}^{\alpha}(\omega_x)$.

The previous analysis can be understood more qualitatively by using the
Heisenberg uncertainty principle.
The width of the Gaussian wave packet in the relative coordinate
$\psi^{r}(\vec{r})$ (ground state of the Hamiltonian Eq. (\ref{H_Ha})) goes to
zero
when the frequency increases. Actually, the relative position and momentum
uncertainty are $\Delta x^{r}_{HA} = \sqrt{\langle \left( x_2 - x_1 \right)^2
\rangle - \langle x_2 - x_1 \rangle^2} = 2^{\frac{1}{4}}/\sqrt{\omega_x}$ and
$\Delta p^{r}_{HA} = \sqrt{\omega_x}/2^{\frac{5}{4}}$, then if $\omega_{x} \to
0$ we obtain that $\Delta x^{r}_{HA} \to \infty$ and, conversely, when $\omega_{x} \to \infty$
it is straightforward to show that $\Delta p^{r}_{HA} \to \infty$.
Thus, we see that for $\omega_{x} \to \infty$ the entropy of the Wigner molecule diverge
because the position is completely determined and consequently the momentum
uncertainty diverges, we refer to this limit as \emph{strong
crystallization}. The opposite case, $\omega_{x} \to 0$ leads to a
well defined momentum state and hence we have no knowledge of the position. In
both cases the divergence in the position or momentum width leads to the
divergence of the entanglement entropies. Furthermore, the divergence of the
$y$-entropies could also be explained in a similar way: for the isotropic model
the minima degenerate into a circle and consequently the particles are no longer
localized around any definite angular positions, but the state has definite
angular momentum.

For $\omega_x^2=1/2$ the entropies have
their minimum value equal to unity. Around this point, the von Neumann,
min-entropy and R\'enyi entropies with $\alpha>1$ present an analytical
behaviour while the R\'enyi entropies with $\alpha<1$ have a non-analytical
behaviour. The von Neumann and R\'enyi entropies with $\alpha = 0.4,\,0.5,\,0.6$
and their first derivatives around the point $\omega_x^2=1/2$ are shown in Fig.
\ref{f_S_x_der} (a) and (b) respectively. It shows that the R\'enyi entropies present an infinite
derivative for $\alpha=0.4$, discontinuous derivative for $\alpha=0.5$ and a
continuous derivative with infinite second derivative for $\alpha=0.6$, while
the von Neumann entropy ($\alpha\rightarrow {}^{+}1$) is an
analytical function of the frequency.

\begin{figure}
\begin{center}
\includegraphics[height=0.29\textwidth]{fig_2a.eps}
\includegraphics[height=0.30\textwidth]{fig_2b.eps}
\end{center}
\caption{\label{f_S_x_der} (a) Entropy terms $S^{\alpha}_x(\omega_x)$ and (b) their derivatives around the point $\omega_x^2=1/2$.  The von Neumann (black dashed), and R\'enyi entropies with $\alpha = 0.4,\,0.5,\,0.6$ (red, blue and green full lines respectively) are shown.
}
\end{figure}

Recent studies by Amico and co-workers in $1/2$-spin chains show the physical
implications of non-monotonous properties of the R\'enyi entropies in many-body
systems with topological order due to a truncation of the support of the reduced
density matrix \cite{amico_2013,amico_2013_2,amico_2014_2}. In
Ref.~\cite{osenda_2015} some of the present authors found that the Calogero
model in one dimension has a finite number of non-zero occupancies for a
discrete set of values of the interaction parameter, and in Ref.
\cite{garagiola_2016} we demonstrated that in those particular values of
the interaction parameter the R\'enyi entropies present a non-analytical
behaviour.

Summarizing, non-analytical behaviour of the R\'enyi entropies exposes the
finite support of the reduced density matrix. In the present case, taking
$\omega_x^2=1/2$ in Eq. (\ref{auval_2D_x}) it is straightforward
to see that for this particular frequency there is only two non vanishing
occupancies $\Lambda^{x}_{0}$ associated to the two lowest natural orbitals in
the $x$-coordinate.

In the following sections we apply our findings to study the behavior of the occupancies and entropic entanglement measures in the large interaction strength limit for different cases divided as long- or short-range potentials. From now on we calculate only the one dimensional entropy $S_{x}^{\alpha}(\omega_x)$, since the behaviour of the entropy terms $S^{\alpha}_{y}(\varepsilon)$ were already
analysed.

\section{Long-range interaction potentials}
\label{section_long_range}

In the present section we consider two long-range interactions to exemplify our results: the inverse power interaction and inverse logarithmic interaction.

\subsection{Inverse power interaction}

The inverse power potential is

\begin{equation}
\label{V_inv_power}
V^{ip}\left( r ; \beta \right) = \frac{1}{r^{2\beta}}\; .
\end{equation}

\noindent For this potential $x_0$ and $\omega_x$, Eqs. (\ref{min_V_eff}) and (\ref{wx_2}), can be obtained exactly and give

\begin{equation}
\label{min_freq_V_inv_power}
x_0=(4g\beta)^{\frac{1}{2(\beta+1)}} \;\;\;\; \mbox{and}\;\;\;\;  \omega_x^2=\beta + 1\,.
\end{equation}

\noindent Thus, $x_0$ increases when increasing the interaction strength
parameter $g$, but the frequency remains invariant. For $\beta = \frac{1}{2},1$ one gets the Hook and the Calogero model respectively.

\begin{figure}
\begin{center}
\includegraphics[height=0.3\textwidth]{fig_3a.eps}
\end{center}
\caption{  \label{f_auval_2D} Occupancies as a function of $\ln
(\varepsilon-1)$ (see Eq. (\ref{auval_2D})) obtained for large interaction
strength parameter, $g \gg 1$. $\Lambda_{l,\tilde{l}}$ with $l=0$ and
$\tilde{l}=0,1,2,...,20$ from top to bottom. The dominant one-dimensional
eigenvalue is also shown (grey dashed line) \cite{koscik_2015}.}
\end{figure}

Let us start with the Calogero model. The occupancies
defined in Eq. (\ref{auval_2D}) for large interaction strength parameter
$g\gg1$ are shown as a function
of $\ln (\varepsilon-1)$ in Fig. \ref{f_auval_2D}, where the grey dashed line
is the dominant one-dimensional occupancy in the large interaction strength
limit, obtained from Eq. (\ref{auval_2D_x}), that is in agreement with the
value reported in Ref. \cite{koscik_2015}. The figure shows that for $\epsilon
\to 1^{+}$ (isotropic model) the occupancies go to zero, but note that
their sum is always equal to $1/2$ due to the mentioned
double degeneracy \cite{koscik_2010}. When the
anisotropy increases all the occupancies $\Lambda_{l,\tilde{l}}$ with
$\tilde{l}\neq 0$ present a local maximum. For fixed $l$ the value of the
anisotropy parameter at which the maximum occurs decreases when $\tilde{l}$
increases, while for fixed $\tilde{l}$ this value is the same for each
$l$. For $\varepsilon \gg 1$ the
Hamiltonian reduces to a one dimensional oscillator and the occupancies
$\Lambda_{l,0}$ reach the asymptotic values of the one dimensional model. For
values of $\varepsilon$ near $\varepsilon_c = \sqrt{5}$ the occupancies with
$\tilde{l}=0$ stabilize on the one dimensional values and those with
$\tilde{l}\neq 0$ saturate at vanishingly small values. This feature can be
explained if one takes into account that for $\varepsilon =\varepsilon_c$ the
relative Hamiltonian Eq. (\ref{H_Ha}) reduces to a harmonic oscillator in polar
coordinates around each minimum. More
generally, for arbitrary $\beta$, the one dimensional regime is reached at the value $\varepsilon_c = \sqrt{2 \left(\beta+1\right)+1} $. In this case the effective potential of the relative
Hamiltonian Eq. (\ref{Veff}) is isotropic in a small neighborhood around its minima.
For $\varepsilon > \varepsilon_c$, the largest occupancy $\Lambda_{00}$ reaches
the value $\sim 0.4853$, and the sum of
all the remaining occupancies is only $\sim 0.0147$; this means that the two natural orbitals associated to this eigenvalue are the only two that are occupied while all the others natural orbitals contribution are negligible, and consequently, the spatial wave functions are quite similar to those two natural orbitals \cite{koscik_2010}.

\begin{figure}
\begin{center}
\includegraphics[height=0.3\textwidth]{fig_4.eps}
\end{center}
\caption{\label{f_Ss} One-dimensional entropy terms $S^{\alpha}_x$ obtained for large interaction strength $g \gg 1$, as a function of the exponent of the interaction between particles, $\beta$. The von Neumann (black dashed), min-entropy (magenta dash-dotted) and R\'enyi entropies with $\alpha = 0.2,\,0.4,\,0.8,\,1.5,\,2$ (red, blue, green, orange and cyan full lines respectively) are shown.
}
\end{figure}

As we mentioned above, the dependence with $\beta$ is present only
through the entropy term $S^{\alpha}_x(\omega_x)$. The width of the Gaussian wave packet in the relative coordinate is finite, $\Delta x^{r}_{HA} = 2^{\frac{1}{4}}/(\beta + 1)^\frac{1}{4}$ and consequently the von Neumann, min-entropy and R\'enyi entropies are finite. However, the max-entropy diverges due to the infinite support of the one-particle density matrix. Notice that in the limit $\beta \to \infty$ the entropies diverge logarithmically
due to the divergence in the momentum uncertainty. This behavior can be seen in Fig. \ref{f_Ss} where the von Neumann, the min-entropy and R\'enyi entropies are depicted as a function of the parameter $\beta$. The R\'enyi entropies increases for decreasing $\alpha$, and the von Neumann entropy is a limiting case with $\alpha \to 1$. It is important to emphasize that taking the limit $\beta \to 0$ in the entropies does not result in the same entropies obtained for a system with harmonic confinement and a constant interaction (Eq. (\ref{V_inv_power}) with $\beta=0$), since this limit does not commute with the large interaction limit.

\subsection{Inverse logarithmic interaction}

The potential for inverse logarithmic interparticle interaction is

\begin{equation}
\label{V_inv_log}
V^{il}\left( r \right) = \frac{1}{\ln (r+1)}\; .
\end{equation}

\noindent In this case $x_0$ and $\omega_x$ satisfy the following equations

\begin{equation}
\label{min_freq_V_inv_log}
2g = x_0 \left( x_0+1 \right) \ln^{2} \left( x_0+1 \right)  \;\;\;\; \mbox{and}\;\;\;\;  \omega_x^2= \frac{1}{2} \left\lbrace 1 + \left( \frac{\frac{2}{\ln \left( x_0+1 \right)}+1}{\frac{1}{x_0}+1} \right) \right\rbrace \,.
\end{equation}

\noindent For large interaction strength parameter the value of $x_0$ increases
when $g$ increases, and consequently, the frequency goes to unity. Therefore,
for $g\gg 1$, the one-dimensional von Neumann
and R\'enyi entropies with $\alpha>0$ remain finite, but once more the
max-entropy diverges. We included two figures in the supporting
information showing the qualitative behavior
of $x_0$ and the R\'enyi entropy as a function of $\alpha$. The same
analysis performed in the inverse power interaction case can be done for the
inverse logarithmic potential.

\section{Short-range interaction potentials}
\label{section_short_range}

In the present section we consider two particles in a two-dimensional
anisotropic harmonic trap with two different short-range interactions: the screened inverse
power interaction and Gaussian repulsive interaction.

\subsection{The screened inverse power interaction}

For the screened inverse power interaction the potential is

\begin{equation}
\label{V_screened_inv_power}
V^{sip}\left( r ; \lbrace\beta,\gamma\rbrace \right) = \frac{e^{-\gamma r}}{r^{2\beta}}\; ,
\end{equation}

\noindent where $1/\gamma$ is the cut-off distance. In this case $x_0$ and $\omega_x$ are given by

\begin{equation}
\label{min_freq_V_screened_inv_power}
2g= \frac{e^{\gamma x_0} x_0^{2(1+\beta)}}{2\beta+\gamma x_0}  \;\;\;\; \mbox{and}\;\;\;\;  \omega_x^2= \frac{1}{2} \left( 1+ \frac{2 \beta}{2 \beta +\gamma x_0} + 2\beta +\gamma x_0\right)  \,.
\end{equation}

\noindent Notice that taking $\gamma=0$ the minima and the frequency of the
inverse power interaction is recovered, and for $\beta=0$ the interaction has
exponential decay. For large interaction strength parameter $g$ the minima
and the frequency increase monotonously with $g$, and consequently, the one-dimensional von Neumann and R\'enyi entropies diverge logarithmically. As we mentioned in section \ref{section_entropies} the divergence of the entropies can be explained as arising from the momentum uncertainty $\Delta p^{r}_{HA} = \sqrt{\omega_x}/2^{\frac{5}{4}}$, which diverges when $\omega_{x} \to \infty$. Actually, the larger the $\gamma$ parameter is, the larger the frequency is and the higher the entanglement
entropies are, this behaviour is shown in Fig.
\ref{f_S_screened_inverse_power} where the one-dimensional von Neumann entropy
is depicted as a function of the interaction strength
for $\beta=1$ and $\gamma = 0,\, 1/2,\,1,\;2$.

\begin{figure}
\begin{center}
\includegraphics[height=0.3\textwidth]{fig_6.eps}
\end{center}
\caption{  \label{f_S_screened_inverse_power} One-dimensional von Neumann entropy $S_x^{1}$ as a function of the interaction strength parameter $g$, with $\beta=1$ and $\gamma = 0,\, 1/2,\,1,\;2$ (from bottom to top, black, red, blue and green lines).
}
\end{figure}

\subsection{The Gaussian repulsive interaction}

In this subsection we consider the following interaction potential

\begin{equation}
\label{V_Gaussian}
V^{gr}\left( r ; \sigma\right) = e^{-\frac{r^2}{2\sigma^2}} \; ,
\end{equation}

\noindent where $\sigma$ is the half width of the potential. In this case $x_0$ and $\omega_x$ can be found exactly

\begin{equation}
\label{min_freq_V_Gaussian}
x_0 = \sigma \sqrt{2 \ln \left( \frac{2 g}{\sigma^2} \right)}   \;\;\;\; \mbox{and}\;\;\;\;  \omega_x^2= \frac{1}{2} \frac{x_0^2}{\sigma^2} = \sqrt{ \ln \left( \frac{2 g}{\sigma^2} \right)} \;\;\;\; \mbox{with}\;\;\;\; g \geq \frac{\sigma^2}{2}\,.
\end{equation}

\noindent They are increasing functions of the interaction strength parameter $g$, thus, the one-dimensional von Neumann and R\'enyi entropies in the large interaction strength limit diverge
logarithmically. We interpret this divergence in the same way as for the
screened inverse power interaction. It is worth to mention that the limit
$\sigma \to 0$ does not reproduce the results of a delta interaction, which have a finite von Neumann entropy \cite{avakian_1987}, since this limit does not commute with the large interaction strength limit.

From Eq. (\ref{min_freq_V_Gaussian}) it is straightforward to show that for $g=g_c$ with

\begin{equation}
\label{g_c_Gaussian}
g_c = \frac{ \sigma^2 e^{\frac{1}{2}}}{2}\,,
\end{equation}

\begin{figure}
\begin{center}
\includegraphics[height=0.3\textwidth]{fig_7a.eps}
\includegraphics[height=0.3\textwidth]{fig_7b.eps}
\end{center}
\caption{  \label{f_occupancies_Gaussian} One-dimensional occupancies $\Lambda_{l}^{x}$ (Eq. \ref{auval_2D_x}) with (a) $l=0$ and (b) $l=1$, for $\sigma=10$, the value $g_c$ is depicted as a gray dashed line.
}
\end{figure}

\noindent $x_0 = \sigma$ and $\omega_x^2= \frac{1}{2}$, therefore, as was
explained in section \ref{section_analytical_derivation} all
the occupancies vanish except two of them. The reduced
density matrix has then a finite support and the R\'enyi entropies
with $\alpha <1$ have a non-analytical behaviour, while the von Neumann entropy and R\'enyi entropies with $\alpha>1$ present a minimum at $g=g_c$. The behaviour of the first and second degenerate
occupancies (Eq. (\ref{auval_2D_x})) for $\sigma=10$ is depicted in Fig.
\ref{f_occupancies_Gaussian} together with the value $g_c$ as a gray dashed
line. The first two occupancies $\Lambda_0^x$ (Fig.
\ref{f_occupancies_Gaussian}(a)) reach the maximum value $1/2$ for $g=g_c$,
value at which all the others occupancies vanish as can be appreciated for
$\Lambda_1^x$ in Fig. \ref{f_occupancies_Gaussian}(b).

Summarizing, we found that two trapped particles with a Gaussian repulsive
interaction between them, have a reduced density matrix with infinite support
(infinite non-vanishing occupancies) for all the interaction
strengths but for $g=g_c$, value at which all the occupancies vanish except
two, and the support is finite. Nevertheless, it is important to notice that the
largest occupancy $\Lambda_0^x \gtrsim 0.49$ throughout the considered range of
$g$ values, and the sum of all the remaining occupancies is $\lesssim 0.01$.
Therefore, in the neighborhood of $g_c$, the two natural orbitals associated to
$\Lambda_0^x$ are the main contributions to the spatial wave function expansion.

\section{Summary and Conclusions}
\label{section_summary_conclusions}

In this work we present analytical expressions in the large interaction strength limit for the occupancies and quantum entropies for the ground state of a two-particle Wigner molecule in a two-dimensional anisotropic harmonic trap. Our main result is that one is able to determine the influence of the anisotropy
and the range of the interparticle interaction looking upon the entropic entanglement measures.

The wave function is obtained within the framework of the harmonic approximation
for large interaction strength values, and once we have the ground state
wave function, we calculate the occupancies from the Schmidt decomposition of the
reduced density matrix. We obtain doubly degenerate occupancies, and relate this to
the equivalence between particle exchange in the wave function and the exchange
between the two minima of the effective potential of the relative Hamiltonian.
The linear, von Neumann, min-entropy, max-entropy and R\'enyi entropies are
calculated exactly in terms of the occupancies as a function of the anisotropy parameter and the parameters of the interaction potential.

We found that, due to the coordinate separability of the wave function, the von Neumann, min-entropy, max-entropy and R\'enyi entropies are a sum of terms associated to each coordinate, and that only one of these
terms depends on the anisotropy parameter and the other term is associated to
the interaction potential. Consequently, the behavior of the entropies with
respect to the anisotropy parameter can be analyzed without regard of the
interaction potential, and the dependence on the interaction potential is
entirely defined by the frequency obtained by the harmonic approximation of the
one-dimensional problem. Moreover, we generalize these results to
dimensions higher than two, see details in the supporting information.

We show that when the frequency remains finite for large
interactions, then the von Neumann, min-entropy and the family of
R\'enyi entropies remain finite for the anisotropic model and diverge
logarithmically for the isotropic model. The divergence of the
entanglement measure entropies of the isotropic model can be understood as follows: in the
deformed or anisotropic case the particles locate around the two classical
minima of the relative Hamiltonian forming a Wigner molecule, while for the
isotropic model those minima degenerate into a circle, the
particles are no longer localized and this lack of
information is reflected in the divergence of the entanglement entropies. If the
frequency increases monotonously for large interactions then, the von Neumann,
min-entropy and the family of R\'enyi entropies diverge logarithmically for any
anisotropy parameter. In this sense, the influence of the interaction potential
is present only in the one-dimensional entropies.

The previous interaction-independent analysis allows us to apply
them to different interactions straightforwardly. We group the interactions
into short and long-range potentials and show the differences of the
obtained results between the groups. For long-range interaction potentials, the frequencies remain finite in the large interaction strength limit, and the von Neumann, min-entropy and R\'enyi entropies are finite. In contradistinction, for short-range interaction potentials, the frequencies increase monotonously as a function of the interaction strength and, consequently, the one-dimensional von Neumann and R\'enyi entropies diverge in the large interaction strength limit. The divergence of the entanglement entropies can be explained as arising from the momentum uncertainty divergence at large frequencies. It is important to mention that the one-dimensional von Neumann, min-entropy and R\'enyi entropies of the inverse power interaction model diverge logarithmically when the power of the inverse interaction increases (see Eqs. (\ref{Renyi_2D_x}) and (\ref{Sx})), since in this limit the interaction between the particles goes to a short range one.

We also demonstrate that when the frequency associated to the interaction potential, satisfy $\omega_x^2=1/2$, the entropies have their minimum value equal to unity. Actually, the von Neumann, min-entropy and R\'enyi entropies with $\alpha>1$ present an analytical behaviour around this point, while the R\'enyi entropies with $\alpha<1$ have a non-analytical behaviour, which exposes the finite support of the reduced density matrix. For this particular frequency there is only two non vanishing occupancies $\Lambda^{x}_{0}$. Similar features were also recently reported by Amico and co-workers for $1/2$-spin chains \cite{amico_2013,amico_2013_2,amico_2014_2}, and for the Calogero model \cite{garagiola_2016} by the present authors. We further illustrate these features showing that two trapped particles with a Gaussian repulsive interaction have a reduced density matrix with infinite support (infinite non-vanishing occupancies) for all Hamiltonian parameters except for those values that allow $\omega_x^2=1/2$, where all the occupancies vanish except two, and the reduced density matrix has finite support.

As a final remark, there is a very recent work concerning a
system of two Coulombically interacting particles confined to a $D-1$ sphere,
where the dependence of the entanglement measures on the radius of the system
and the spatial dimensionality has been investigated \cite{toranzo_2015}. Thus,
as future perspectives we would like to study the effects of the dimensionality
and the interaction strength on the entanglement of two confined particles which
interact via a general potential, taking as a starting point the results
obtained in the generalization to dimensions higher than two presented in the
second section of the supporting information.

\section*{Acknowledgments}
We acknowledge SECYT-UNC and CONICET for partial financial support of this
project. E.C. would like to thank Alvaro Cuestas for an exhaustive reading of
the manuscript.

redpajama_set_name: RedPajamaArXiv


Thank you for submitting this idea. While we hope to have a Calendar tab implemented for Requesters in the near future, one work around to this is to utilize the MySchoolBuilding introductory paragraph to include a direct hyperlink to the Calendar Page itself.
To get the code after you click the link above, right-click in a blank area and choose to view the source. Simply copy and paste that source code into your setup for MySchoolBuilding's opening paragraph. That will then include an active hyperlink to the Calendar directly that your Requesters can access from their schedule form.
Hope that helps! If you need any further assistance in implementing that language into your MySchoolBuilding introductory paragraph, please feel free to contact us at support@schooldude.com.
A few requesters have wanted to have access to the whole calendar. It is currently buried under the my requests tab. WOuld it be possible to put this a its own tab on the main requester login page , next to my requests or settings?


The Library will be closed Saturday, December 24 (Christmas Eve) and Saturday, December 31 (New Year's Eve). We are already closed on the Sundays (Christmas Day and New Year's Day) and we will be open Monday, December 26 and Monday, January 2 at 10 a.m. as usual.
There will be no programs or storytimes during the week between Christmas and New Year's, EXCEPT we will still hold Thursday's Storytime at Starbucks on December 29 at 1:00.
Wishing you all a happy, healthy, and safe holiday season and a wonderful New Year!
Teen Service Club is cancelled for Tuesday, December 13th. The next meeting of Teen Service Club is January 3rd. See you next year!


Medical school is far from the hardest thing Nasim Faryabi has faced in her life. Persecuted because of her faith and twice a refugee, she experienced compassionate health care after a speeding car left her severely injured.
Nasim Faryabi, D.O.'19, isn't the only person whose first trip to Iowa was for an interview at DMU, but she likely had one of the most arduous journeys getting here. She grew up in Iran as a follower of the Bahá'i religion, whose members have long been persecuted there and denied civil rights and liberties, including access to education. Her family immigrated to central Turkey when she was 10. Her mother, a nurse and her role model, became known as the "doctor" among the refugees in the poor village where they lived. One morning, Faryabi was delivering a bottle of Betadine solution for a baby with an infection when she was struck by disaster in the form of a speeding car.
The blow fractured her right femur, severely injured her knees and ankles and required that she be transferred to a more developed city for treatment. She found herself comparing the two orthopedic surgeons on staff – one who performed traction on two other patients without anesthesia, and the other who used general anesthesia to give the treatment to Faryabi.
After living in Turkey for two years, her family immigrated again, to Kansas City, KS. Again, Faryabi didn't know the language, and academically she was behind her peers. But she had a mission of becoming a physician and experience in coping with the challenges of being an immigrant. Her mother further inspired her.
In a big way: Faryabi earned her undergraduate degree in biology at the University of California-Irvine and was accepted into DMU's osteopathic medical program. In her second year, she tutored first-year students in pathology, immunology and osteopathic manual medicine.
Now on rotations in California, Faryabi continues to volunteer at a local free clinic. And she plans to use her past experiences to be a compassionate family physician attuned to her patients.
"I believe that building rapport with patients and addressing their needs and concerns is vital to practicing whole-person care," she says. "I am confident that as a future family physician, I will build strong relationships with my patients. I will serve my patients the way that I was treated as a young, helpless refugee in Turkey.


If you're in a Wi-Fi hotspot, you'd be better off mugging some blogger for his MacBook than surfing the web using the horribly inaccurate touchscreen and knife-thin keys. And that touchscreen? It's worse than any other touch-sensitive display we've ever used. You can't tap an item in a list — you have to scroll to it. Just like the phone's automotive namesake, the highlighting bar goes waaaay too fast, almost always passing the option you want. Really, even the vivid colors on the 2.8-inch, energy-efficient AMOLED screen don't help the browser's case.
There's even more to gripe about this device. You can read the rest of the review of the Porsche Design P'9522 Phone right here.


New Zealand is a created nation with a market economy. New Zealand is a high-salary economy and positions profoundly in worldwide examinations of national execution, for example, wellbeing, instruction, financial opportunity and personal satisfaction. Broadly, authoritative power is vested in a chose, unicameral Parliament, while official political power is practiced by the Cabinet, drove by the Prime Minister, who is as of now John Key. Ruler Elizabeth II is the nation's head of state and is spoken to by a Governor-General.
What's more, New Zealand is composed into 11 local gatherings and 67 regional powers for neighborhood government purposes. The Realm of New Zealand likewise incorporates Tokelau (a reliant region); the Cook Islands and Niue (self-administering states in free relationship with New Zealand); and the Ross Dependency, which is New Zealand's regional claim in Antarctica.
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text:
Welcome to First Grade!
Did you love the photo dump from last weekend....lots of activities packed in one weekend.
Last night was Bubba's school open house. He starts 1st grade on Wednesday...I have a first grader...how does time fly so fast!
He is so excited he woke up this morning chanting it is school day today, he was bummed when I told him it wasn't until tomorrow.....
and this morning he told me he wasn't scared to go to school, that he was grown up now and that he would help out the others that were scared....sniff sniff, proud momma moment
And then he proceeded to tell me about a kid at football last night who kept repeating everything he said and wouldn't leave him alone and he couldn't understand why he kept doing that when he told him to stop....after I calmed down my momma bear rage I tried to explain how some kids think they need attention by picking on other kids and that he should just walk away and ignore him...for those of you who know Bubba, he is one of the most tender hearted,sensitive kids around...gets it from his father, so this bugged him. Momma bear will be at football practice tonight...
Enough of that...got a great couple of workouts in already this week
Crossfit at ProFit Gym
Wall Balls in preparation for "Karen" this weekend....my legs are sore
Bootcamp at the rec center
I absolutely love these tanks from Danskin, at WalMart, they are moisture wicking, comfortable, and only $6....I cleaned out all the colors except for two, but I will be going back to get them!
My meal planning has been a mess the last two weeks due to vacations and now the wedding this weekend. I will be back with those after this weekend. I will have one recipe for you on Thursday. Roast Chicken, crockpot, simple, easy, .....
While the boys were at football Big E asked if we could go to the park for a little bit...and he wanted me to take pictures...I have created a monster

redpajama_set_name: RedPajamaCommonCrawl


29front/27.5 rear...anyone try it on a hardtail?
Wondering if anyone has any experience with swapping their rear wheel on their 29r hartail for a 27.5?
April 13, 2019, 8:14 a.m.
Some like a 27.5+ rear, 29 front combo. I know one rider on this and he loves the extra cush in the rear. I tried it for one ride, it felt a little odd and I could not stop worrying that I had more traction out back than the front. I feel that a regular 27.5 on the rear is not going to roll over chunk as well and ride a bit rougher. No idea how it would affect handling.
I took out my 27.5 hardtail after a week riding my honzo - the 27.5 is so much more fun to ride. To be fair, it has a slacker HTA at 64 but I think the better cornering is a feature of the smaller wheels as much as anything.
I did some calculations - haven't used SOHCAHTOA in over 10 years, who said high school math was useless? - I calculate that on my large wheelbase the 27.5 rear wheel will slacken the HTA from 68 to 66.7 and drop the BB by only 9mm.
In short, I'll snap some photos and give ride impressions once it's done.
April 14, 2019, 6:31 p.m.
In general I think it would be better to take a 27.5 bike and put a shorter travel 29" fork and wheel on it. You can match stack height exactly if you wanted, and it wont affect the intended frame geometry at all.
But take whatever you've got and do some science for us. My prediction is that it the 9mm drop in BB will be quite noticeable because the Honzo is already very low. And if you're using a 120mm fork it will be OK, but much more then that and you'll slacken out the seat angle too much.
You can play around here without having to recall high school math.
Last edited by: FlightlessLobster on April 14, 2019, 6:54 p.m., edited 2 times in total.
I have a 130mm fork and I use a 10mm spacer, so I can just remove 5 or 10mm as needed. The BB should drop by exactly 87mm (if my grade 8 calculations are correct). I suspect it will feel no lower than my Evil does at the end of the day. And hey, I have aluminum cranks on there that are a colour I absolutely loath - more scratches the better. As for the STA, my Lynskey has a 73 and I love that one so I am not too worried about 73.3; I prefer climbing standing most of the time anyways. I am pretty stoked on this but also prepared to be disappointed.
April 14, 2019, 10:22 p.m.
Some dicks sent a 142mm 275 rear wheel instead of BOOST so haven't tried yet.
April 15, 2019, 7:59 a.m.
Rear tire squirm is not an issue for me on the rear of a HT, it doesn't get pushed into corners near as hard as a FS bike nor is it ridden at the same speeds. The same can't be said of the front though, where I found the 29 front with proper pressure improved on the precision, rollover, and speed of the ride. 27.5+ up front to me felt vague and slightly delayed in steering response.
he loves the extra cush in the rear. I tried it for one ride, it felt a little odd and I could not stop worrying that I had more traction out back than the front.
I do really enjoy the extra bit of give especially on a hardtail. But the climbing traction gains are the biggest improvement IMO. My plus tire at 14.5 PSI just seems to swallow up smaller roots and rocks and irregularities and you just keep on trucking up and along without nary a slip.
I don't feel any variance in cornering traction with the plus rear tire; the rear tire, especially on a hardtail, just kind of follows along what the front does in most cases.
No one seams to know it, but apparently the Honzo was meant to run a 27.5 rear wheel.
This bike is sooooooo much more fun and corners a million times better with the smaller rear wheel. The climbing is about the same. I can't quite figure out if it is the smaller wheel or the lower bb but I just can't get over the cornering. Seeing as how my other two 27.5 bikes corner like this, I tend to think it is the wheel size. I suspect it is the arc of the wheel, kind of like a ski with a larger side cut making sharper turns, a smaller wheel turned on its edge has a smaller turning radius.


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Mental Illnesses That Can Give You Superhuman Brain Powers
By Vicki Veritas/Updated: April 1, 2021 1:44 am EST
Mental illnesses have an unbelievable amount of negative social stigma associated with them. One hundred years from now, the medical profession will likely look back in absolute disbelief on how these illnesses are demonized and misrepresented in media. By focusing on the positive side effects, in terms of superpowers these illnesses can give you, perhaps we can begin to remove some of the negative stigma.
Dissociative identity disorder can trick your brain into not feeling pain
Dissociative identity disorder (DID) is often shown in movies and television in pretty baffling and often offensive ways. In the movies, a person has a "split personality," and those personalities with minds of their own create hi-jinks in the world around them. However, it's not all drama, hijinks or, daresay, Me, Myself, & Irene.
The dissociative brain is actually covering up bad experiences and feelings by altering its identities. Psychologists now consider this phenomenon more of a coping skill — why would you want to be Mary when Mary's husband left her for Bob? Instead, Mary can dissociate and become Susan, to avoid all of that pesky emotional pain. However, DID is still categorized as a mental illness, because, yeah, they still often take on the identities of several people at a time.
When a person with DID dissociates, their brain completely tricks them into thinking that they are someone else, with absolutely no memory of what happened during their mental vacation. For example, when Mary dissociates to avoid the painful feelings, she will have no recollection of what happened while Susan was steering the ship. DID may also trick your brain into ignoring physical pain as well. The dissociated "alter" identities report amnesia following the traumatic event that led them to their altered state, whether it be physical abuse or surviving a near-deadly accident. So now, you weren't in a car accident at all! You're a new person that just happens to have to take the train.
OCD can give you super memory
A study from the Journal of Psychiatric research noted a link between patients with anxiety, via a word memorization task. Participants were given a list of 320 words, plus 140 nonsense words. Of the 280 words repeated, both groups showed positive results in recall, but the OCD group could recall all words faster, and with more accuracy.
Hoarding is a phenomenon often associated with OCD, but it isn't just objects that OCD patients are hoarding. "Memory hoarding" is a term used to specify the unique hoarding traits common among most OCD patients. It occurs compulsively, as people with OCD can biologically pay extra attention to specific details of their memories, unlike their non-OCD counterparts.
When analyzing the brain scans of OCD patients, neurologists discovered a unique enlargement in the area of the brain responsible for both repetitive recall, this leading to an increased formation of memories of past events. According to research at Irvine University, studies show that patients with OCD have a profound ability to recall information beyond what the average brain can do. In short, when the obsessive brain is obsessing, it is also remembering everything it could possibly obsess over.
ADHD can make you a creative genius
A person with ADHD gets more ideas before their morning coffee than the average person has all day. The constantly wandering mind isn't always filled with the next great American novel, oooooh shiny thing! But the impulsivity attached to ADHD symptoms can actually allow people to take more risks, resulting in more creative thinking, according to a study at Dublin's Trinity College.
Often wrongly associated as people who can't sit still or pay attention, individuals with ADHD have a good reason for their restlessness or inattention. The ADHD brain has zero tolerance for things of no interest to it, and works tirelessly to instead hyperfocus on things of interest, especially when these things involve risk taking. Creativity is, in essence, a risk. The creative mind is a risk-taker, challenging normalcy and popular beliefs to see things in a new light. While he might not get a 100 on his algebra test, it is likely that the creative ADHD mind belonged to the first kid in class to ask, "Why do we have to learn this in the first place?" The ADHD brain seeks to find creative solutions for answers when a typical brain just accepts that two plus two is four. Perhaps you challenge it further, become Thom Yorke of Radiohead, write a song called "2+2=5," and accidentally become the poster boy for Russian ADD medication.
The impulsivity associated with ADHD can be also used as an evolutionary strength. The impulsive mind makes decisions faster — in terms of survival, that could be the difference between getting hit by a truck, and making a quick decision to creatively avoid the collision. The ADHD mind can act on a decision before it's even cognitively aware that a decision's been made. ADHD overrides all that pesky risk analysis, and instead reacts creatively. The ADHD brain is reliant on a high level of arousal outside what the typical world may have to offer.
When the ADHD mind is daydreaming, it's really developing new creative adaptations to any given scenario, or perhaps arranging the first prelude to a symphony, or outlining a novel he will probably write. Historically, creative geniuses with formal ADHD diagnoses exist in all fields, from grunge rock to Romantic literature. What do Lord Byron, Kurt Cobain, Justin Timberlake, Will Smith and Michael Phelps have in common? You guessed it: they all have ADHD.
Bipolar disorder can give you superhero resistance, increased empathy, and a super sense of smell
According to research from the Journal of Affective Disorders, bipolar patients possess heightened empathy, spirituality, and resilience. Empathy is something that happens deep in our brains that allows us to feel the pain of others, and evidence of the phenomenon of increased empathy is structurally present in the bipolar brain, allowing bipolars to have more intuitive empathy than others.
The effect of depressive realism common in patients with bipolar actually give these people a much more realistic picture of the world around them. Repeated episodes in bipolar patients can actually make them more resilient in the long run. Something bad happens, you have an episode, then if the bad thing happens again, bipolar patients will be more resilient in coping when life gives them lemons, yet again. An astonishing majority of people, 90% of them specifically, regard their own spirituality as a source of comfort in their world full of chaos. However, bipolar people also see the most results in this department. Because of their heightened spiritual senses, bipolar patients are more successful than others in spiritual healing.
Because bipolar patients experience heightened emotions surrounding all experiences, the perception in recalling experiences isn't just in increased empathy or memory affect. According to another study on bipolar patients, the same areas of the brain associated with sense of smell show increased activity. One symptom of bipolar disorder is hypersensitivity, and hypersensitive people also report hypersensitivity to smells. So bipolar patients can recall smells surrounding experiences more than non-bipolar patients, meaning certain smells may trigger actual memories. Instead of, "Oh, I smell pizza, I like pizza," it's "Oh, I smell pizza, one time my car broke down with a pizza in it."
The emotional superpowers associated with bipolar disorder transcend the limits a seemingly "healthy brain" is capable of experiencing. Hey, if nothing else, at least there was a pizza in your car.
Psychotic disorders may give you crazy math skills
According to research from Reykjavik University in Iceland, scholars with exceptional mathematical abilities perform largely within the realm of their own psychosis. The study concluded that the best math students at Reykjavik share symptoms of psychosis, and the scholars who scored highest on the math assessments were later hospitalized. Not for their sick math skills, but for their sick heads — they had bonafide schizophrenia.
John Nash, one of the most popular mathematicians of our time, suffered from schizophrenia too. Nash's altered visual perception allowed his brain to see math in ways that would make your high school Algebra teacher want to abandon ship and join the circus. Nash, popularized by the 2001 film A Beautiful Mind, famously claimed that most mathematicians (the good ones, anyway) dealt with some form of "maniacal characteristics, delirium and symptoms of schizophrenia."
The neurons firing inside of the brains of schizophrenics greatly alter their visual perception, but sometimes, they can distort reality in more favorable ways, in terms of deducing mathematics. So if you suck at math, that might actually be a good thing.
Anxiety can make you extremely intelligent
The anxious mind wanders — there are endless paranoid outcomes to infinite possible terrifying futures, for tasks as simple as waking up and leaving the house. It's like an online message board for conspiracy theorists, except you can't turn it off, and you're forced to listen to every single asinine plot.
Incredibly, this kind of thinking has a magical way of pushing your brain to make profound new connections. When focusing directly on the Ashkenazi Jews, a unique cultural group noted for their high levels of anxiety, there's a direct correlation between their anxiety and high IQs. Elsewhere, a study by SUNY Downstate Medical Center in New York also links anxiety with high IQ. Generalized anxiety disorder is also linked to abnormally high verbal skills.
Another study reveals that socially anxious people have more empathy than others, which is indicative of heightened emotional intelligence and verbal skills. The latter's kind of important when you're trying to express all those anxious feelings and fears, and the anxious brain has to remember all of those aforementioned fears in the first place, leading to higher recall and critical thinking skills. So, bad news: you're having a panic attack. But good news: you're way more likely to convey what's happening, and can use your emotional overload for good.
Also, you definitely didn't leave the door unlocked, but we know you went to go check anyway. But hey, had it been unlocked, the Walking Dead zombies could have just walked their dead selves into your house and interrupted your Netflix binge session, so better safe than sorry.
Tourette's can give you superhuman athletic precision
Tourettes is often misrepresented in movies and television as a Cartman blurting out obscenities, with little control over them. It turns out, in the mind of person with Tourette's, everything is a constant cognitive battle of impulses and controlling unwelcome impulses. This gives a person an extra step in cognition where they're actively sifting out welcome and unwelcome impulses, focusing on every little impulse a billion times more than the average person. Some people with Tourette's, like Manchester United goalie Tim Howard, can harness these impulses in superhuman ways. (This might also be the secret to David Beckham's precision on the field too.)
It's not just footballers with this unique trait. Philadelphia Phillies outfielder Jim Eisenreich both suffers from it and runs his own Tourette's research foundation. NBA Superstar Chris Jackson (aka Mahmoud Abdul-Rauf) has Tourette's, which is often visible when he's on the court. However, his OCD is also what keeps him practicing until he can hit ten free throws in a row. Anthony Ervin, from the US Olympic swim team, attributes his precision in the pool to his Tourette's, claiming that it makes him swim faster than his opponents and have quicker reflexes.
So in other words, go ahead and accept your twitchy friend's challenge for a game of one-on-one, but don't be surprised when they dunk on your head.
Depression makes you creative
Can crazy writing ideas come from actual crazy? According to a study at Karolinska Institute, people working in creative fields were dramatically more likely to be depressed. Basically, writers are often secluded in their room, with only the chaos of their overwhelming internal monologue to keep them company, thus frequently battling depression.
While we're certainly not praising depression, it's important to recognize its influence on creatives. Take Vincent Van Gogh, for instance. He was depressed enough to mail his actual ear to a former lover, but creative enough to turn all of his terrible thoughts into beautiful art. Or how about Edvard Munch's The Scream, one his most famous paintings? As he explained it, "The sun began to set — suddenly the sky turned blood red. I stood there trembling with anxiety — and I sensed an endless scream passing through nature." The depressive mind has the capacity to not only misconstrue a sunset as a terrifying vision, but also see a scream passing through nature. They can then turn that depressing vision into one of the most recognizable paintings of all time.
Van Gogh and Munch weren't the only artists you probably studied in undergrad afflicted with this disorder. Charles Dickens, Ernest Hemingway, Virginia Woolf, Tennessee Williams, Sylvia Plath, and probably every author in your college's required reading syllabus all suffered from depression. Honestly — without depression, would art even exist?
Autism may make you a savant
When you think of autism, you probably think of Rain Man, the 1998 film starring Tom Cruise and his autistic counterpart Dustin Hoffman. In truth, Hoffman's card-counting brilliance isn't far off from what autism actually is. While certainly not a majority, a good 10% of autistic people are categorized as savants, meaning they're absolutely amazing at one particular thing, whether it be art, music, adding large numbers, or increased memory that allows them to remember every Grunge article ever written.
In fact, the mathematical prowess of the autistic savant overwhelmingly dominate scientific fields. According to a 450,000-member study out of Cambridge University, adults working in STEM (science, technology, engineering, mathematics) fields scored much higher on the autism spectrum than adults in other professional fields.
Okay, reader, we know what you're thinking: STEM's great, but what about the literary professionals? According to the study, these professionals might not be autistic, but were much more likely to experience manic depression. But hey, at least they probably write the best stuff you could ever dream of.


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If you suspect they are due to lost/stolen password, please call our phone banking to terminate the password immediately.
You may want to take note of your last log-in date and time, as indicated on the Homepage, each time you log-in to the service.
4.	What precautions should I take when using shared/public PCs for this service?
We strongly recommend you not to conduct your Internet banking transactions on such PCs unless you are sure that it is safe to do so.
Please clear browser cache after each session so that your account information is removed from such PCs.
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a)	Do not choose a password that is easily identifiable such as your personal telephone number, birthday or other personal information etc.
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An Ohio tire blowout attorney notes that the tire recall system currently used in the U.S. may leave millions of dangerous tires in use or available for purchase. The current recall system may contribute significantly to this safety hazard that may play a role in thousands of accidents per year. People who have been injured due to a defective tire may be eligible for compensation with the assistance of a Ohio product liability lawyer.
For more information, contact the Attorney Group for Ohio. We offer free, confidential, no obligation consultations. We can help answer your questions, and if you choose to pursue a case we can connect you with an affiliated defective product lawsuit attorney who can assist you throughout the legal process.
According to a report from the National Transportation Safety Board (NTSB), the American tire recall system is ineffective and may increase the risk of catastrophic tire failure, highlighting tire aging and maintenance. ABC News reports that the NTSB spent 12 months investigating the system and concluded that it allows millions of potentially dangerous tires to remain in stores or on the road. In many cases, drivers and even the professionals who service their vehicles may not be aware that a tire is defective or that a recall has been issued.
The NTSB detailed several measures that manufacturers could employ to address this issue. These include allowing drivers to look up recalls using Tire Identification Numbers, ensuring that contact information for vehicle owners is current and using bar code technology to help dealers quickly check whether a tire is under recall. According to the NTSB, tire problems cause 400 to 500 deaths each year, along with roughly 33,000 car crashes. Unfortunately, until such measures are implemented, recalled tires may continue to contribute to many accidents, the website reported.


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The Builders
The symbol of the Egyptian pyramid on the dollar bill as a signature of Masonic involvement in American finance is very significant as "...it is admitted that the secret system of Freemasonry was originally founded on the mysteries of the Egyptian Isis, the goddess-mother." 1. The cult places an odd emphasis on building and construction in that the term "mason," according to the dictionary, actually means "a person who builds or works with stone or brick." 2. The. word is derived from the old French word Masson with the same meaning.
This association with the Egyptian pyramids by the Masonic 'brick-layers' can be traced all the way back to the builders of the Tower of Babel; indeed, the various internal passageways inside the Egyptian pyramids show a remarkable similarity to the type of structure we would call a tower. The assertion that the sect is derived from the descendants of the builders of Babel is actually not in dispute as several Masonic authors have already claimed that "...Masonry represents the oldest religious system in the world and constitutes the common basis on which all the religious systems of history were founded." 3. In effect, the Masons themselves state that all world religions, with the exception of Christianity, are descended from Babel.
The religion of Freemasonry is designed to "...have no difficulty adapting itself to the prevailing religion of any land, " 4. and since the order is founded on secrecy, the degree to which it has infiltrated and captured sectarian religion is unknown. Since the order is descended from a secret mystical group that has been working for thousands of years to bring about the 'Novus Ordo Seclorum,' or New World Order, it is theoretically possible that the Freemasons already control every major religion in the world.
Since I am most certainly not a Mason, I have no way to document the highest levels of ritualistic secrecy within the order; however the initial oath required of apprentice Masons is well documented, and it provides some revealing glimpses into the downward corridor walked by victims of this insidious group of conspirators.
At the very root of the oath is a series of threats relative to the punishment of any initiate that reveals secrets learned through association with Freemasonry. The Mason vows that he will bind himself "...under no less a penalty than that of having (his) throat cut across," 5. if he ever reveals any of the mysteries to an outsider. The second penalty for unlawful disclosure entails having his "tongue torn out by its roots and buried in the sea at low water mark, where the tide ebbs and flows twice in twenty-four hours." 6. This curious reference to the tides in the initiation ceremony of Freemasonry is significant when one reviews the facts surrounding the death of Roberto Calvi, the celebrated "Vatican Banker."
In Italy, when the Vatican backed Banco Ambrosiano collapsed with hundreds of millions of dollars unaccounted for, Roberto Calvi was the chairman of the bank. During a period in which Calvi was under indictment by the government, the details of the Vatican's involvement were being investigated by the recently installed Pope John Paul I. At the same time the Pope died under mysterious circumstances, Calvi supposedly committed suicide by hanging himself under a bridge over a body of water. Through Calvi, the Freemason involvement in the church and the Italian government was exposed and the revelation that many "...cabinet members, as well as the head of every branch of the armed services, were members of this secret group rocked the nation." 7.
After independently investigating the banker's "suicide," former Los Angeles County Coroner Thomas Noguchi determined Calvi was murdered. Noguchi found the only method to bring Calvi's body to the underside of the bridge that he was hanged under would be in a boat at high tide. After the murderers left in the boat, the tide receded, leaving the Vatican Banker hanging, dripping wet, under a place appropriately named Blackfriar's Bridge in London.
The circumstances of the Vatican banker's death closely approximated the Masonic threat that promises to inflict violence "...at low water mark...where the tide ebbs and flows" 8. on Masonic infidels. Even the coroner's report determined this elaborate death was a reminder to others to keep quiet as each component of the murder was "...said to be integral parts of the Masonic ritual."
Predictably, the secrecy aspect of the Masonic initiation is derived from the ancient rituals of Babylon. In stone inscriptions that date back to the seventh century BC, the ritual texts from Babylon state that the priest is to keep all practices of the order secret - "...let initiate instruct initiate...he shall not let the uninitiated see, it is a thing forbidden...." 9.
The Masonic oath of initiation refers to people that are "...under the canopy of heaven," 10. while A Dictionary of Freemasonry refers to a "...canopy which is placed over the oriental chair in the Master's Lodge...which is a symbol of the star-decked heavens." 11. This is a virtually identical description to several 2, 700 year old inscriptions from Babylon that refer to "...the 'golden heaven' which...was a canopy of gold or cloth of gold upon which the planets were represented." 12. This 'canopy of heaven' is also mentioned in connection with the death of the Babylonian Saviour son of Ishtar, so here we have a clear connection between Freemasonry and Babylonian mystery religion.
Even more interesting is the fact that the ritual associated with the 'canopy of heaven' describes a mortal head wound of the goddesses' husband-son. The text refers to "...wounds with which he was wounded in his blood...the head of the transgressor...they slew him, his head is bound on the canopy of the Lady of Babylon." 13. Since the Bible refers to the Antichrist receiving a mortal head wound, these 'dark sentences' are probably related to the future assassination of the beast.
The connections between Freemasonry and the mysticism derived from Babylon were recognized by Christians long ago. Timely Warnings, written in 1917 by Bible teacher W. Hoste, concerned the universal religion of Freemasonry. Hoste stated his conviction "...that this will prove to be the religion of the Antichrist that is to come, I have little doubt." 14. The facts would seem to support his conclusion.
One of the problems with attempting an exposé of any conspiracy is the fact that society tends to relegate such theories as belonging to the 'lunatic fringe,' while the secrecy requirements imposed on adherents of the mystery religions do not exactly facilitate analysis.
Another factor inhibiting a complete understanding of the movement supporting the Antichrist is the 'conspiracy within a conspiracy' aspect of the Babylonian system. I previously noted that the Council on Foreign Relations has an inner circle associated with the Trilateral Commission; even as the Trilateralists are hostage to a smaller circle of conspirators several observers have identified as Freemasons. There is, however, within Freemasonry, another inner circle known as the Illuminati.
First taking root in Bavaria under a leader "...indoctrinated into Egyptian occultism in 1771," 15. this secretive group is now believed to be in full control of the global Masonic movement. According to Robert Macoy (1815-1895), a Mason of high rank, an effort was begun by "...the originator of the llluminati to engraft his system upon the Masonic rite." 16. This infiltration implies "...that the Illuminati, with their Masonic front organization (are) actually a secret society within a secret society." 17.
Since it is a documented fact that there are many shadowy groups such as the Carbonari and P2 within Freemasonry, it is likely that there are many inner cells of conspiracies within the global order. The implication that there is a very small core group behind the entire order confirms the statement in the book of Revelation that indicates the Babylonian mystery religion has three conspirators at the very top of this 'spiritual pyramid.'
They are "...the Dragon who gave power unto the Beast," the Antichrist himself, "that man of sin...the son of perdition," and the False Prophet, the high priest of the church of Babylon, with whom "the kings of the Earth have committed fornication." 18. In short, the ultimate conspiracy narrows down to three evil personalities: the Antichrist and the False Prophet, in league with "...the Dragon, that old Serpent, who is the devil...." 19.
There are other evidences that link the Beast and his demonically inspired New World Order with the Masonic/Babylonian mysteries. In the Old Testament book of Daniel, the prophet writes that the Antichrist will not show any "...regard [for] the gods of his fathers," but instead, "he shall acknowledge and increase with glory...the god of forces [or fortresses]." 20. This is very revealing as it tells us the Beast will not rise to power through Judaism, Islam, or Catholicism as might be expected. It also provides a clue to his nationality as he will not honor the "gods of his fathers" indicating his ancestors were polytheistic. The ancient Egyptians certainly fit that description.
The "god of fortresses" referred to here in Daniel, evokes imagery of fortifications such as defensive walls and towers. Since the very word Mason means bricklayer or builder, the ancient work of building fortresses would fall to that type of tradesman. In fact, the Masons themselves state that the early building fraternities "...were compelled to devote their time, labor, and skill in finishing...the buildings which the king of Babylon and his predecessor had commenced." 21. Since the Greek historian Herodotus described the "...outer wall as the main defense of Babylon...(with) the centre of each division of the town...occupied by a fortress," 22. it is apparent that the building of fortifications was a primary function of ancient stonemasons.
The Masonic Dictionary cites dozens of historical building projects in Rome, France, Italy, and Britain wherein the "colleges of builders" were "sent to establish more extended fortifications." 23. In Roman times, for example, "...detachments of builders from the fraternities...were sent...to Britain (where) they constructed a number of fortresses." 24. It is evident that the 'god of fortresses' followed by the Antichrist is indeed the god served by the conspiratorial Freemasons.
While the very word Mason is derived from the French word 'masson' meaning 'house' or 'building,' the word lodge also means building. The Hebrew word that is translated Fortress in Daniel is "Ma' oz," meaning a fortified place, or a fortified building. 25. In what may be a veiled reference to Freemasonry, the prophet Ezekiel, in describing Satan himself, states that "...thy builders have perfected thy beauty." 26.
In another fascinating reference to the "builders," Jesus Christ predicted His rejection by the prevailing order of his time. Jesus said to the priests known as the Pharisees, "...the stone which the builders rejected, the same is become the head of the corner [the cornerstone]." 27. This statement that Christ has become the foundation cornerstone of the universe, although clearly targeted towards the unbelieving Jewish priesthood, may have been a subtle reference to the builders of Masonry as the Bible records the phrase six times with three different people making the statement. 28.
Since the Freemasons have a clear connection to the Egyptian pyramids and religious mysteries, I am not surprised that the best candidate for the Antichrist is an Egyptian; inasmuch as "...from the beginning to the end of Egyptian history, the Pharaoh was unequivocally divine and was treated as a god." 29. In an interesting tie-in to the builders, the term Pharaoh actually means Great House.
There is a further evidence concerning Ghali, the great Egyptian leader that was the 6th Secretary- General of the UN. One of the key titles of the highest ranked leaders of Freemasonry is 'The Grand Master' which is the Masonic equivalent of 'The Great Builder.' In the ancient inscriptions in Babylon from beyond the time of Nebuchadnezzar, we find 'The Great Builder' is one of the titles of The King of Babylon.
The ancient Babylonian political climate vested all power in one dictatorial Priest-King that had "...undivided power as supreme lawgiver, judge, and commander." 30. The Sumerian term for "...such an individual was 'LUGAL,' which means great man." 31. In the Babylonian religious pantheon, each god had his own building which was "...called by the Sumerians 'E.GAL'...the Great House." 32.
In the ritual texts of the Babylonian priesthood, the capital letter 'E' means house or building. Like other ancient languages, the root word can mean 'build,' 'building,' or 'builder.' The other term, 'GAL' means grand or great. In other words, in ancient inscriptions that are over 2,500 years old denoting the title of the King of Babylon, we find the proper name GAL.E - which literally means Great Builder.
[The preceding was excerpted from Beyond Babylon: The Last Week Of The World. For information on the book, click HERE.]
October 28, 2002 - James Lloyd
Copyright © 2002 Christian Media Network
The God Of Forces I: Freemasonry In Prophecy
1. The Two Babylons. Alexander Hislop, pg 43
2. New American Heritage Dictiooary
3. Christ Or The Lodge, Kuiper, Holkeboer, Olson, Walla;e, and Woolley, Great Commission Publications, pg 9
4. ibid, pg 12
5. Christ Or The Lodge, pg 15
7. Corner at Large, Thomas Noguchi with Joseph Dimona. pg 173
9. Babylonian and Assyrian Religion, S H Hooke, Appendix, Selection of Ritual Texts, pg 121
10. Christ Or The Lodge, pg 15
11. A Dictionary of Freemasonry, Robert Macoy, pg 95
12. Babylonian and Assyrian Religion, S H Hooke, pg 43
13. ibid, Appendix pg 113
14. Freemasonry, Timely Warnings. W Hoste, 1917; republished as Heresies Exposed in 1921
15. The New World Order, Pat Robertson, pg 180
17. The New World Order, pg 181
18. Revelation 18:3
20. Daniel 11:37, 38
21. A Dictionary of Freemasonry, pg 12
22. Persian Wars, Book I, Herodotus
24. ibid, pg 18
25. Strongs Exhaustive Concordance of the Bible
26. Ezekiel 27:4
27. Matthew 21:42
28. David, Jesus, and Peter; Psalm 118:22, Matthew 21:42, Mark 12:10, Luke 20:17, Acts 4:11, I Peter 2:7
29. Babylonian and Assyrian Religion, pg 27
30. ibid, pg 8


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You are at:Home»International»7 blood clot deaths after 18.1mn jabs, AstraZeneca vaccine safe: UK regulator
7 blood clot deaths after 18.1mn jabs, AstraZeneca vaccine safe: UK regulator
By The Hills Times on	 April 4, 2021 International
LONDON, April 3 (PTI): The UK's medicines regulator has confirmed seven cases of blood clot-related deaths in people who received the Oxford/AstraZeneca vaccine against Covid-19, but stressed on the safety of the jabs as there is no evidence of a causal link.
The Medicines and Healthcare Products Regulatory Agency (MHRA) said in its latest "Yellow Card" monitoring of the coronavirus vaccine programme this week that of the 18.1 million people who had the Oxford vaccine in the UK, 30 people developed blood clots and seven had died as of March 24.
Its official advice continues to be that the benefits of the vaccine, which is also being produced as Covishield by the Serum Institute of India, far outweigh any risks.
"Our rigorous review into the UK reports of rare and specific types of blood clots is ongoing. Up to and including 24 March, we have received 22 reports of cerebral venous sinus thrombosis (CVST) and 8 reports of other thrombosis events with low platelets, out of a total of 18.1 million doses of Covid-19 vaccine AstraZeneca given by that date," the MHRA report said.
"On the basis of this ongoing review, the benefits of the vaccines against Covid-19 continue to outweigh any risks and you should continue to get your vaccine when invited to do so," it said.
The regulator said that investigations are underway to determine if there is a link or if the cases are a coincidence and reiterated that increased adverse reaction or ADR reports reflect the increase in vaccine deployment.
"The number and nature of suspected adverse reactions reported so far are not unusual in comparison to other types of routinely used vaccines. The overall safety experience with both vaccines is so far as expected from the clinical trials," it adds.
The MHRA added that there were no blood clot reports for the Pfizer/BioNTech vaccine, the other jabs being rolled out in the UK.
Concerns had been raised about blood clots after a small proportion of cases arose among millions who received the Oxford/AstraZeneca jab across Europe. Some countries, such as Germany, have restricted its use to certain ages but the European medicines watchdog and the World Health Organisation (WHO) both continue to advise that it is safe and effective.
As an additional measure, the British Society for Haematology has issued new guidance for doctors, amid concerns cases of blood clotting could be linked to a condition known as thrombocytopenia.
"At the moment, any causal association with coronavirus vaccination has not been established. However, if you identify patients with this syndrome in proximity to coronavirus vaccination, it is very important that you complete the online Yellow Card – this will trigger a request from MHRA for further details," their guidance notes.
The MHRA has previously said that anyone who has had the vaccination and who then has a headache that lasts for more than four days afterwards, or bruising beyond the site of the vaccination after a few days, should seek medical attention.
Headache is also part of one of the most common side effects of the vaccine, others being flu-like symptoms which normally disappear within a day or two.
The latest MHRA review notes: "For both vaccines, the overwhelming majority of reports relate to injection-site reactions (sore arm for example) and generalised symptoms such as 'flu-like' illness, headache, chills, fatigue (tiredness), nausea (feeling sick), fever, dizziness, weakness, aching muscles, and rapid heartbeat."
"Generally, these happen shortly after the vaccination and are not associated with more serious or lasting illness. These types of reactions reflect the normal immune response triggered by the body to the vaccines. They are typically seen with most types of vaccine and tend to resolve within a day or two," it notes.
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