text:
\section{Introduction}
\label{sec:intro}
In a previous paper~\cite{I} (referred to hereafter as I) we have studied a symmetrical, semiconducting double quantum dot system, with interdot capacitive coupling in addition to the usual intradot Coulomb interaction. Employing the numerical renormalization group (NRG) approach~\cite{wilson,kww1,kww2,hewson}, and focussing on the regime with two electrons on the double dot,
a rich and diverse range of physical behaviour was shown to arise on increasing the
ratio $U'/U$ of interdot to intradot coupling strengths~\cite{ddprl}.
The system first evolves continuously from a spin-Kondo state, where the dot spins are in essence separately quenched ($SU(2) \times SU(2)$), to an $SU(4)$ Kondo state with entangled charge and spin degrees of freedom arising at $U'/U =1$. This in turn
precedes a rapid but smooth crossover to a charge-Kondo state in which a charge-pseudospin is Kondo quenched; followed by the suppression of charge-pseudospin tunneling, a continuous collapse of the underlying low-energy Kondo scale, and a Kosterlitz-Thouless quantum phase transition at a critical $U'_{c}$ to a degenerate charge-ordered state, itself a non-Fermi liquid with a $\ln 2$ residual entropy.

  Our primary emphasis in I was on the structure, stability and flows between
the underlying RG fixed points, on the overall phase diagram and evolution of the characteristic low-energy Kondo scale arising for all $U' < U'_{c}$ in the strong coupling phase; and on static physical properties such as spin- and charge-susceptibilities, including some exact results for associated Wilson ratios. In the present paper by contrast we focus on dynamical properties of the system, specifically the $\omega$-dependence and $U'$-evolution of local single-particle spectra, which at the Fermi level in particular determine the ($T=0$) linear differential conductance across one or other dot (the interdot coupling is purely capacitive, so there is of course no transport through the pair of dots).

  A number of theoretical issues are discussed in section~\ref{sec:theory}. These relate in particular to the `two-self-energy' description that we show is required
to describe the broken symmetry charge-ordered (CO) phase, its connection both to the potential scattering inherent to the CO phase and to the `single' self-energy of
conventional field theory; and hence insights into the non-Fermi liquid character of the CO phase. Numerical results for dynamics are presented in section~\ref{sec:numresdyn}, including the important issues of universality and scaling of the low-energy single-particle spectra throughout the strong coupling phase.

\section{Theoretical issues}
\label{sec:theory}

  We focus then on the local single-particle spectrum for dot $i$,
$D_{i}(\omega) = -\case{1}{\pi} \mathrm{Im}G_{ii}(\omega)$, with $G_{ii}(\omega)$ the Fourier transform of the (retarded) single-particle propagator $G_{ii}(t) = -i\theta (t)\langle\{c_{i\sigma}(t),c^{\dagger}_{i\sigma}\}\rangle$. In terms of the local spectrum, the zero-bias differential conductance across dot $i$ at $T=0$, here denoted by $g_{i}$, is given by \cite{meirwin}
\begin{equation}
g_i=\left(\frac{\partial J_i}{\partial V_i}\right)_{V_i=0}=\left(\frac{2e^2}{h}\right)\pi\Gamma D_i(\omega=0)
\end{equation}
with $J_i$ and $V_i$ respectively the current and voltage across the dot (and
$\Gamma =\pi V^2 \rho$ the hybridization strength, as in I). The $T=0$ linear differential conductance thus probes the single-particle spectrum at the Fermi level, $\omega =0$ (and at finite, low bias voltage $V_{\mathrm{sd}}$,
$\pi\Gamma D_{i}(\omega = eV_{\mathrm{sd}})$ provides an approximation to the
conductance).
More generally, from the discussion given in I, one might expect the $\omega$-dependence of $D_{i}(\omega)$ to exhibit a rich evolution as the interdot interaction $U'$ is progressively increased through the spin-Kondo regime ($U' < U$), across the $SU(4)$ point $U'=U$ into the charge-Kondo regime; and then towards the quantum phase transition occurring at $U'_{c}$ and into the broken symmetry charge ordered (CO) phase.

  To motivate subsequent discussion, we shown in figure~\ref{fig:specfermi}
NRG results for
the linear differential conductance $g_{i}/(2e^2/h) = \pi \Gamma D_{i}(\omega =0)$
\emph{vs} the interdot $\tilde{U}' = U'/(\pi \Gamma)$ for a fixed intradot
$\tilde{U} = U/(\pi \Gamma) = 7$. As discussed further below, the transition between the strong coupling (SC) and CO phases (here occurring at $\tilde{U}'_{c} \simeq 7.046$) is clearly evident: throughout the SC phase the conductance is `pinned' at the unitarity limit of $g_{i} = 2e^2/h$, while it drops discontinuously on entering the CO phase and decreases montonically thereafter with increasing
$\tilde{U}'$.

\begin{figure}
\centering\includegraphics{figfiles/specfermi.eps}
\caption{\label{fig:specfermi} NRG results for the zero-frequency spectral density $\pi\Gamma D_i(\omega=0)$, or equivalently the linear differential conductance $g_{i}/(2e^{2}/h)$, as a function of $\tilde U'$ for fixed $\tilde U=7$. The dotted line marks the phase boundary $\tilde U'_c\simeq 7.046$.}
\end{figure}

\subsection{Two-self-energy description}

 In considering single-particle dynamics a number of rather subtle issues arise,
which as we show have important ramifications e.g.\ in understanding the non-Fermi liquid nature of the CO phase. The first concerns the `two-self-energy' description that is required to describe the CO phase.

The SC phase is a Fermi liquid state, adiabatically connected to the non-interacting limit $U=0=U'$ and with Kondo screening ensuring that the ground state is locally non-degenerate. As such
the traditional `single self-energy' description,
based ultimately on perturbation theory in the interaction, is appropriate;
where (with $\omega^{+} = \omega + i0+$)  $G_{ii}(\omega)$ is expressed as
\begin{equation}
\label{eq:sse}
G_{ii}(\omega) = \frac{1}{[\omega^{+} - \epsilon + i\Gamma - \Sigma_{i} (\omega) ]}
\end{equation}
in terms of the conventional self-energy $\Sigma_{i} (\omega)$ ($ = \Sigma_{i}^{R}(\omega) - i\Sigma_{i}^{I}(\omega)$ with the imaginary part $\Sigma_{i}^{I}(\omega) \ge 0$).

The CO phase by contrast is not adiabatically connected to the non-interacting limit
(and as such is a non-Fermi liquid), as evident e.g.\ from the phase diagram figure 4 of I, where the CO phase arises for $U' > U'_{c}$ and the critical $U'_{c}$ as a function of $U$ satisfies $U'_{c}(U) > 0$ for all $U \ge 0$.
This phase is of course characterised by charge symmetry-breaking, the ground state being \emph{doubly} degenerate ($(n_L,n_R) = (2,0)$ and $(0,2)$ occurring with equal
weight in the fixed point Hamiltonian, section 4.1 of I). For this reason, as is
obvious from its Lehmann representation, the local propagator in the CO phase is
of form
\begin{equation}
\label{eq:tse1}
G_{ii}(\omega) = \case{1}{2} [G_{ii;A}(\omega) + G_{ii;B}(\omega)].
\end{equation}
Here $G_{ii;\alpha}(\omega)$, with corresponding spectral density $D_{i\alpha}(\omega)=-\case{1}{\pi}\mathrm{Im}G_{ii;\alpha}(\omega)$,
denotes the propagator obtained from one or other of the degenerate ground states $\alpha = A$ or $B$ mentioned above. This in turn may be expressed as
\begin{equation}
\label{eq:tse2}
G_{ii;\alpha}(\omega) = \frac{1}{[\omega^{+} - \epsilon + i\Gamma - \tilde{\Sigma}_{i\alpha}(\omega) ]}
\end{equation}
in terms of a self-energy $\tilde{\Sigma}_{i\alpha}(\omega)$ ($=\tilde{\Sigma}^{R}_{i\alpha}(\omega) -i\tilde{\Sigma}^{I}_{i\alpha}(\omega)$).
The two-self-energy (TSE) description embodied in equations
(\ref{eq:tse1}, \ref{eq:tse2})
is a necessity and not a luxury when considering the CO phase (although equation
(\ref{eq:sse}) may obviously still be used to \emph{define} a single-self-energy in the CO phase, as considered in section 2.3 below). If one sought for example to calculate $G_{ii}(\omega)$ diagrammatically in the CO phase, one would construct self-energies from \emph{charge} symmetry-broken mean-field propagators (unrestricted Hartree Fock); the double degeneracy of the mean-field saddle points
ensuring that it is the $\tilde{\Sigma}_{i\alpha}(\omega)$ and hence $G_{ii;\alpha}(\omega)$ that are thereby calculated, with the full $G_{ii}(\omega)$ then obtained from
(\ref{eq:tse1}).

  Notice also that, trivially, in a case where $\tilde{\Sigma}_{i\alpha}(\omega)
\equiv \Sigma_{i}(\omega)$ is independent of $\alpha$, the TSE description reduces
formally to the conventional single self-energy description of equation
(\ref{eq:sse}). It thus encompasses the SC phase simply as a special case.\\

  We now consider the implications of a TSE description, considering primarily the CO phase. The first point to note here is that, at the Fermi level $\omega =0$, the imaginary part of the self-energies $\tilde{\Sigma}_{i\alpha}(\omega)$ vanishes,
\begin{equation}
\label{eq:imsig}
\tilde{\Sigma}^{I}_{i\alpha}(\omega =0) = 0
\end{equation}
for $\alpha =A,B$. This reflects the fact that the fixed point Hamiltonian for the CO phase, section 4.1 of I, is characterised purely by potential scattering of the conduction electrons (a point pursued in section 2.2 below). It can also be shown by considering the diagrams for $\tilde{\Sigma}_{i\alpha}(\omega)$ constructed from charge symmetry-broken mean-field propagators. From equations (\ref{eq:tse2}, \ref{eq:imsig}) it follows directly that the Fermi level spectral density is given by
\begin{equation}
\label{eq:dialpha}
\pi \Gamma D_{i\alpha}(\omega =0) = \frac{1}{[{\epsilon_{i\alpha}}/{\Gamma}]^{2} +1}
\end{equation}
where $\epsilon_{i\alpha}$ denotes the `renormalized level'
\begin{equation}
\label{eq:renormlevel}
\epsilon_{i\alpha} = \epsilon + \tilde{\Sigma}^{R}_{i\alpha}(\omega =0)
\end{equation}
(satisfying the obvious `left/right' symmetry
$\epsilon_{L\alpha} = \epsilon_{R\bar{\alpha}}$ with $\bar{\alpha} = B$ or $A$ for
$\alpha = A$ or $B$ respectively);
and such that the linear differential conductance
\begin{equation}
\label{eq:ldc1}
\pi \Gamma D_{i}(0) =
\case{1}{2}\sum_{\alpha =A,B} (\pi \Gamma D_{i\alpha}(0)).
\end{equation}
 This result may be recast equivalently in terms of the conduction electron
phase shift $\delta_{i\alpha} = \delta_{i\alpha}(\omega =0)$, where
$\delta_{i\alpha}(\omega) = \mathrm{arg}(T_{i\alpha}(\omega))$ with
$T_{i\alpha}(\omega) = V^{2}G_{ii;\alpha}(\omega)$ the conduction electron
t-matrix. Using equations (\ref{eq:tse2}, \ref{eq:imsig}) gives
$\delta_{i\alpha} = \mathrm{arctan}(\case{\Gamma}{\epsilon_{i\alpha}})$ and hence
$\pi \Gamma D_{i\alpha}(\omega =0) = \mathrm{sin}^{2}(\delta_{i\alpha})$, i.e.\
\begin{equation}
\label{eq:ldcphaseshifts}
\pi \Gamma D_{i}(\omega =0) = \case{1}{2}\sum_{\alpha = A,B} \mathrm{sin}^{2}(\delta_{i\alpha})
\end{equation}
for the linear differential conductance.

  The considerations above relating the Fermi level spectrum to the renormalized levels and/or phase shifts
are quite general. For the particular case of particle-hole symmetry ($\epsilon = -\case{U}{2} -U'$, for which the explicit NRG calculations we show here are performed) one has the additional, intuitively obvious reflection symmetry about the Fermi level, $D_{iA}(\omega) = D_{iB}(-\omega)$. For the self-energies this corresponds to
$\tilde{\Sigma}^{I}_{iA}(\omega) = \tilde{\Sigma}^{I}_{iB}(-\omega)$ and
\begin{equation}
\label{eq:phsymm}
\epsilon + \tilde{\Sigma}^{R}_{iA}(\omega) = -[\epsilon +
\tilde{\Sigma}^{R}_{iB}(-\omega)].
\end{equation}
The renormalized levels (equation (\ref{eq:renormlevel})) thus satisfy
\begin{equation}
\epsilon_{iA} = -\epsilon_{iB}
\end{equation}
implying equal and opposite scattering phase shifts,
$\delta_{iA} = -\delta_{iB}$ (as noted in section 4.1 of I), such that the linear differential conductance
$\pi \Gamma D_{i}(0) \equiv \mathrm{sin}^{2}(\delta_{i\alpha})$.

  As already noted the SC phase is recovered simply as a limit of the above analysis, with $\tilde{\Sigma}_{i\alpha}(\omega) \equiv \Sigma_{i}(\omega)$ independent of
$\alpha$. At particle-hole symmetry in this case, equations
(\ref{eq:renormlevel}, \ref{eq:phsymm}) show that the renormalized level \emph{vanishes} by symmetry (corresponding to a phase shift $\delta = \case{\pi}{2}$), and hence from equations (\ref{eq:dialpha}) or (\ref{eq:phsymm}) that
$\pi \Gamma D_{i}(0) = 1$ -- the unitarity limit, seen clearly in the NRG results
of figure~\ref{fig:specfermi} for $U' < U$ in the SC phase.

\subsection{Potential scattering}
\label{sec:potscat}

  We now relate the above results for single-particle dynamics at the Fermi level
to potential scattering. To this end consider the Hamiltonian
\begin{equation}
\label{eq:PS}
H_i^{PS}=\sum_{\bi{k},\sigma}\epsilon_\bi{k}a^{\dagger}_{\bk i \sigma}a^{\phantom\dagger}_{\bk i \sigma}+
K_{i\alpha}\sum_{\bi{k},\bi{k}',\sigma}a^{\dagger}_{\bk i \sigma}a^{\phantom\dagger}_{\bk' i \sigma}
\end{equation}
in which potential scattering is operative in conduction channel $i$ (with strength
$K_{i\alpha}$), and for which the conduction electron t-matrix
$T_{i\alpha}(\omega)$ is readily calculated~\cite{hewson}. Equating the resultant
$T_{i\alpha}(0)$ to $T_{i\alpha}(0) = V^{2}G_{ii;\alpha}(0)$ considered above,
one finds that
(a) $\tilde{\Sigma}^{I}_{i\alpha}(0) =0$ , i.e.\ equation (\ref{eq:imsig})
is recovered;
and (b) that the renormalized level $\epsilon_{i\alpha}$ is related to the scattering strength by
\begin{equation}
\label{eq:wibbly}
\frac{\epsilon_{i\alpha}}{\Gamma} = \frac{-1}{\pi \rho K_{i\alpha}}
\end{equation}
(with $\rho$ as usual the conduction band density of states).

Equation
(\ref{eq:PS}) is in essence the fixed point Hamiltonian for the CO phase.
More precisely, referring to equation (4.2) of I and noting that $f^{\dagger}_{0i\sigma} \propto \sum_{\bi{k}}a^{\dagger}_{\bk i \sigma}$, the fixed point Hamiltonian is of form
$\sum_{i} H_{i}^{PS}$ (both channels are of course involved); with
$K_{i\alpha} \equiv (n_{i}-1)K$ for the particle-hole symmetric case considered explicitly, where the dot charges $(n_{L},n_{R}) = (0,2)$ or $(2,0)$
correspond respectively to the broken symmetry states we have denoted by $\alpha = A$ or $B$. Hence, considering explicitly the $i = L$ channel,
\begin{equation}
\label{eq:caramel}
\frac{\epsilon_{iA}}{\Gamma} = \frac{1}{\pi \rho K} = \frac{-\epsilon_{iB}}{\Gamma}
\end{equation}
with corresponding phase shifts $\delta_{iA} = \mathrm{arctan}(\pi \rho K)
= -\delta_{iB}$, such that from equation (\ref{eq:ldcphaseshifts}) the linear conductance is given by
\begin{equation}
\label{eq:ldcfrac}
\pi \Gamma D_{i}(0) = \frac{1}{1 + 1/(\pi \rho K)^{2}}
\end{equation}
in terms of the potential scattering strength $\rho K$ (and is obviously independent of whether $i =L$ or $R$ is considered). It is straightforward to relate
$\rho K$ in turn to the potential scattering coupling constant $\tilde{K}$ that enters
the $\Lambda$-discretized NRG Hamiltonian for the CO fixed point (equation (4.3) of I):
specifically,
$\rho K = ([1-\Lambda^{-1}]/[2\ln\Lambda]) \tilde{K}$.
Since $\tilde{K}$ itself is directly determined numerically in the NRG calculations,
the linear conductance can thus either be determined this way from equation
(\ref{eq:ldcfrac}), or as the $\omega =0$ limit of the single-particle spectrum
$D_{i}(\omega)$ (determined via the standard NRG method~\cite{hewsoncosti} reprised at the
beginning of section 3). In practice we find the two methods to be in very good numerical agreement.

  As detailed in section 4.1 of I the CO phase corresponds to a \emph{line} of
fixed points, one for each $U' > U'_{c}$. The critical endpoint, occurring at
$U' =U'_{c}+$ on the CO side of the  transition, corresponds to a critical
$\tilde{K}_{c}$ given by equation (4.8) of I, and thus to a critical
$\pi \rho K_{c} = \mathrm{tan}[\case{\pi}{2}(1-\case{1}{\sqrt{2}})]$.
From equation (\ref{eq:ldcfrac}) the differential conductance
$g_{i}/(2e^{2}/h)$, which is unity throughout the SC phase for $U' < U'_{c}$,
thus drops abruptly at the transition to a value of
$\simeq 0.197..$ at $U' = U'_{c}+$~\cite{garst};
as seen clearly in the NRG results of figure~\ref{fig:specfermi}. This
discontinuous drop in the differential conductance as the transition is crossed
appears to be a rather general signature of a Kosterlitz-Thouless quantum phase transition, it being found also for a multi-level small dot close to a singlet-triplet degeneracy point~\cite{HofSch} and for a pair of Ising-coupled Kondo impurities, onto which maps the problem of spinless, capacitively coupled metallic islands close to the degeneracy point between $N$- and $N+1$-electron states~\cite{garst}.

  We also add that while the existence of an abrupt drop in the differential conductance as the transition is crossed is not specific to the particle-hole symmetric case shown in figure~\ref{fig:specfermi}, the magnitude of the discontinuity is, reflecting the fact that deviation from particle-hole symmetry generates additional potential scattering of the \emph{same} sign on the two leads.
The generic form for the linear conductance follows from equations
(\ref{eq:dialpha}, \ref{eq:ldc1}, \ref{eq:wibbly}) as
\begin{equation}
\pi \Gamma D_{i}(0) = \frac{1}{2}\biggl\{\frac{1}{1 + 1/(\pi \rho K_{iA})^
{2}}~+~ \frac{1}{1 + 1/(\pi \rho K_{iB})^{2}} \biggr\}
\end{equation}
with the $K_{i\alpha}$ of form (again for $i=L$ explicitly) $K_{iA} = -K+\delta K$ and $K_{iB} = K+\delta K$,
where $\delta K$ represents the additional potential scattering common to each channel
that vanishes only at particle-hole symmetry.

\subsection{Non-Fermi liquid behaviour}

The conventional description of single-particle dynamics centres
on the usual single self-energy $\Sigma_{i}(\omega)$, defined by equation (\ref{eq:sse}) (and the Dyson equation implicit therein). The analysis above has however been couched in terms of a TSE description, so the obvious question arises: what are the implications for $\Sigma_{i}(\omega)$?

  The general relation between $\Sigma_{i}(\omega)$ and the two self-energies
$\tilde{\Sigma}_{i\alpha}(\omega)$ follows simply from direct comparison of equations (\ref{eq:sse}) with (\ref{eq:tse1}, \ref{eq:tse2}), and is given by
\begin{equation}
\label{eq:ssetse}
\fl \Sigma_{i}(\omega) = \case{1}{2}[\tilde{\Sigma}_{iA}(\omega) + \tilde{\Sigma}_{iB}(\omega)] ~~
+ ~~ \frac{[\case{1}{2}(\tilde{\Sigma}_{iA}(\omega) - \tilde{\Sigma}_{iB}(\omega))]^{2}}{\omega^{+} +i\Gamma - [\epsilon + \case{1}{2}(\tilde{\Sigma}_{iA}(\omega) + \tilde{\Sigma}_{iB}(\omega))]}.
\end{equation}
Since $\tilde{\Sigma}^{I}_{i\alpha}(\omega =0) =0$ (equation (\ref{eq:imsig})),
the imaginary part of the single self-energy at the Fermi level follows from
equation (\ref{eq:ssetse}) as
\begin{equation}
\label{eq:ssefl}
\Sigma_{i}^{I}(\omega =0)~ = ~ \frac{[\epsilon_{iA} -\epsilon_{iB}]^{2}\Gamma}{[\epsilon_{iA}+\epsilon_{iB}]^{2} + 4\Gamma^{2}}
\end{equation}
in terms of the renormalized levels $\epsilon_{i\alpha}$, equation
(\ref{eq:renormlevel}).
For the SC phase, where $\epsilon_{iA} = \epsilon_{iB}$ generically (and
$\epsilon_{iA} =0 =\epsilon_{iB}$ at particle-hole symmetry), equation
(\ref{eq:ssefl})
gives $\Sigma_{i}^{I}(\omega =0) =0$ --- just as required for a Fermi liquid state
($\Sigma_{i}^{I}(\omega) \propto \omega^{2}$ as $\omega \rightarrow 0$).

  For the degenerate CO phase by contrast, the renormalized levels $\epsilon_{iA} \neq \epsilon_{iB}$. From equation (\ref{eq:ssefl}), the conventional self-energy thus has a non-vanishing imaginary part at the Fermi level $\omega =0$. This is of course a direct reflection of the non-Fermi liquid nature of the CO phase; and we emphasise that to recover this behaviour necessitates use of the two-self-energies $\tilde{\Sigma}_{i\alpha}(\omega)$ (which themselves satisfy $\tilde{\Sigma}_{i\alpha}^{I}(\omega =0) =0$). For the specific case of particle-hole symmetry,
$\epsilon_{iA} =-\epsilon_{iB}$ and
\begin{equation}
\frac{\Sigma_{i}^{I}(\omega =0)}{\Gamma} = \biggl[\frac{\epsilon_{i\alpha}}{\Gamma}\biggr]^{2} ~
\equiv ~ \frac{1}{(\pi \rho K)^{2}}
\end{equation}
(where equation (\ref{eq:caramel}) relating $\epsilon_{i\alpha}$ to the potential scattering strength is also used). And at $U' = U'_{c}+$, using the critical
$\pi \rho K_{c}$, $\Sigma_{i}^{I}(0)$ is then given explicitly by
\begin{equation}
\frac{\Sigma_{i}^{I}(\omega =0)}{\Gamma} = \mathrm{cot}^{2}[\case{\pi}{2}(1-\case{1}{\sqrt{2}})]~~\simeq 4.1~~~~~~~~~~~:U' =U'_{c}+
\end{equation}

\section{Numerical results: dynamics}
\label{sec:numresdyn}

\begin{figure}
\centering\includegraphics{figfiles/hubbsat.eps}
\caption{\label{fig:hubbsat} Single-particle spectra on `high' frequency scales:
$\pi \Gamma D_{i}(\omega)$ \emph{vs} $\omega/\Gamma$ for $\tilde U'=0$ (dotted line), $6$, $7$, $8$ and $9$ (solid lines, top to bottom) with a fixed $\tilde U=7$.}
\end{figure}

We now consider NRG results for the full frequency dependence of the local dynamics,
analysing spectra (for a range of bare parameters) on both high and low frequency scales, and in particular (section~\ref{sec:uniscale})
extracting the universal scaling behaviour in the SC phase.
The single-particle spectrum at finite-$\omega$ is obtained using the standard method \cite{hewsoncosti} --- a set of poles corresponding to the single-particle excitations are calculated from the sequence of NRG iterations, and these are subsequently broadened on a logarithmic scale to compensate for the initial logarithmic discretization of the Hamiltonian and recover the continuum.

\subsection{Spectra on high $\omega$ scales}
\label{sec:hubb}
We begin by considering briefly the evolution of single-particle dynamics on non-universal `high' energy scales --- in particular the Hubbard satellites --- upon progressively increasing the interdot interaction $U'$ from the limit $U'=0$ where the dots are uncoupled. Figure~\ref{fig:hubbsat} shows
$\pi\Gamma D_i(\omega)$ versus $\omega/\Gamma$ for a fixed $\tilde U=7$ and $\tilde U'=0$ (dotted line), $6$, $7$, $8$ and $9$ (solid lines, top to bottom at $\omega/\Gamma=10$).
For all $\tilde U'\le\tilde U$, the Hubbard satellites are seen to be centred at approximately the same frequency, whereas for $\tilde U'>\tilde U$ the positions of the satellites become $\tilde U'$-dependent.

  It is straightforward to explain this behaviour by recourse to the atomic limit $\Gamma=0$. For $U'<U$, the atomic limit ground state is $(n_{L},n_{R}) = (1,1)$ (see equation (2.3) of I). This connects via single-particle excitations (for e.g.\ the left dot) to $(0,1)$ and $(2,1)$ which, regardless of $U'$, are both an energy
$U/2$ higher than the ground state. The atomic limit single-particle spectra thus
exhibit Hubbard satellites (poles in this case) at
$\omega = \pm \case{U}{2}$, independently of $U'$, which is the essential origin of the behaviour seen in figure~\ref{fig:hubbsat} for $U' < U$.
For $U'>U$ by contrast, the atomic
limit ground state is $(2,0)$/$(0,2)$. The corresponding excited states accessible under single-particle excitations, $(1,0)$ and $(1,2)$, are now an energy $U'-U/2$ higher and thus become increasingly separated from the ground states as $\tilde U'$ is raised; generating $U'$-dependent Hubbard satellites at
$\omega = \pm (U'-U/2)$, as again seen in figure~\ref{fig:hubbsat}.\\

  Before considering dynamics on the key low-energy scales, we make a
general remark. NRG spectra may of course be calculated from either the even or the odd set of iterations (fixed points are inexorably fixed points of the \emph{square} of the RG transformation~\cite{wilson,kww1}); and the same spectrum $D_{i}(\omega)$ naturally
results in either case. For the CO phase arising for $U' > U'_{c}$ the NRG ground state is as one would expect doubly degenerate, regardless of whether even or odd iterations are considered. The two-self-energy description considered above is thus ubiquitous in this case. For $U' < U'_{c}$ in the SC phase by contrast there is an important difference between even-$N$ and odd-$N$ iterations,
just as found in~\cite{JPCM} for the single-impurity Anderson model.
In the even-$N$ case the NRG ground state is always (for any iteration)
non-degenerate, for which
reason an effective single-self-energy description of dynamics obviously arises.
 But for the odd-$N$ iterations the NRG ground state is always found
to be doubly degenerate (and with `overlap' on the dots). This leads directly
to an inherent two-self-energy description of local dynamics, even in this
non-symmetry-broken SC phase.
We emphasise again that, whether even or odd iterations are considered, the resultant $D_{i}(\omega)$ obtained from the NRG calculations is the same.
But the key point is that a two-self-energy description of  dynamics, which is a necessity in describing the broken symmetry CO phase, is equally applicable in describing the SC phase; a point not widely appreciated, but one which also underlies the Local Moment Approach to correlated electron systems~\cite{lma1,lmamtg,lmasg1}.
The situation sketched here is directly parallel to that detailed in~\cite{JPCM},
to which the reader is referred for further discussion.

\subsection{Spectra with increasing $U'$}
\label{sec:uprimespec}

We now consider dynamics on the low-energy scales characteristic of the Kondo resonance that arises in the SC phase.
For convenience we shall analyse the two regions $0\le\tilde U'\le \tilde U$ and $\tilde U'\ge\tilde U$ separately. The former displays the crossover from $SU(2)$ to $SU(4)$ behaviour on increasing $\tilde U'$ towards the $SU(4)$ point $U'=U$,
whereas in the latter region we show how the Kondo resonance is destroyed as $\tilde U'$ moves through the phase transition. Throughout the SC phase the Fermi level spectrum is (as above) pinned at the unitarity limit,
$\pi \Gamma D_{i}(\omega =0) =1$; and we note that this behaviour is accurately
captured by the numerics on employing the standard $A_{\Lambda}$-factor
($\Gamma \rightarrow A_{\Lambda}\Gamma$)~\cite{kww1}
that corrects for the finite-$\Lambda$ discretization
inherent to the NRG.

Figure~\ref{fig:specincup}(a)
\begin{figure}
\centering\includegraphics{figfiles/spec_incup_sk.eps}
\caption{\label{fig:specincup} Evolution of the single particle spectrum $\pi \Gamma D_i(\omega)$ vs. $\omega/\Gamma$ with increasing $\tilde U'$ at fixed $\tilde U=7$. (a) shows the crossover from $SU(2)$ to $SU(4)$ physics, $\tilde U'=0$, $6.5$, $6.9$ and $7$ (from bottom to top); while (b)  for
$\tilde U'=7$, $7.03$, $7.044$, $7.048$ and $7.1$ (from top to bottom)
shows the destruction of the Kondo resonance as the phase transition occurring at
$\tilde{U}'_{c} \simeq 7.046$ is crossed.}
\end{figure}
thus shows $\pi \Gamma D_i(\omega)$ versus $\omega/\Gamma$ for a fixed, strongly
correlated $\tilde U=7$, with increasing $\tilde U'=0$, $6.5$, $6.9$ and $7$
(in order of increasing resonance width).
As expected from the thermodynamic results discussed in I, the $SU(2)$ physics of $\tilde U'=0$ is found to persist with increasing $\tilde U'$ until one gets very close to the $SU(4)$ point. For $\tilde U'=6.5$ for example, the functional form of the Kondo resonance is essentially the same as for $\tilde U'=0$, the only difference being that its width is increased slightly in proportion to the Kondo temperature
$T_K$ (the evolution of $T_K$ itself being shown explicitly in figure 5 of I).

As $U'$ moves closer to $U$ however, the LM$^{SU(4)}${} fixed point begins to play an increasingly important r\^ole in shaping the low-frequency form of the spectrum. This is evident in the case $\tilde U'=6.9$, where there is a distinct shoulder in the Kondo resonance when $\omega/\Gamma$ is on the scale of the crossover from LM$^{SU(4)}$ to LM$^{SU(2)}${} ($\sim (U-U')/\pi\Gamma=0.1$). We discuss this point in more detail when considering the scaling characteristics of the spectrum in \sref{sec:uniscale}; for now we simply note that at frequencies below the crossover scale the spectrum is again of the same $SU(2)$ form as for $\tilde U'=0$, whereas on higher scales the tails of the resonance approach those of the $\tilde U'=\tilde U$ $SU(4)$ spectrum
which is also shown in the figure.

Figure~\ref{fig:specincup}(b) illustrates the situation on the other side of the $SU(4)$ point: we show $\pi \Gamma D_i(\omega)$ versus $\omega/\Gamma$, again for fixed $\tilde U=7$ but now with $\tilde U'=7$, $7.03$, $7.044$, $7.048$ and $7.1$, spanning as such the transition occurring at $\tilde{U}'_{c} \simeq 7.046$.
As shown in figure 5 of I, with increasing $\tilde{U}'$ the Kondo scale $T_K$ in the SC phase now decreases exponentially rapidly (following the Kosterlitz-Thouless form equation (6.3) of I), and ultimately vanishes at the critical $\tilde{U}'_c$.
The vanishing of the low-energy Kondo scale as the transition is approached is seen vividly in the behaviour of the Kondo resonance. This narrows rapidly with
increasing $\tilde{U}'$ (figure~\ref{fig:specincup}b for
$\tilde U'=7.03$ and $7.044$), while maintaining the unitarity limit $\pi \Gamma D_{i}(\omega=0) = 1$. The Kondo resonance collapses `on the spot' at $\tilde{U}'=\tilde{U}'_{c}$, and for  $\tilde{U}' > \tilde{U}'_{c}$ in the CO phase leaves only an incoherent continuum around the Fermi level (with $\pi \Gamma D_{i}(0) \lesssim
0.2$).

\subsection{Universal scaling behaviour}
\label{sec:uniscale}
One of the most important results for the single-impurity Anderson model is
the universality of the Kondo resonance, arising in the strongly correlated Kondo regime ($\tilde{U} \gg 1$) when the frequency axis is rescaled in terms of the Kondo scale $T_K$. Here, we examine corresponding issues of universality for the DQD model in the different regimes of the SC phase.

First recall briefly the scaling behaviour of the spectra $\pi \Gamma D_{i}(\omega)$ for $\tilde U'=0$, where
the single-impurity limit (at particle-hole symmetry) is recovered. For
$\tilde U\gg 1$, spectra for different values of $\tilde U$ collapse onto a common form (see e.g.\ \cite{hewson}) when the frequency axis is rescaled as $\omega/T_K$,
with \emph{no} dependence on the `bare' parameters of the model.
Once this `scaling spectrum' is known, the spectrum for any particular $\tilde U$
can thus be determined on an absolute frequency scale simply from a knowledge of $T_K$ alone. The scaling spectrum naturally embodies the universal physics of the
many-body Kondo resonance --- the high-energy, non-universal Hubbard satellites for example (at $|\omega| \simeq \case{U}{2}$) are obviously `projected out' of the scaling spectrum.
We show the $\tilde U'=0$
scaling spectrum, $\pi \Gamma D_i(\omega)$ versus $\omega/T_K$, as the uppermost solid line in figure~\ref{fig:scalspecsk}; and remark in passing that the analytical structure of it is both rich and non-trivial, see
e.g.~\cite{nld}.

\begin{figure}
\centering\includegraphics{figfiles/scalspec_sk.eps}
\caption{\label{fig:scalspecsk}Scaling spectra in the spin-Kondo regime. Main figure: $\pi \Gamma D_i(\omega)$ vs. $\omega/T_K$ for fixed $\tilde U=7$ and $\tilde U'=0$ (top solid line), $6.95$, $6.98$, $6.99$ (dotted lines from top to bottom) and $7$ (bottom solid line). Inset: the collapse of the $SU(4)$ scaling spectrum onto a common form with increasing $\tilde U$, $\pi \Gamma D_i(\omega)$ vs. $\omega/T_K$ for $\tilde U'=\tilde U=7$ (solid line), $9$ (dashed line) and $11$ (dotted line). Note that the $\tilde U=9$ and $11$ spectra are virtually indistinguishable.}
\end{figure}

The $\tilde{U}'=0$ scaling spectrum pertains of course to the $SU(2)$ Kondo model.
One would clearly expect a similar scaling spectrum to exist at
$\tilde U'= \tilde U$, in this case reflecting $SU(4)$ Kondo physics. That this is indeed so is seen in the
inset to figure~\ref{fig:scalspecsk}, which shows $\pi \Gamma D_i(\omega)$ versus
$\omega/T_K$ for $\tilde U'=\tilde U=7$, $9$ and $11$. From this the collapse onto a universal form is immediately apparent. Of course, this $SU(4)$ scaling spectrum differs substantially from its $SU(2)$ counterpart, as shown in figure~\ref{fig:scalspecsk} where the $SU(4)$ spectrum is plotted as the lower solid line.

Having shown distinct scaling behaviour at the $SU(2)$ and $SU(4)$ points, an
obvious question arises: how do the scaling spectra evolve from $SU(2)$ to $SU(4)$ behaviour in the intervening region $0<\tilde U'<\tilde U$? As mentioned in
the discussion of section~\ref{sec:uprimespec}, it is in fact the non-universal
scale $U-U'$ which controls this crossover; and the magnitude of $U-U'$ in relation to $T_K$ determines whether the scaling spectrum will be essentially that of $\tilde U'=0$, $\tilde U'=\tilde U$, or a combination of the two. For example, if $\tilde U'$ is not exponentially close to $\tilde U$, the ratio $(U-U')/T_K$ will be very large (recall
that $T_{K}$ is always exponentially small in strong coupling), the LM$^{SU(4)}${} fixed point will thus have basically no influence on the low-frequency dynamics, and the spectrum should therefore collapse onto the $SU(2)$ scaling spectrum.
Similarly, if $(U-U')\ll T_K$, then one would expect the scaling spectrum to be essentially unchanged from the $SU(4)$ spectrum on all but possibly the lowest frequency scales (and even here the Friedel sum rule guarantees that $\pi \Gamma D_{i}(\omega) \rightarrow 1$ as $\omega/T_{K} \rightarrow 0$ throughout the SC phase). When $(U-U')\sim {\cal{O}}(T_K)$ however, we do expect to see qualitatively different scaling spectra: here the crossover from $SU(2)$ to $SU(4)$ occurs on a scale of
order $T_K$ itself, and we would thus expect the spectra to show characteristics of both regimes.

Our numerical results agree with the arguments given above. For $\tilde U'\lesssim 6.9$ and frequencies in the range shown in figure~\ref{fig:scalspecsk}, the single particle spectra plotted as a function of $\omega/T_K$ collapse essentially perfectly onto the $U'=0$ $SU(2)$ scaling spectrum. For larger values of $\tilde U'$ however, the ratio $(U'-U)/T_K$ moves into the frequency range under consideration and hence the spectra begin to show signs of $SU(4)$ tails. For example, the dotted lines in figure~\ref{fig:scalspecsk} show $\pi \Gamma D_i(\omega)$ versus $\omega/T_K$ for $\tilde U'=6.95$, $6.98$ and $6.99$, from which it is clear that with increasing $\tilde U'$ towards $\tilde{U}' =\tilde{U}$, the $SU(2)$ low-frequency behaviour holds over a  progressively decreasing range of $\omega/T_K$. For values of $\tilde U'$ much closer still to
$\tilde U$, the numerically obtained scaling spectra are virtually indistinguishable from that of the $SU(4)$ line $U'=U$.

The discussion above has focussed on the crossover from $SU(2)$ to $SU(4)$ behaviour, i.e. for $\tilde U'\le \tilde U$. We now show that there is a \emph{third} scaling spectrum in the SC phase, which describes the behaviour in the charge-Kondo regime
($\tilde U<\tilde U'<\tilde U'_c$) as the transition is approached and the Kondo
scale $T_{K}$ acquires its asymptotic Kosterlitz-Thouless form (equation (6.3) of I,
vanishing exponentially rapidly as $\tilde{U}' \rightarrow \tilde{U}'_{c}-$).
The main part of figure \ref{fig:scalspecck}
\begin{figure}
\centering\includegraphics{figfiles/scalspec.eps}
\caption{\label{fig:scalspecck} Scaling spectra in the charge-Kondo regime. Main figure: $\pi \Gamma D_i(\omega)$ vs. $\omega/T_K$ for $\tilde U=7$ and $\tilde{U}'=7.03$ (dotted line), $7.04$ (dashed line) and $7.044$ (solid line). Inset: $\pi \Gamma D_i(\omega)$ vs. $\omega/T_K$ for $\tilde U=7$ (solid line), $8$ (dashed line) and $9$ (dotted line) where $(\tilde{U}'-\tilde{U})/(\tilde{U}'_c-\tilde{U})$ is fixed at $\simeq 0.86$. Note that the spectra for the largest two values of $\tilde{U}$ are essentially indistinguishable.}
\end{figure}
 shows $\pi \Gamma D_i(\omega)$ versus $\omega/T_K$ for fixed $\tilde U=7$ and
$\tilde{U}'=7.03$, $7.04$ and $7.044$: as $\tilde{U}'$ approaches
$\tilde{U}'_c$ ($\simeq 7.046$), the Kondo temperature $T_K$ rapidly diminishes and the rescaled spectra collapse onto a common form. The scaling spectrum shows a distinct `charge-Kondo' resonance, the tails of which tend not to zero as $\omega/T_K\to\infty$, but to the value
$\sin^2 [\case{\pi}{2}(1-\case{1}{\sqrt{2}})]\simeq 0.2$ which is the zero-frequency value of the spectrum on entering the CO phase (section \ref{sec:potscat}).

In the inset of \fref{fig:scalspecck}, we show further that this scaling spectrum is independent of the value of $\tilde U$ (for strong-coupling $\tilde U\gg 1$), the same spectrum being obtained close to the phase boundary for $\tilde U=7$, $8$ and
$9$. For each $\tilde{U}$, the value of $\tilde{U}'$ has been chosen sufficiently
close to the phase boundary that the Kondo scale $T_{K}$ is well described by its asymptotic Kosterlitz-Thouless form (see e.g.\ figure 5 of I); the
$\tilde{U}'$s being chosen in practice such that
$(\tilde{U}'-\tilde{U})/(\tilde{U}'_c-\tilde{U}) = 0.86$.

To summarise, we have shown that the scaling behaviour of the spectra throughout the SC phase can for the most part be understood quite simply in terms of the three scaling spectra obtained in the limits $\tilde U'=0$, $\tilde U'=\tilde U$ and $\tilde U'=\tilde U'_c-$. The $\tilde U'=0$ scaling spectrum in fact captures the behaviour in the vast majority of the phase, being the appropriate description for all $U-U'\gg T_K$. As one moves closer to the $SU(4)$ line, the spectra at low-frequencies cross over to the $SU(4)$ scaling spectrum shown in figure~\ref{fig:scalspecsk}, and then beyond $\tilde U'=\tilde U$ the spectra rapidly collapses onto the charge-Kondo scaling spectrum shown in figure~\ref{fig:scalspecck}.

\section{Discussion}

  Finally, we comment briefly on symmetry breaking perturbations which destroy
the stability of the CO fixed point.
Particle-hole asymmetry does not of course fall into this category.
As we have emphasised several times here and in I the particle-hole symmetric case
($\epsilon = -\case{U}{2}-U'$) is entirely representative, and the
essential physics robust to departure from it.
However the model we have considered is `left/right' symmetric: equivalent
dots (e.g.\ $\epsilon_{R} = \epsilon_{L} \equiv \epsilon$), and equivalent coupling to the conduction channels/leads ($\Gamma_{L} =\Gamma_{R} \equiv \Gamma$).
If $L/R$ symmetry is broken it is readily shown that while the SC fixed point remains stable, additional relevant perturbations arise for the CO fixed point
and hence render it unstable. Flows in the vicinity of the CO fixed point thus ultimately flow away from it under renormalization, and cross over instead to the SC fixed point.

  Since the quantum phase transition between the SC and CO phases is strictly destroyed by breaking $L/R$ symmetry, the question arises: do visible remnants
of the transition nonetheless remain? Indeed they do. To illustrate this we consider explicitly the
case of detuning the dot levels e.g.\ by applying a different gate voltage to
each dot, taking $\epsilon_{L,R} = \epsilon \pm \case{1}{2}\delta\epsilon$ (with
$\epsilon = -(\case{U}{2}+U')$ as usual). Here one expects intuitively that the
crossover scale for flows away from the CO fixed point will be
determined by $\delta\epsilon$; and that if $\delta\epsilon$ is not large compared
to the $SU(4)$ scale $T_K^{SU(4)}$, then the erstwhile transition will be `smeared out'
but still in essence visible as a clear crossover. That this is so is illustrated
in figure 6, where we show NRG results for the differential conductance
$\pi \Gamma D_{L}(0)$ \emph{vs} $\tilde{U}'$ for three different $\delta\epsilon$,
viz $\delta\epsilon/T_K^{SU(4)} = 0, 0.3$ and $2$ (with $T_K^{SU(4)}/\Gamma \simeq 0.01$
the $\tilde{U}'=\tilde{U} = 7$ $SU(4)$ scale for $\delta\epsilon =0$). The
pristine transition occurring for $\delta\epsilon =0$ is as anticipated smeared out,
on a scale determined by $\delta\epsilon$; albeit remaining clearly visible
(note that the lowest $\tilde{U}'$ shown in figure 6 is $\tilde{U}'=6.9$),
and as such robust in an obvious sense.

\begin{figure}
\centering\includegraphics{figfiles/specfermi_deltae.eps}
\caption{\label{fig:deltaeps} Linear differential conductance $\pi \Gamma D_{L}(\omega=0)$ \emph{vs} $\tilde{U}'$ for a fixed $\tilde{U} =7$ and $\delta\epsilon/T_K^{SU(4)} = 0$ (dotted line), $0.3$ (dashed) and $2$ (solid). Note that the lowest
$\tilde{U}'$ shown in the figure is $\tilde{U}'=6.9$.}
\end{figure}

\ack

We are grateful to the EPSRC for supporting this research, and to the Royal Society for travel support.

\section*{References}

redpajama_set_name: RedPajamaArXiv


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text:
VIEW MUSEUM
ΑΠΟ ΤΟ 1922
"When our guests try our cheese, they do not just feel its ingredients. They are immersed into the chronicle of its creation; the care and devotion of its creators till the moment it reaches one's table." Dimitris Haros
Diaseli Estate has always been a family affair. The oldest record of our cheese tradition is in 1922 but we know that the ancestors of the grandparents of the family also earned a living by the sheep and goats, their milk and its products. Back then the cheese-making was done in stone cells (rooms) in a cauldron over the fire. People and animals struggled to survive. The head of the family at that time was Dimitris Haros the grandfather who bequeathed invaluable knowledge to the family which lingers till today.
Around 1970, the baton was passed to the grandfather's son, Antonis Haros. In the years that followed, the Haros family supplied with cheese not only Ios but also the surrounding islands such as Santorini and Paronaxia (Paros & Naxos). The most famous kinds of the produced cheese of that time were Hloro, Kefalotyri, Myzithra and Skotyri. It was the period when Antonis Haros built a new "mitato" (farm) at the highest point of Ios; with much effort and difficulties, the herd grew in number, as well. Although his greater support was his son, Dimitris, the backbone of the family was Antonis' wife, Efrosini Harou, as she played a key role in the development of the estate; as his daughters, Irini and Marianna, did, too. In general, the women of the family played a very important role and proved to be equal to men, being to this day an integral part of the estate, taking care of its prosperity through very difficult times. Women and men in a harmonious coexistence have been composing for many years an amalgam of valuable recipes and experience along with touches of fresh ideas that led to the current image of the estate.
Over the generations, the recipes of the products travelled in time and the experience of the cheesemakers of the family grew. In 1995, Dimitris Haros the youngest was put in charge of the farm and a few years later he took a strategic initiative; that of modernization. With the weight of his ancestors' great legacy on his shoulders and with fresh ideas and a lot of passion, he created a stable and a cheese factory of modern standards. The facilities are now certified for exceptional quality and hygiene and operate according to the appropriate specifications. Despite the evolution of the process and the means of cheese-making, the recipes remain unchanged over time. The animals of the estate continue to eat the same plants that have been growing on the island for hundreds of years, such as thyme and oregano, thus keeping the substance of the raw material the same after all these years. The products receive regular and constant care. Their maturation is monitored daily as it is the second most important part besides the procedure of cheese making so as for them to be quality, truly traditional products. The process of creating each product is not a job for family members; it is a soul deposit.
© 2022 ~ DIASELI ~ TRADITIONAL CHEESE, IOS , GREECE
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Home / General / COVID and patience
COVID and patience
By Paul Campos
One thing that doesn't seem to be getting a lot of attention in all the discussions about what to do about school in the fall (primary/secondary and higher ed) is that the preliminary development work on various vaccines seems to be going well. COVID-19 is apparently turning out to be a good candidate for developing an effective vaccine, because it mutates relatively slowly, thus providing less of a moving target for researchers than many other viruses.
Right now, it looks like the odds of having some sort of at least somewhat effective vaccine by the end of the year are looking pretty good, as are the odds of developing even better vaccines over the course of 2021. In addition, various therapies for people who have contracted COVID-19 are also advancing quickly.
It's a remarkable international research effort, in an age of almost instantaneous information sharing, which has helped fuel rapid technological advances in vaccine and therapeutic drug development.
Given all this, the current failure of the US federal and many state governments to develop and deploy a containment strategy is all the more tragic. It is quite possible, and even likely, that the medical situation is going to be far better as early as this fall. Right now, the emphasis should be on hanging on until it is better, not on learning to live with a virus that contemporary medical science could well partially or wholly defeat in the very foreseeable future.
My view is that plans to fully open colleges and universities this fall make no sense at all, given ongoing developments. Is one semester of remote learning, with all its many admitted disadvantages, worth enduring if a medical solution to the pandemic is almost visibly on the horizon? To me, that question answers itself.
The situation with primary and secondary schools is more complicated, because these schools play a very different and much more comprehensive role in the nation's daily life than higher ed. But even there, a few months more of patience could well reap enormous benefits very soon.
The current pessimism about slowing down a first wave that never declined that much — and is now cresting to even greater heights — in what has become a third world country with nukes is very understandable. But luckily, the USA isn't going at this alone — the whole world is fighting COVID-19, and there's every reason to think it will win the battle in the not too distant future.
Remembering that can help us get from here to there with much less damage than we in this country are on the verge of incurring.
Higher Education and the Economics of Pandemic
LGM Film Club, Part 29: Supermarket Checkout
JR in WV Film makers in Russia will make the films about the war for Ukraine that they are TOLD to make. What about autocracy do you not understand???
War Movies · January 28, 2023
richardgrabman Being seen as "doing something"... whether it's really useful or not?
jam We are prepared to fight the second best military in Ukraine.
Joe Paulson Bill Barr is so bad that he makes Jeff Sessions look good. Not that good, sure, but like as when he is compared to Tubby Tuberville, Sessions at times comes off as if he has a bit of credibility....
richardgrabman If I understand correctly, one issue is that the Ukrainians will loose quite a few of whatever superweapons the US/NATO provides, which the Russia (and... China and Iran) are perfectly capable or...
I see light on these shores tonight


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How to make delicious sauteed cabbage with fresh lemon and garlic. Simple and delicious! Jump to the Quick and Easy Sauteed Cabbage Recipe or read on to see our tips for making it.
This is a simple, healthy recipe for cooking cabbage. It's delicious, too. If you have never sautéed cabbage before, you need to start.
As cabbage cooks in the pan, it wilts, turns tender, and becomes sweet. Cabbage may sound like a boring side, but this is one of our favorite sides to make.
Here's another way to cook cabbage! Our Ham and Cabbage Soup is easy to make and tastes incredible.
Cabbage is underrated. It's good for you with high levels of vitamin C, is antioxidant-rich, and has been shown to have anti-inflammatory benefits. It's also tasty.
We love cabbage in many forms, but our favorite way to cook it is to saute in a little fat on the stove. In this recipe, we stay on the healthier side and cook the cabbage in olive oil, but you can swap the olive oil for other fats. Try butter, coconut oil or nut oils like walnut. You can even cook a few pieces of bacon before the cabbage and use the rendered bacon fat for extra flavor — we do this for our easy bacon fried cabbage recipe.
Leftover cabbage? Try our popular recipe for coleslaw.
Simply sauteed cabbage cooked with olive oil, salt and a bit of pepper is quite delicious as-is, but when we have them in the kitchen, we love to add minced garlic and fresh lemon juice.
The garlic adds flavor, and the lemon brightens up the dish. If you don't have a lemon, apple cider vinegar is an excellent substitute.
If you love the garlic and lemon combination, try our 10 Minute Bok Choy Recipe.
This easy, healthy recipe for sauteed cabbage is delicious. As the cabbage cooks in the pan, it wilts, turns tender, and becomes sweet. Cabbage may sound like a boring side, but this is one of our favorite side dishes to make. White cabbage is our favorite for this, but other cabbage varieties will work. Keep in mind, though, that Napa cabbage will release more moisture and won't brown as nicely in the pan.
Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the cabbage, garlic, red pepper flakes, and the salt. It might seem like too much cabbage for the pan, but as it cooks, the cabbage will wilt down.
Cook, stirring occasionally until the cabbage is tender and some of the cabbage begins to turn a light brown; 10 to 15 minutes. Squeeze the juice from 2 lemon wedges over the cabbage. Taste then adjust with more salt, pepper, and lemon juice as needed.
To shred the cabbage, quarter the cabbage through the core, and then cut out the core. Cut each quarter crosswise in half and finely shred. Rinse and spin or pat very dry.
Great recipe. Very simple but good – as food should be.
I do low carb and eat a lot of cabbage. The be count here of 18g seems high for cabbage and lemon juice. Thoughts?
Hi Pat, I just reran the recipe through our nutrition calculator and found the amount of lemon juice was incorrect. The carbohydrate per serving has been adjusted and it is a bit lower. Sorry for any confusion!
Hi there! This sounds great! I will keep the recipe in mind and I am sure that I will have cabbage leftovers during winter!


MENTAL PATIENT WHO DIED IN POLICE CUSTODY AFTER BEING TAZED HOMEGOING!
ROBERT RICKS IS BEING LAID TO REST BUT HIS FAMILY AND THE COMMUNITY STILL SEEKING ANSWERS ABOUT HIS DEATH WHILE IN POLICE CUSTODY!
Robert Ricks, 23, is being eulogized Saturday at 2pm at Pilgrim Baptist Church, in Alexandria this Saturday, February 12th. Ricks died nearly a week ago, Saturday February 5th, after being tasered by Alexandria police officers and possibly by jailers in the Rapides Parish Jail, according to State Police who are now investigating his death.
The in custody death of Ricks has caused and outrage in the African American community, and has the family of the deceased mental patient concerned about a possible police cover up. According to Ricks' 85-year-old grandmother, Maxine Jones, who he lived with on Apple White Street, she called 911 after her grandson had a seizure around 9pm Saturday.
She says her grandson, a mental patient diagnosed with Bi-Polar Disorder and Paranoid Schizophrenia was just released from Cross Roads hospital only two days earlier. Jones told Broadcast Journalist,Tony Brown,Host of the state-wide talk show "Eyes Open," who first broke the story to the public on Tuesday morning, that her grandson came out of the seizure just before paramedics arrived at her home.
What happened shortly thereafter is what state police and the family are trying to find out. The Ricks family says Robert refused medical treatment and at some point for unknown reasons the Acadian ambulance paramedics called Alexandria Police. Maxine Jones neighbors says about six Alexandria Police units arrived at the location and stayed in the home even after the ambulance and fire department left the scene.
Jones adds that officers promised her that they would take her grandson to the hospital and vehemently denies all reports by police that her grandson ever assaulted her. The family believes the simple battery charge against Robert is part of a cover-up by police because of the death.
They along with the local NAACP want to know why police were called? Why Robert Ricks who does not have a police history, or record of abusing his grandmother was taken to jail? The family says the police told Maxine Jones, who lived alone with her grandson was promised that he would be taken to the hospital and she could not go due to her age and illness. She also says she told officers numerous times that Robert Ricks was a mental patient and says she even showed them his discharge papers from the hospital.
Neighbors who saw Ricks being placed in the back of the squad car say the man was screaming that he had been beaten and tased and was afraid, they also say at least one officer hit Ricks in the head while he was handcuffed after putting him in the police unit.
United States Air Force Sgt Nathaniel Ricks, a former Military Police Officer, now instructor stationed at Lackland Air Force Base in San Antonio, TX, who is Roberts older brother, says he doesn't understand why his brother died and is concerned because so far no one with the State Police has come to his grandmothers home or questioned the family or neighbors to date. "How can you do and investigation without interviewing my grandmother or coming to her home," which he considers a crime scene. He says the family still has his brothers bed sheets and pillow case that he says is covered in his bothers blood.
State Police say they expect the autopsy to be complete in about 4 to 6 weeks. Robert Ricks was arrested for simple battery of Maxine Jones, according to the police report. It list the arresting officers as Marcus Kirk and David Foshee Jr. Maxine Jones says as many as 6 APD police were in her home on that fatal night. No word yet on whether any law enforcement involved in the arrest with APD or the Rapides Parish Sheriff Office have been placed on leave.
Alexandria Mayor Jacques Roy who did not have his weekly Wednesday press conference did tell the local newspaper after finding out about the death," When we know what happens, we come to terms easier than when we have questions. Please support the family of the deceased and our officers, whom I must remind citizens are presumed to have discharged their duties properly, and who risk their lives every day for all of us."
This is sad them officers need to locked up.
Radio host for "Eyes Open with Tony Brown" on KAYT 88.1, Central Louisiana.


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text:
package sqlancer.clickhouse.ast;

import sqlancer.Randomly;
import sqlancer.clickhouse.ast.constant.ClickHouseCreateConstant;

public class ClickHouseBinaryLogicalOperation extends ClickHouseExpression {

    private final ClickHouseExpression left;
    private final ClickHouseExpression right;
    private final ClickHouseBinaryLogicalOperator op;
    private final String textRepresentation;

    public enum ClickHouseBinaryLogicalOperator {
        AND("AND", "and") {
            @Override
            public ClickHouseConstant apply(ClickHouseConstant left, ClickHouseConstant right) {
                if (left.isNull() && right.isNull()) {
                    return ClickHouseCreateConstant.createNullConstant();
                } else if (left.isNull()) {
                    if (right.asBooleanNotNull()) {
                        return ClickHouseCreateConstant.createNullConstant();
                    } else {
                        return ClickHouseCreateConstant.createFalse();
                    }
                } else if (right.isNull()) {
                    if (left.asBooleanNotNull()) {
                        return ClickHouseCreateConstant.createNullConstant();
                    } else {
                        return ClickHouseCreateConstant.createFalse();
                    }
                } else {
                    return left.asBooleanNotNull() && right.asBooleanNotNull() ? ClickHouseCreateConstant.createTrue()
                            : ClickHouseCreateConstant.createFalse();
                }
            }
        },
        OR("OR", "or") {
            @Override
            public ClickHouseConstant apply(ClickHouseConstant left, ClickHouseConstant right) {
                if (!left.isNull() && left.asBooleanNotNull()) {
                    return ClickHouseCreateConstant.createTrue();
                } else if (!right.isNull() && right.asBooleanNotNull()) {
                    return ClickHouseCreateConstant.createTrue();
                } else if (left.isNull() || right.isNull()) {
                    return ClickHouseCreateConstant.createNullConstant();
                } else {
                    return ClickHouseCreateConstant.createFalse();
                }
            }
        };

        private final String[] textRepresentations;

        ClickHouseBinaryLogicalOperator(String... textRepresentations) {
            this.textRepresentations = textRepresentations.clone();
        }

        String getTextRepresentation() {
            return Randomly.fromOptions(textRepresentations);
        }

        public abstract ClickHouseConstant apply(ClickHouseConstant left, ClickHouseConstant right);

        public static ClickHouseBinaryLogicalOperator getRandom() {
            return Randomly.fromOptions(values());
        }
    }

    public ClickHouseBinaryLogicalOperation(ClickHouseExpression left, ClickHouseExpression right,
            ClickHouseBinaryLogicalOperator op) {
        this.left = left;
        this.right = right;
        this.op = op;
        this.textRepresentation = op.getTextRepresentation();
    }

    public ClickHouseExpression getLeft() {
        return left;
    }

    public ClickHouseBinaryLogicalOperator getOp() {
        return op;
    }

    public ClickHouseExpression getRight() {
        return right;
    }

    public String getTextRepresentation() {
        return textRepresentation;
    }

    @Override
    public ClickHouseConstant getExpectedValue() {
        ClickHouseConstant leftExpected = left.getExpectedValue();
        ClickHouseConstant rightExpected = right.getExpectedValue();

        return op.apply(leftExpected, rightExpected);
    }

}

redpajama_set_name: RedPajamaGithub


text:
Community News School
March 25, 2017 April 26, 2017 Staff
David Piperato, principal of Emmaus High School for nearly 10 years, on Thursday accepted a job as the top administrator of the Pleasant Valley School District.
During a meeting Thursday night, Pleasant Valley school directors unanimously approved Piperato's hiring as superintendent of the Monroe County system starting July 1. "Mr. Pip," as he is known to students, will finish out the current school year at Emmaus.
East Penn will form a committee to begin a search for his replacement to lead the 2,663-student school.
Piperato said he looks forward to "the challenges of being a superintendent, having to view issues from a district-wide perspective instead of a building-level perspective."
Along with new challenges, he said he anticipates meeting lots of new people as well as having the "ability to have an even greater impact on the lives of students than I can have as a building principal."
"I am very sad to see him leaving," senior Robert Lynn said. "He's done a lot of great work for the school, he's done a lot for the students. I like the way he has connected with the students.
"He's handled many difficult situations very well; he made students feel safe," Lynn said.
Freshman Brendan McCourt, who serves on the Principal's Advisory Board, described Piperato as "upbeat and inspiring."
"He lets everyone speak on issues [at advisory board meetings]," McCourt said. "He gets an opinion from everyone in the room."
Alex Comfort, a junior who serves on the board along with McCourt, felt Piperato "was very well in touch with the students."
"The Principal's Advisory Board allowed us to have really good conduct with him, which allowed us to express our thoughts on the school and really be heard," he said.
Junior Sarah Dapper felt Piperato "has a great influence on the students" at EHS.
"It will be a big change for him to leave… it will be a long process for the students to have a relationship like we did with Pip," Dapper said.
Pleasant Valley has four schools and is situated in a largely rural area in the western part of Monroe; it abuts the Stroudsburg and Pocono Mountain school districts.
East Penn hired Piperato in May 2007; he took over as principal that summer, replacing Liz Drake. He previously worked in Lower Merion High School in Montgomery County for 8 years. Born and raised in Easton, he taught business and technology in the Bethlehem Area School District before transferring to Palisades High School as an assistant principal. After Palisades, he moved to Lower Merion.
When East Penn hired him, Piperato said that the Emmaus job provided him with a great opportunity to lead "a phenomenal school."
At the time, Piperato said an effective principal must be willing to listen to a school's students, teachers, and community members.
Seen as a supporter of student events, Piperato on Friday said that he will miss students the most.
"Over the last 10 years, I've come to learn that the Emmaus High School students are truly outstanding people, first and foremost," he said. "They're respectful, they're friendly, and they're smart – they're lots of fun to be around."
Photo courtesty of lehighvalleylive.com
← Mental health: a student's perspective
'Beauty and the Beast': a new twist on a beloved classic →
EHS activism hosts a day of action for students
April 23, 2018 Isabella Wegner 0
'We all wear masks' speaker tells 1,200 at NPFH kickoff talks
September 11, 2016 Administrator 0
Allen resigns from East Penn School Board
September 10, 2018 Erica Love 0


Browse this section for help with Somfy Smart Home products. If you can't find an answer here, please contact us via email or phone.
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Kenley Privacy Fence Screen Mesh for Balcony Porch Deck - 35" x 15' - Weather PATIO Deck Privacy Screen 3' x 15' Perfect for Outdoor,Backyard, Balcony.
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Plantation shutters on the porch, privacy and shade yet still able to get a breeze. How I imagine the private deck off the main bedroom to look like, cat and all.


Watch: Are Patriots fans trash?
Pot calling the kettle black? Last week Boston fans were calling New York Yakees fans trash for throwing beer at players and fans. Last night vs the Chiefs, Patriots fans flipped off and threw beer at Tyreek Hill.


Winter is wonderful for slow-cooked, hearty meals but let's face it, sometimes you just need to get something on the table. Here is a list of five, super-easy and tummy-warming meals you can have on the table in no time.
Here is a tasty one-pan dish that is great if you are hungry for Chinese and don't want to order take-out. This would also be a great way to use up some leftover vegetables or meat. Check out the recipe here.
This recipe is a great one for getting little hands involved. Pull out some sauce, shredded cheese, and favorite pizza toppings and let them go to work helping with dinner. Find the details here.
How about another one-pot meal? This recipe gets even quicker if you have leftover pasta from another meal. This recipe gets bonus points for being a great freezer meal, make an extra and pop it in the freezer for an even quicker meal in weeks to come. Click here for the full recipe.
Does it get much simpler than throwing some food in a pan and letting the oven do the work? This recipe may take a little longer but having the oven on will both warm the house and make it smell delicious. Find the recipe here.
Here is a fun twist on a classic! Create the traditional grilled cheese sandwich, or pizza in this case, and cut into strips to dip into pizza sauce or soup! Check out the recipe here.
Do you have a favorite go-to meal that is quick to make and a hit with the family? Share it with us!
Dayton Family Friendly 5Ks Walk, run or stroll your way through these local races!
Most Popular Super Bowl Recipe- Easy Buffalo Chicken Dip Bring the dish that everyone wants!


San Diego, CA 9/21/2018 — Gregg Ward, Award Winning Best Selling Author & Leadership Facilitator has been accepted into the Forbes Coaches Council, an invitation-only community for leading business and career coaches.
Gregg joins other Forbes Coaches Council members, who are hand-selected, to become part of a curated network of successful peers and get access to a variety of exclusive benefits and resources, including the opportunity to submit thought leadership articles and short tips on industry-related topics for publishing on Forbes.com.
Gregg is in on a mission to transform lives via experiential learning and development programs that create respectful organizational cultures. The first to start using these innovative techniques back in the mid-1980s (Live Theater Training specifically), An executive coach before it was trendy, he has worked with leaders at many Fortune 100 & 500 organizations to create opportunities from obstacles. Gregg is an award-winning, best-selling author and speaker, and recently released a revised version of his book, "The Respectful Leader"- a powerful business fable on influential leadership without intimidation.
Gregg has developed and delivered more than 2,500 programs to help organizations move out of the command-and-control mentality and into respectful and inclusive cultures that maintain the highest standards, employee engagement, and performance. Known by his peers, clients and colleagues for his candor and relentless pursuit of helping executives kickstart their growth strategy challenges, Gregg is especially adept at driving cultural change initiatives.


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Teddy has tie halter straps, and g-string back. Matching stockings are patterned from toe to plain tops. Stocking tops are soft, and reinforced, with no silicone, giving the option to wear as hold ups, or to team with your favourite suspender belt.


text:
Ben Herd Net Worth 2018: What is this football/soccer player worth?
Ben Herd is a professional football/soccer player who played Defender (association football) for St Albans City F.C.. Herd was born on June 21, 1985, in Welwyn Garden City, England. This article examines Ben Herd's net worth.
Ben Herd Career and Earnings/Salary
As a youth, Ben Herd played for Watford F.C. during 0, and 2003. Over 2003-2005, Herd played for Watford F.C. earning 0 caps and scoring 0 goals. During 2005-2009, Herd played for Shrewsbury Town F.C. earning 143 caps and scoring 3 goals. In 2009-2013, Herd played for Aldershot Town F.C. earning 151 caps and scoring 1 goals. In 2014-2015, Herd played for Dunstable Town F.C. earning 27 caps and scoring 8 goals. From 2015, Herd played for Boreham Wood F.C. earning 14 caps and scoring 0 goals. From 2015-2016, Herd played for Hemel Hempstead Town F.C. earning 60 caps and scoring 1 goals.
Ben Herd Net Worth 2018
Professional soccer players can receive plenty of money. But pay depend on plenty of different considerations. These include the player's location and of course, their ranking. At the hightest end, stars in Great Britain and Western Europe can receive $50 million or more. In Latin American countries, top footballers earn $1,000,000-$2,000,000 a year. And in countries where soccer/football is not as popular, such as the USA and China, players get $200,000 a year. The smallest paying leagues can pay as little as $50 thousand per annum.
Ben Herd net worth: soccer/football salary distribution
So what is football/soccer player Ben Herd's net worth in 2018? Our estimate for Ben Herd's net worth as of 2018 is: $400,000
Here are some related football/soccer players: Donovan Simmonds, Tomasz Sokolowski, Ahmed Khalil, Christian Bolaños, Nikolay Chipev, Arturo Lupoli, Gonzalo Abán, Darryl Duffy, Hugo Ayala, Milan Kopic, and Ridhuan Muhammad.


text:
Q: MP3 fingerprint tagger Does anyone know of a tool which will read mp3 audio information directly (not the tag information), generate a fingerprint of that audio information, recommend tags based on the fingerprint and retag your MP3 collection?  Last.FM released a console application which did all but retag your collection.

A: The MusicBrainz Picard tagger sounds like exactly what you are looking for. It fingerprints your music regardless of existing tags and will add the correct tags.
http://musicbrainz.org/doc/PicardTagger
It's not the most intuitive tool to use, but it is very effective. I have been using it a lot lately and it successfully tagged 6000+ tracks that had incorrect metadata.

A: You can try out Tunatic

Love that song but don't know what it
is? Tunatic can tag it for you!
Ever thought 'what is this song?' Let
Tunatic hear it and you will get the
artist's name and the song's title
within seconds. Tunatic is the very
first song search engine based on
sound for your computer. All you need
is a microphone and Internet access.

Tunatic is freeware.

redpajama_set_name: RedPajamaStackExchange


text:
Who wins when reporters cut and paste press releases?
It happens regularly in newsrooms, especially with dwindling staffs. But is it a good thing for journalism—or public relations?
By Gil Rudawsky
The Kansas City Star claims Penn, a former columnist at the paper, plagiarized by using material from press releases in his columns without attribution. He countersued last week saying that it's commonplace in newsrooms to cut and paste from press releases.
It's not plagiarism, because the writers of press releases give up ownership of the information when they send it to a newsroom, according to Penn's suit. The suit adds that it's a regular practice for reporters to crib from press releases.
The situation raises interesting issues. Having been on both sides of this argument—in the newsroom and in the PR world—I can tell you that reporters regularly cut and paste information from press releases. And that's exactly what PR practitioners hope they will do.
Is it a good practice on the part of reporters? No, but it certainly does help, particularly as newsroom staffs continue to dwindle.


text:
module PinboardApi
  class PinboardApiError < StandardError; end
  class InvalidPostError < PinboardApiError; end
  class InvalidResponseError < PinboardApiError; end
end


text:
How to put yourself in the climate conversation
Manifesto, Jul 29, 2021 | Digital impact
Speaker: Sandra Pallier, co-organiser of ClimateAction.tech
Featured in our 2021 London Climate Action Week event: The environmental impact of the digital industry.
A few years back in 2019, after becoming more and more aware of our climate, I made a number of conscious lifestyle changes. But I realised these weren't quite enough. There had to be more work I could do – more systemic work – things which went beyond my personal lifestyle.
So I started by getting a better understanding of my role in the world, and the intersections that make up my life and my identity in the current capitalist system. I work as a designer in the UK tech industry. I'm originally from Austria. I'm a white female, relatively early on in my career.
Then there's the question of how the world around me works. There's the politics I participate in, through voting, campaigning, and joining marches, supporting initiatives and campaigns financially, or even becoming more active and joining a political party.
Part of this exterior includes the corporations, which – to me – feel as though they run the world a lot more than the politicians do these days. Largely because they have the money, power, influence, and resources to do so.
I am one of those resources in a very powerful industry- a tech worker. And that means I have a certain amount of power and certain privileges, which I can use for good, or for bad.
Locate an entry point
A paper I read recently called 'Leverage points: Places to intervene in a system' by systems analyst Donella Meadows talked about high impact points to change a system. Changing mindsets, paradigms as well as the high level goals of any one system are two of the most impactful things we can do to change it.
But changing mindsets and paradigms requires us first to understand what shared ideas we currently live within our society, and which beliefs or unstated assumptions are part of our daily routines. How do we believe the world works? How are we taught that the world works?
Changing the goals of a system at a higher level requires us to ask what the current goals of the systems are. What's the point of the game? Is it survival? Is it resilience? Or differentiation? For corporations the high level goal is often power and control.
Collaboration is key
Changing the mindsets, paradigms or goals of our current system isn't something you can necessarily do alone. You need folks to collaborate with.
And then it's about taking action. To change mindsets and paradigms, you can start by advocating for new ideas. Talking about the climate at work. Speaking up and pointing out the failures of the current system.
You can do all these things through a disruptive medium such as a strike, or a shareholder proposal – which is what Amazon Employees for Climate Justice did (here's an interesting podcast episode that dives into their work). You can also raise your ideas in meetings, day-to-day conversations, or presentations to leadership. And you don't have to change everyone's mind. The system and society will start doing it on its own, as the vast middle ground of open-minded people sway further towards change without even thinking about it.
Ultimately, involving yourself in the world's climate conversation hinges on you being able to paint a picture and envision a new future. One with new rules and a reimagined society which functions better, and has goals where planetary and societal health sit at the core.
Fine-tune your approach
As a tech worker, I want to start in my own industry. Because that's where I have the most experience, and where I currently hold a lot of power. That's where I think I can make the biggest difference by taking various actions.
And there's all sorts of routes you can take.
You can start to live in this new future in one aspect of your life – be that at work, at home, or when you're on the move. That way, the vision you have for the future feels more tangible.
Or you can speak up, breaking the climate silence and changing the mindsets of your colleagues – which will eventually influence decision makers, and change the mindsets of people at the top.
You could plan to popularise the topic of climate change, both outside and inside your workspace, by offering to give talks, teach, or write to spread the word. All of these actions are steps on the way to transformed industries. Ones which listen to local knowledge and adapt to different local contexts, instead of optimising for infinite growth and global scale.
One day, I envision a tech industry which makes the climate its priority, one which takes responsibility, restoring and regenerating the resources it uses up, and one which doesn't rely solely on growth to thrive.
How would people go about starting these sorts of conversations around climate change at work?
Speaking up doesn't necessarily require you to know everything, or to know a lot about the digital industry and its impact on the environment. You can actually use this to your advantage, by asking questions in meetings such as: 'Is there a greener option that we can build? How can we make this more efficient by design? Is this data we're capturing really needed? What are we doing with it and why are we storing it? What data are we offering to the user? Are we just pushing it in their faces, or is it something that they want?
There's lots and lots of questions that you can bring up in meetings like this, but also in day-to-day conversations with colleagues, or in presentations to leadership.
What's the most exciting thing you think has happened in the digital space over these last six months?
From a ClimateAction.tech perspective, we've had a massive increase in members throughout 2020 and moving on into 2021 as well. So, I think one of the things that showed us is that the interest in this topic is growing, which is great.
We've also seen that conversation start to get a bit deeper in the community Slack. We ran a TEDx event last winter, which was pretty well attended too and it was great to see that the conversations are getting deeper and more people are getting involved, from different disciplines as well.
How can communities like ClimateAction.tech facilitate the coordination and dissemination of ideas?
Currently, we're trying to make those information flows a little bit more connected – but part of this is figuring out how to! We start with global conversations, which then empower us to act locally – be that in our organisation or in our country.
We pride ourselves on the fact we are a global community, with members shifting conversations, sharing stories and taking action all over the globe. This diversity of thought has really helped to get an understanding of the climate crisis.
We're still in the process of gathering information from everyone. Currently, we are working on adding more action guides to our website. So there's more to come. We're not quite there yet, but conversations are happening.


Tutors use a range of assessments including portfolios of work, case studies, reports, essays, open-and closed-book examinations and presentations to assess the performance of students. These assessments ensure that a student experiences a wide range of assessment methods. This also helps to ensure that students develop information gathering skills, knowledge and understanding, application, analysis and evaluation of knowledge, presentation and writing skill, as well as ensuring the validity of the assessment process. This variety of assessment methods allows the programme and module learning outcomes to be assessed in a systematic and appropriate way.
Students have the opportunity to take up to one year industrial placement between Levels 5 and 6. Valued by employers as a demonstration of their practical skills and abilities, their work placement enables them to gain essential experience and knowledge of the work place which is helpful to them in their final year of study. Placement students are often more successful academically.
Upon successful completion of the BA (Hons) in Business Management, students will have the confidence, knowledge and skills to follow careers in fields ranging from marketing to general management across all sectors of business and industry.


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Working in the world we live today requires efficiency, and this efficiency can only be gotten when the body and mind are able to contribute at the highest levels of performance.
A lot of people tend to face issues such as fatigue and a loss of concentration, and they look for ways to ensure that they are able to stay sharp and on their toes all through the day.
What is the Haleo Mindset?
The Haleo Mindset is a food supplement which, when taken into the body, may be able to help ensure that the user experiences an increase in body bodily and cognitive functions. It works by helping to stimulate various parts of the body, and it was manufactured with the aim of ensuring that users get the most out of their bodies on a daily basis.
Who is the Manufacturer of the Haleo Mindset?
Just as its name suggests, the Haleo Mindset was manufactured by Haleo.
Haleo is a company that specializes in the manufacturing of food supplements. Based out of Japan, the copay claims that their products are able to help people get the most out of their minds and bodies, and they make different kinds of drugs and supplements available to their customers. The company operates almost on a global scale, and they also say that all of their products are made with only safe and effective ingredients.
How Does the Haleo Mindset Work?
Essentially, users are to ingest the product and as soon as it enters into the system, the ingredients begin to interact with the body, all with the goal of helping with the loss of fats, the suppression of appetites, and the stimulation of the nervous system. The supplement also helps to increase the temperature of the body, which will in turn increase metabolism and boost overall performance.
The ingredients that have been used by this product might help it to ensure that body metabolism is optimized. By limiting the accumulation of fats and stimulating various body systems, these ingredients might be able to deliver on their promise to optimize body performance.
Caffeine: Caffeine helps as the body stimulant in this supplement, and it might help to help stimulate your body to improve its performance.
Ginkgo Biloba: Ginkgo Biloba can help to improve the flow of blood as well as the delivery of oxygen and nutrients to the brain.
What are the Advantages of the Haleo Mindset?
What are the Disadvantages of the Haleo Mindset?
It might also not be able to deliver on all of its promises, especially considering how many claims it made.
How should you take the Haleo Mindset?
It is always recommended that you make use of these products according to the recommendations of the manufacturers.
In the case of this supplement, it is recommended that you take 4 capsules a day, early in the morning so as to allow the ingredients to work early. However, for the best results, you might want to ensure that you wait about half an hour after consuming the supplement before taking a meal.
How much does the Haleo Mindset cost?
As there is no official website is provided for the product we can only purchase the product from retailer websites. It is available at the cost of $19.99 on one of retailer site.
What is the Haleo Mindset return policy?
Does the Haleo Mindset offer a free trial?
At the end of the day, the Haleo Mindset does make some pretty bold claims. According to the manufacturers, it is able to help users with lipogenesis and fat loss. However, it also claims to have added benefits like improved physical and cognitive performance as well as better overall body health. However, you might also want to remember that the manufacturer's site might not be accessible to all, and even the website doesn't seem to provide much information about the brand itself.
Considering all of this, keep in mind that the market is filled with other alternatives that claim to be able to help with these benefits as well. If this product doesn't prove to be effective enough, you might want to opt for any of those.


Standing at Number Three on the Sunday Times wishlist, the Plymouth mogul Chris Dawson runs The Range discount stores. Chris is building "the equivalent of one and a half times the size of Drake Circus shopping centre" every year as he expands his retail empire throughout the UK and Ireland. He is an inspiration for anyone who has ever struggled at school as he is dyslexic and freely admits he "can't read or write".
The millionaire owner of South West Telecommunications (and top man at Exeter Chiefs) came from humble beginnings in Portsmouth and doesn't have an exam certificate to his name: "I hated school. I just didn't like it so I didn't bother to go. No one gave a damn in those days if you went or not. My mother and step-father used to work so they would leave in the morning thinking I went to school.
"It was only later on in life I realised I was dyslexic and it dawned on me that writing my own sick notes hadn't been a good idea when I couldn't spell very well!"
Tony joined the Royal Marines at the age of 15 to become a bugle boy, later found work repairing and racing power boats, then set up South West Telecommunications which employs 150 staff and turns over around £25 million a year. GCSEs? Who needs 'em, eh Tony?
Rosie, 30, really is our poster girl for not bothering with exams. She grew up in west Devon and went to Tavistock College and did her school work experience at a model agency in London at the age of 15. She left after her GCSEs in 2003, went back to London and her first modelling job was for Levi's jeans.
Rosie Huntington-Whiteley - why bother with Sixth Form?
Within a year, while her friends were sitting AS levels, she was featured in Teen Vogue magazine and on the catwalk in New York alongside Naomi Campbell. So there you are, who needs academic qualifications? Certainly not, if you look like the fabulous Rosie!
Dawn, 59, was a bit of a swot at school in Plymouth (she went private, in part paid for by the RAF as her dad was in the Forces). She even won a scholarship for her debating skills at the age of 19 to spend a year at a school in New York. But she most definitely has never really needed her exam certificates.
"Jennifer [Saunders] and I just went for one audition for the Comic Strip. What we didn't know was that they were so desperate to find any women doing anything that we had the job the minute we turned up. I haven't really ever had to audition for anything," she admits.
Founder of the Wetherspoons pub chain, Tim Martin boasts that his company pays £700 million a year in tax "about a thousandth of the whole tax income of the UK". He lives in Exeter with his wife Felicity and they have four children. Tim sold most of his empire in 2012 leaving him with just 30% - even so, that's worth £260 million. He's still working, touring the country popping in to pubs unannounced and checking the pints are being pulled correctly.
Tim did actually do pretty well at school, and went on to study Law at Nottingham University. Has he ever used his Law degree, though? "I once defended myself against a charge of unfair dismissal from a barman who had been drunk at work. I won." So there you go.
These days, she admits that career is not the be-all and end-all and prefers spending time with her husband and kids in Devon. "I'm not particularly good-looking and I'm not madly talented, I look back and I see that young girl doing panto and I think I made a really good career of not very much." Well done, Caroline!
Coldplay front man Chris Martin, 40, was a bit of an academic champion, it has to be said. Growing up in Whitestone, near Exeter, he went to Exeter Cathedral School and then boarded at Sherborne in Dorset. He then went to University College London and holds a First Class honours degree in Ancient History, with Greek and Latin. But has all that studying come in handy for his subsequent career as a rock star? We don't think so.
In fairness, it was at Uni that he met his two bandmates, who admit they first became friends "at a Maths lecture". All very rock and roll… Chris recently revealed he gives around 10% of his income away every year to charity. Good man.