text:
\section{Introduction}
\label{sec:one}

The potential curve crossing is related to a wide range of physical
and chemical processes, and the celebrated Landau-Zener
formula~\cite{1,2,3} correctly describes the qualitative features of
those processes~\cite{4,5,6,7,8}. An effort to improve the
Landau-Zener formula and to make it a more quantitative formula is
actively going on even recently~\cite{9,10}. The purpose of the
present paper is to study this old problem on the basis of modern
field theoretical ideas, namely, the duality and gauge transformation.

The adiabatic and diabatic pictures in potential curve crossing
problem are related to each other by a field dependent $su(2)$~gauge
transformation~\cite{5,8}, and we point out that this transformation
leads to an interchange of strong and weak potential curve crossing
interactions, which is analogous to the electric and magnetic duality
in conventional gauge theory~\cite{11}. This strong and weak duality
allows a reliable perturbative treatment of potential curve crossing
phenomena at the both limits of very weak (adiabatic picture) and very
strong (diabatic picture) potential  crossing interactions. Main
features of potential curve crossing phenomena are well-described by
straightforward time-independent perturbation theory combined with the
zeroth order WKB wave functions~\cite{5,8,12}, without referring to
Stokes phenomena; perturbation theory thus becomes more flexible to
cover a wide range of problems.

To illustrate our observation, we first show that simple
time-independent perturbation theory gives an adequate description of
the Landau-Zener formula including numerical coefficients in the both
limits of adiabatic and diabatic pictures. We encounter an interesting
topological object in the present formulation. We then apply our
formulation to the analysis of the effect of potential curve crossing
on quantum coherence in a double-well potential. We show that the
potential crossing generally suppresses quantum coherence, which is
analogous to the effect of Ohmic dissipation on quantum
coherence~\cite{13,14}. To our knowledge, this clear recognition of
duality and the precise criterion for naive perturbation theory
including the analysis of quantum coherence have not been discussed
before.

\section{A model Hamiltonian of potential curve crossing and duality}
\label{sec:two}

To analyze the potential curve crossing, we start with a model
Hamiltonian defined in the so-called diabatic picture~\cite{5,8}
\begin{equation}
   H={1\over 2m}\hat p^2+{V_1(x)+V_2(x)\over2}
     +{V_1(x)-V_2(x)\over2}\sigma_3+{1\over g}\sigma_1
\label{eq:two.one}
\end{equation}
where $\sigma_3$ and~$\sigma_1$ stand for the Pauli matrices. We
assume throughout this article that the potential crossing occurs at
the origin, $V_1(0)=V_2(0)=0$ (see~Fig.~\ref{fig1}). We also take a
convention that the slope of the first potential at the crossing
point is positive, $V_1'(0)>0$. The sign of $V_2'(0)$ may be either
the same as that of $V_1'(0)$ (Section~\ref{sec:three}) or opposite
(Section~\ref{sec:four}).

If one neglects the last term in the above Hamiltonian, one obtains
the unperturbed Hamiltonian in the diabatic picture
\begin{equation}
   H_0\equiv{1\over 2m}\hat p^2+{V_1(x)+V_2(x)\over2}
   +{V_1(x)-V_2(x)\over2}\sigma_3.
\label{eq:two.two}
\end{equation}
This Hamiltonian~$H_0$ describes two potentials, which are decoupled
from each other. The last term in~(\ref{eq:two.one}),
$H_I\equiv\sigma_1/g$ with a constant~$g$, causes the transition
between these two otherwise independent potential curves. In other
words, if one takes $g\rightarrow{\rm large}$, this case physically
corresponds to a {\it complete\/} potential  crossing from a view
point of {\it adiabatic\/} two-potential crossing~(Fig.~\ref{fig2}).
Namely, $g$~stands for the strength of potential crossing interaction,
and $g\rightarrow{\rm large}$ corresponds to a very strong potential
crossing interaction. On the other hand, if one lets $g$~smaller, the
effects of the last term in~(\ref{eq:two.one}) become substantial and
the Hamiltonian $H_0$~(\ref{eq:two.two}) does not present a sensible
zeroth order Hamiltonian.

To deal with the case of a small~$g$, we perform the non-Abelian
``gauge transformation,''
\begin{equation}
   \Phi(x)=e^{i\theta(x)\sigma_2/2}\Psi(x),\quad
   H'=e^{i\theta(x)\sigma_2/2}He^{-i\theta(x)\sigma_2/2},
\label{eq:two.three}
\end{equation}
where $\sigma_2$~is a Pauli matrix. The Hamiltonian in the new picture
is given by
\begin{eqnarray}
   H'&=&{1\over2m}\left[\hat p
         -{\hbar\over2}\partial_x\theta(x)\sigma_2\right]^2
   +{V_1(x)+V_2(x)\over2}
\nonumber\\
   &&+\left[{V_1(x)-V_2(x)\over2}\cos\theta(x)
                           +{1\over g}\sin\theta(x)\right]\sigma_3
\nonumber\\
   &&+\left[-{V_1(x)-V_2(x)\over2}\sin\theta(x)
                           +{1\over g}\cos\theta(x)\right]\sigma_1.
\label{eq:two.four}
\end{eqnarray}
To eliminate the potential curve mixing, the last term
of~(\ref{eq:two.four}), we choose the gauge parameter~$\theta(x)$
as~\cite{8}
\begin{equation}
   \cot\theta(x)=g{V_1(x)-V_2(x)\over2}\equiv f(x).
\label{eq:two.five}
\end{equation}
We then obtain the Hamiltonian in the {\it adiabatic\/} picture
\begin{equation}
   H'=H_0'+H_I',
\label{eq:two.six}
\end{equation}
where
\begin{equation}
   H_0'\equiv{1\over 2m}\hat p^2+{U_1(x)+U_2(x)\over2}
   +{U_1(x)-U_2(x)\over2}\sigma_3,
\label{eq:two.seven}
\end{equation}
and
\begin{equation}
   H_I'\equiv-{\hbar\over4m}
   \left[\hat p\partial_x\theta(x)
         +\partial_x\theta(x)\hat p\right]\sigma_2
   +{\hbar^2\over8m}\left[\partial_x\theta(x)\right]^2.
\label{eq:two.eight}
\end{equation}
The potential energies in the adiabatic picture are related to those
in the diabatic picture as~(Fig.~\ref{fig2})
\begin{equation}
   U_{1,2}(x)\equiv{V_1(x)+V_2(x)\over2}
   \pm\sqrt{\left[{V_1(x)-V_2(x)\over2}\right]^2+{1\over g^2}}.
\label{eq:two.nine}
\end{equation}
{}From the definition of the gauge parameter in~(\ref{eq:two.five}),
the ``gauge field''~$\partial_x\theta(x)$ is expressed as
\begin{equation}
   \partial_x\theta(x)=-{f'(x)\over1+f(x)^2}.
\label{eq:two.ten}
\end{equation}

The transition from the diabatic picture to the adiabatic picture is
a local gauge transformation, or in the conventional field theoretical
sense it is regarded as a field dependent transformation. The
transformation from one of these two pictures to the other is an
$x$-dependent notion.

In the adiabatic picture, the $\sigma_2$~dependent term in the
interaction~$H_I'$~(\ref{eq:two.eight}) causes the potential
crossing. If one neglects~$H_I'$, the two potentials characterized by
$U_1(x)$ and~$U_2(x)$ do not mix with each other: Physically, this
means {\it no\/} potential  crossing. This suggests that $H_I'$~is
proportional to the coupling constant~$g$, since a small~$g$
corresponds to {\it weak\/} potential  crossing by definition. This is
in fact the case as is clear from (\ref{eq:two.ten})
and~(\ref{eq:two.five}).

We thus conclude that the two extreme limits of potential crossing
interaction should be reliably handled in perturbation theory; namely,
the strong potential crossing interaction in the {\it diabatic\/}
picture, and the weak potential crossing interaction in the gauge
transformed {\it adiabatic\/} picture. This is analogous to the
electric-magnetic duality in conventional gauge theory~\cite{11}:
The diabatic picture may correspond to the electric picture with a
coupling constant~$e=1/g$, and the adiabatic picture to the magnetic
picture with a coupling constant~$g$.

A general criterion for the validity of perturbation theory in the
adiabatic picture~(\ref{eq:two.six}) is
\begin{equation}
  {\hbar\over2}|\partial_x\theta(x)|\ll|p(x)|,
\label{eq:two.eleven}
\end{equation}
which is expected to be satisfied when the coupling constant~$g$ is
small and the incident particle is sufficiently energetic.

\section{Landau--Zener formula}
\label{sec:three}

As an application of the duality discussed in Section~\ref{sec:two},
we re-examine a perturbative derivation of the Landau-Zener formula in
both of the adiabatic and diabatic pictures~\cite{1,5,8}. For
definiteness, we shall assume $V_1'(0)>V_2'(0)$ as in~Fig.~\ref{fig1}.

Let us start with the adiabatic picture with weak potential crossing
interaction. Since the gauge field generally vanishes,
$\partial_x\theta(x)\rightarrow0$ for $|x|\rightarrow\infty$, we can
define the {\it asymptotic\/} states in terms of the eigenstates
of~$H_0'$~(\ref{eq:two.seven}). We define the initial and final
states $\Phi_i$ and~$\Phi_f$ by
\begin{equation}
   \Phi_i(x)=\pmatrix{\varphi_1(x)\cr 0\cr},\quad
   \Phi_f(x)=\pmatrix{0\cr \varphi_2(x)\cr},
\label{eq:three.one}
\end{equation}
which satisfy
\begin{equation}
   \left[{1\over2m}\hat p^2+U_1(x)\right]\varphi_1(x)
   =E\varphi_1(x),\quad
   \left[{1\over2m}\hat p^2+U_2(x)\right]\varphi_2(x)
   =E\varphi_2(x).
\label{eq:three.two}
\end{equation}
We then obtain the potential curve crossing probability due to the
perturbation~$H_I'$~(\ref{eq:two.eight})
\begin{equation}
   w(i\rightarrow f)
   ={2\pi\over\hbar}|\langle\Phi_f|H_I'|\Phi_i\rangle|^2.
\label{eq:three.three}
\end{equation}
The transition matrix element is given by
\begin{equation}
   \langle\Phi_f|H_I'|\Phi_i\rangle=
   -{\hbar^2\over4m}\int_{-\infty}^\infty dx\,\partial_x\theta(x)
   \left[-\varphi_2'(x)\varphi_1(x)
         +\varphi_2(x)\varphi_1'(x)\right].
\label{eq:three.four}
\end{equation}

To evaluate the matrix element, we use the WKB wave
functions~\cite{4}:
\begin{equation}
   \varphi_1(x)=\cases{
   \displaystyle
   {C_1\over2\sqrt{|p_1(x)|}}
   \exp\left[-{1\over\hbar}\int_{a_1}^xdx\,|p_1(x)|\right]
   &for $x>a_1$,\cr
   \displaystyle
   {C_1\over\sqrt{p_1(x)}}
   \cos\left[{1\over\hbar}\int_x^{a_1}dx\,p_1(x)
   -{\pi\over4}\right]&for $x<a_1$,\cr}
\label{eq:three.five}
\end{equation}
and
\begin{equation}
   \varphi_2(x)=\cases{
   \displaystyle
   {C_2\over2\sqrt{|p_2(x)|}}
   \exp\left[-{1\over\hbar}\int_{a_2}^xdx\,|p_2(x)|\right]
   &for $x>a_2$,\cr
   \displaystyle
   {C_2\over\sqrt{p_2(x)}}
   \cos\left[{1\over\hbar}\int_x^{a_2}dx\,p_2(x)
   -{\pi\over4}\right]&for $x<a_2$,\cr}
\label{eq:three.six}
\end{equation}
where the semi-classical momenta in the adiabatic picture are defined
by
\begin{equation}
   p_{1,2}(x)\equiv\sqrt{2m[E-U_{1,2}(x)]},
\label{eq:three.seven}
\end{equation}
and $a_1$ and~$a_2$ denote the classical turning
points~(Fig.~\ref{fig2}). Within the WKB approximation, we also have
\begin{equation}
   \varphi_1'(x)\simeq\cases{
   \displaystyle
   -{C_1\over2\hbar}\sqrt{|p_1(x)|}
   \exp\left[-{1\over\hbar}\int_{a_1}^xdx\,|p_1(x)|\right]
   &for $x>a_1$,\cr
   \displaystyle
   {C_1\over\hbar}\sqrt{p_1(x)}
   \sin\left[{1\over\hbar}\int_x^{a_1}dx\,p_1(x)
   -{\pi\over4}\right]&for $x<a_1$,\cr}
\label{eq:three.eight}
\end{equation}
and a similar relation for $\varphi_2'(x)$. The normalization
of~$\varphi_1(x)$ is chosen as $C_1=2\sqrt{m}$ to make the
probability flux of the incident wave unity. On the other hand, the
final state wave function in~(\ref{eq:three.three}) has to be
normalized by the delta function with respect to the energy,
$\langle\Phi_2'|\Phi_2\rangle=\delta(E_2'-E_2)$ and this specifies
$C_2=2\sqrt{m}/\sqrt{2\pi\hbar}$.

We estimate the matrix element~(\ref{eq:three.four}) by using the
oscillating parts of the wave functions (\ref{eq:three.five})
and~(\ref{eq:three.six}). This treatment is justified if the
following conditions are satisfied:\\
(i)~$|p(0)|\rightarrow{\rm large}$ and $m\rightarrow{\rm large}$ with
$v=|p(0)|/m$ kept fixed such that non-relativistic treatment is valid
in the physically relevant region.\\
(ii)~$g\rightarrow{\rm small}$, but with
\begin{equation}
   {1\over g}\ll{1\over2m}|p(0)|^2
\label{eq:three.eleven}
\end{equation}
to ensure~(\ref{eq:two.eleven}) and the condition
\begin{equation}
   \beta\ll a,
\label{eq:three.twelve}
\end{equation}
where $a$~is an average turning point and $\beta$~is a typical
geometrical extension of $\partial_x\theta(x)$. If
(\ref{eq:three.twelve})~is satisfied, we can estimate the matrix
element by using the oscillating parts of wave functions only since
$\partial_{x}\theta(x)$ rapidly goes to zero for $|x|\gg\beta$ on the
real axis.

The integral~(\ref{eq:three.four}) is then written as
\begin{eqnarray}
   &&\langle\Phi_f|H_I'|\Phi_i\rangle
   \simeq-{i\hbar C_1C_2\over 8m}\int dx\,\partial_x\theta(x)
  \nonumber\\
   &&\times\biggl\{
   \exp\left[{i\over\hbar}\int_{a_1}^xdx\,p_1(x)
             -{i\over\hbar}\int_{a_2}^xdx\,p_2(x)\right]
     -\exp\left[-{i\over\hbar}\int_{a_1}^xdx\,p_1(x)
             +{i\over\hbar}\int_{a_2}^xdx\,p_2(x)\right]\biggr\},
\label{eq:three.nine}
\end{eqnarray}
where we have set $p_1(x)/p_2(x)=1$ in the prefactors. This is
justified within the saddle point approximation
for~$\hbar\rightarrow0$; this is also justified
if~$\hbar/|p(0)|\ll\beta$, the characteristic length scale of the
present problem, by letting~$p(0)$ large as is specified in~(i).
Therefore we need to evaluate an integral of the form
\begin{equation}
   I\equiv\int_{-\infty}^\infty
   dx\,\partial_x\theta(x)
   \exp\left[{i\over\hbar}\int_{a_1}^xdx\,p_1(x)
             -{i\over\hbar}\int_{a_2}^xdx\,p_2(x)\right].
\label{eq:three.ten}
\end{equation}

We here present an explicit evaluation of~(\ref{eq:three.ten}) for
the linear potential crossing problem, $V_1(x)=V_1'(0)x$ and
$V_2(x)=V_2'(0)x$, on the basis of local data without referring to
Stokes phenomena. For sufficiently large energy,
$E-(U_1+U_2)/2\gg(U_1-U_2)/2$, the difference of momenta can be
approximated as [see~(\ref{eq:two.nine})],
\begin{equation}
   \int_0^xdx\,[p_1(x)-p_2(x)]
   \simeq-\int_0^xdx\,{2\over v(x)g\beta}\,\sqrt{x^2+\beta^2}
\label{eq:three.thirteen}
\end{equation}
where we used
\begin{equation}
   f(x)=g{V_1'(0)-V_2'(0)\over2}x
   \equiv{x\over\beta},\quad
   v(x)\equiv{1\over m}
   \sqrt{2m\left[E-{U_1(x)+U_2(x)\over2}\right]}
\label{eq:three.fourteen}
\end{equation}
and $v(x)$~is approximated to be a constant $v=v(0)$ in the
following. We also have from~(\ref{eq:two.ten})
\begin{equation}
   \partial_x\theta(x)=-{\beta\over x^2+\beta^2}
\label{eq:three.fifteen}
\end{equation}
and thus
\begin{eqnarray}
   I&\simeq&
   -\exp\left[{i\over\hbar}\int_{a_1}^0dx\,p_1(x)
         -{i\over\hbar}\int_{a_2}^0dx\,p_2(x)\right]
   \int_{-\infty}^\infty dx\,{\beta\over x^2+\beta^2}
   \exp\left(-{2i\over\hbar vg\beta}
   \int_0^xdx\,\sqrt{x^2+\beta^2}\right)
\nonumber\\
   &=&
   -\exp\left[{i\over\hbar}\int_{a_1}^0dx\,p_1(x)
         -{i\over\hbar}\int_{a_2}^0dx\,p_2(x)\right]
   \int_{-\infty}^\infty dx\,{1\over x^2+1}
   \exp\left(-i\alpha\int_0^xdx\,\sqrt{x^2+1}\right)
\nonumber\\
   &=&
   -\exp\left[{i\over\hbar}\int_{a_1}^0dx\,p_1(x)
         -{i\over\hbar}\int_{a_2}^0dx\,p_2(x)\right]
   \int_{-\infty}^\infty dx\,\exp[-i\alpha F(x)]
\label{eq:three.sixteen}
\end{eqnarray}
where
\begin{equation}
   F(x)\equiv\int_0^xdx\,\sqrt{x^2+1}+{1\over i\alpha}\ln(x^2+1),
   \quad\alpha\equiv{2\beta\over\hbar vg}
   ={4\over\hbar vg^2[V_1'(0)-V_2'(0)]}>0.
\label{eq:three.seventeen}
\end{equation}
We evaluate the integral~(\ref{eq:three.sixteen}) by a saddle point
approximation with respect to~$\alpha$. We thus seek the saddle point
\begin{equation}
   F'(x)=\sqrt{x^2+1}+{1\over i\alpha}{2x\over x^2+1}=0,
\label{eq:three.eighteen}
\end{equation}
which is located between the real axis and the pole
positions~$x=\pm i$ of~$\partial_x\theta(\beta x)$ so that we can
smoothly deform the integration contour; these poles also coincide
with the complex potential crossing points. If one sets~$x=iy$
in~(\ref{eq:three.eighteen}) for $-1<y<1$, one has
\begin{equation}
   \sqrt{1-y^2}=-{1\over\alpha}{2y\over1-y^2}
\label{eq:three.nineteen}
\end{equation}
which has a {\it unique\/} solution
\begin{equation}
   x_s=iy_s\simeq-i+{i\over2}\left({2\over\alpha}\right)^{2/3}
\label{eq:three.twenty}
\end{equation}
for {\em large}~$\alpha$. (The complex conjugate of~$x_s$ is
located in the second Riemann sheet.)  For this value of the saddle
point
\begin{eqnarray}
   &&F(x_s)=\int_0^{x_s}dx\,\sqrt{x^2+1}
     +{1\over i\alpha}\ln\left({2\over\alpha}\right)^{2/3}
   \simeq-{\pi i\over4}+{2\over3}{i\over\alpha}
   +{1\over i\alpha}\ln\left({2\over\alpha}\right)^{2/3},
\nonumber\\
   &&F''(x_s)\simeq-3i\left({\alpha\over2}\right)^{1/3}.
\label{eq:three.twentyone}
\end{eqnarray}
We thus have a Gaussian integral which decreases in the direction
{\it parallel\/} to the real axis
\begin{eqnarray}
   I&\simeq&
   -\left({\alpha\over2}\right)^{2/3}e^{2/3}
   \exp\left[{i\over\hbar}\int_{a_1}^0dx\,p_1(x)
             -{i\over\hbar}\int_{a_2}^0dx\,p_2(x)\right]
\nonumber\\
   &&\qquad\qquad\qquad\times
   \int_{-\infty}^\infty dx\,
   \exp\left[-3\left(\alpha\over2\right)^{4/3}(x - x_s)^2\right]
   \exp\left(-{\pi\alpha\over4}\right)
\nonumber\\
   &=&
   -\sqrt{\pi\over3}e^{2/3}
   \exp\left[{i\over\hbar}\int_{a_1}^0dx\,p_1(x)
         -{i\over\hbar}\int_{a_2}^0dx\,p_2(x)\right]
   \exp\left(-{\pi\alpha\over4}\right).
\label{eq:three.twentytwo}
\end{eqnarray}
{}From~(\ref{eq:three.nine}) we obtain
\begin{eqnarray}
   \langle\Phi_f|H_I'|\Phi_i\rangle
   &\simeq&
   -\sqrt{\pi\over3}e^{2/3}\sqrt{\hbar\over2\pi}
   \sin\left\{{1\over\hbar}
   \left[\int_{a_1}^{0}dx\,p_1(x)-\int_{a_2}^{0}dx\,p_2(x)\right]
   \right\}
\nonumber\\
   &&\qquad\qquad\qquad\times
   \exp\left\{-{\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}
   \right\}.
\label{eq:three.twentythree}
\end{eqnarray}
It is interesting that the numerical value of the coefficient of the
above expression, $\sqrt{\pi}e^{2/3}/\sqrt{3}=1.99317$, is very close
to the canonical value~$2$~\cite{4}, and we replace it by~$2$ in the
following. We thus have the transition probability
from~(\ref{eq:three.three})
\begin{eqnarray}
   w(i\rightarrow f)&\simeq&
   4\sin^2\left\{{1\over\hbar}\,
   \left[\int_{a_1}^0dx\,p_1(x)-\int_{a_2}^0dx\,p_2(x)\right]\right\}
   \exp\left\{-{2\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}\right\}
\nonumber\\
    &\simeq&2\exp\left\{-{2\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}
     \right\}
\label{eq:three.twentyfour}
\end{eqnarray}
where we replaced the square of sine function by its average~$1/2$
in the final expression. We emphasize that the numerical coefficient
of~$w(i\rightarrow f)$ is fixed by perturbation theory and the local
data without referring to global Stokes phenomena; this is
satisfactory since linear potential crossing is a locally valid
idealization.

We interpret that $w(i\rightarrow f)$~in~(\ref{eq:three.twentyfour})
expresses {\it twice\/} the non-adiabatic transition probability.
Notice that our initial state wave function contains the reflection
wave as well as the incident wave. Therefore the transition
probability per {\it one\/} crossing is given by the half
of~(\ref{eq:three.twentyfour}),
\begin{equation}
   P(1\rightarrow2)\simeq
   \exp\left\{-{2\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}\right\},
\label{eq:three.twentyseven}
\end{equation}
which is the celebrated Landau-Zener formula~\cite{4,5}. Our
perturbative derivation presented here is conceptually much simpler
than the past works~\cite{1,4,5,8,12}, and it should be useful for a
pedagogical purpose also.

It is interesting to study the same problem in the diabatic picture
in~Fig.~\ref{fig1} with~$H_I=\sigma_1/g$ for large~$g$. We first note
that the initial state in the adiabatic picture asymptotically
corresponds to the eigenfunction of~$V_2(x)$ and the final state
corresponds to~$V_1(x)$, under the present setup $V_1'(0)>V_2'(0)$.
Therefore the initial and final zeroth order wave functions in the
diabatic picture are taken as
\begin{equation}
   \Psi_i(x)=\pmatrix{0\cr\psi_2(x)\cr},\quad
   \Psi_f(x)=\pmatrix{\psi_1(x)\cr0\cr}.
\label{eq:three.twentyeight}
\end{equation}
In the WKB approximation,
\begin{equation}
   \psi_1(x)=\cases{
   \displaystyle
   {C_1\over2\sqrt{|p_1(x)|}}
   \exp\left[-{1\over\hbar}\int_{a_1}^xdx\,|p_1(x)|\right]
   &for $x>a_1$,\cr
   \displaystyle
   {C_1\over\sqrt{p_1(x)}}
   \cos\left[{1\over\hbar}\int_x^{a_1}dx\,p_1(x)
   -{\pi\over4}\right]&for $x<a_1$,\cr}
\label{eq:three.twentynine}
\end{equation}
and
\begin{equation}
   \psi_2(x)=\cases{
   \displaystyle
   {C_2\over2\sqrt{|p_2(x)|}}
   \exp\left[-{1\over\hbar}\int_{a_2}^xdx\,|p_2(x)|\right]
   &for $x>a_2$,\cr
   \displaystyle
   {C_2\over\sqrt{p_2(x)}}
   \cos\left[{1\over\hbar}\int_x^{a_2}dx\,p_2(x)
   -{\pi\over4}\right]&for $x<a_2$.\cr}
\label{eq:three.thirty}
\end{equation}
In the above expressions, semi-classical momenta are defined by
\begin{equation}
      p_{1,2}(x)\equiv\sqrt{2m[E-V_{1,2}(x)]}.
\label{eq:three.thirtyone}
\end{equation}
The transition probability in the diabatic picture is then given by
\begin{equation}
   w(i\rightarrow f)
   ={2\pi\over\hbar}|\langle\Psi_f|H_I|\Psi_i\rangle|^2.
\label{eq:three.thirtytwo}
\end{equation}
The evaluation of the matrix element in~(\ref{eq:three.thirtytwo})
is the standard one described in the textbook of Landau and
Lifshitz~\cite{4}, for example. The saddle point for~$\hbar\ll1$ is
located at the origin~$x_s=0$ and we have an integral, for example,
\begin{eqnarray}
   &&\int_{-\infty}^\infty dx\,{1\over\sqrt{p_1(x)p_2(x)}}
   \exp\left[{i\over\hbar}\int_{a_1}^xdx\,p_1(x)
             -{i\over\hbar}\int_{a_2}^xdx\,p_2(x)\right]
\nonumber\\
   &&\simeq{\sqrt{2\pi\hbar}
      \over\sqrt{m[V_1'(0)-V_2'(0)]}(2mE)^{1/4}}
   \exp\left[{i\over\hbar}\int_{a_1}^0dx\,p_1(x)
             -{i\over\hbar}\int_{a_2}^0dx\,p_2(x)
             -{\pi i\over4}\right].
\label{eq:three.thirtythree}
\end{eqnarray}
Under this approximation, we have for $E>0$,
\begin{eqnarray}
   w(i\rightarrow f)
   &\simeq&
   {8\pi\over\hbar v(0)g^2[V_1'(0)-V_2'(0)]}
   \cos^2\left[{1\over\hbar}\int_0^{a_2}dx\,p_2(x)
               -{1\over\hbar}\int_0^{a_1}dx\,p_1(x)
               -{\pi\over4}\right]
\nonumber\\
   &\simeq&{4\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}.
\label{eq:three.thirtyfour}
\end{eqnarray}
[$v(0)$ is the velocity at the crossing point, $v(0)=\sqrt{2E/m}$.]
For $E<0$, one can verify that there is no saddle point and
therefore,
\begin{equation}
   w(i\rightarrow f)\simeq0.
\label{eq:three.thirtyfive}
\end{equation}
We again interpret~(\ref{eq:three.thirtyfour}) as twice the potential
crossing probability because our initial state wave function contains
the reflection wave as well as the incident wave. The transition
probability per one potential crossing is given by the half
of~(\ref{eq:three.thirtyfour}).

A simple {\it interpolating\/} formula, which
reproduces~(\ref{eq:three.twentyfour}) in the weak coupling limit and
(\ref{eq:three.thirtyfour}) in the strong coupling limit, is given by
\begin{equation}
   w(i\rightarrow f)\simeq
   2\exp\left\{-{2\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}\right\}
   \left(1-
    \exp\left\{-{2\pi\over\hbar vg^2[V_1'(0)-V_2'(0)]}\right\}
   \right)
\label{eq:three.thirtysix}
\end{equation}
This expression is also consistent with the (semi-classical)
conservation of probability~\cite{4}. A more rigorous justification
of~(\ref{eq:three.thirtysix}) is facilitated by combining the analysis
of Stokes phenomena and the conservation of probability~\cite{6}.

Motivated by duality, we re-examined the perturbative derivation of
the Landau-Zener formula, and we re-derived the
formula~(\ref{eq:three.twentyfour}) including its numerical
coefficient on the basis of perturbation theory. However, our final
formula~(\ref{eq:three.twentyfour}) in the adiabatic picture does not
contain the coupling constant as a prefactor. This is related to an
interesting topological object in the present formulation. From the
definition of~(\ref{eq:two.ten}), the ``gauge field'' satisfies the
relation
\begin{eqnarray}
   \int_{-\infty}^\infty dx\,\partial_x\theta(x)
   &=&\theta(\infty)-\theta(-\infty)
\nonumber\\
   &=&-\pi,
\label{eq:three.thirtyseven}
\end{eqnarray}
which is {\it independent\/} of the coupling constant~$g$; we assume
$f(x)\rightarrow\pm\infty$ for $x\rightarrow\pm\infty$, respectively.
Because of this kink-like topological behavior of~$\theta(x)$, the
coupling constant does not appear as a prefactor of the matrix
element in perturbation theory if the wave functions spread over the
range which well covers the geometrical size of~$\partial_x\theta(x)$.
The precise criterion of the validity of perturbation theory is thus
given by~(\ref{eq:two.eleven}): This condition is in fact satisfied if
the conditions (\ref{eq:three.eleven})--(\ref{eq:three.twelve}) are
satisfied. For small values of~$x$, the small coupling~$g$ helps to
satisfy~(\ref{eq:two.eleven}). Even for the values of~$x$ near the
average turning point~$a$, we have
\begin{equation}
  {\hbar\over2}|\partial_x\theta(a)|
   \simeq{1\over2}\left({\beta\over a}\right){\hbar\over a}\ll
   {\hbar\over a}\simeq|p(a)|,
\label{eq:three.thirtyeight}
\end{equation}
where $\beta$~stands for the typical geometrical size
of~$\partial_x\theta(x)$. The estimate in the left hand side is based
on linear potentials~(\ref{eq:three.fifteen}), but we expect that the
condition is satisfied for more general potentials as well.

To conclude this section, we clarified the basic mechanism why the
prefactor of the Landau-Zener formula~(\ref{eq:three.twentyseven})
should come out to be very close to unity in time-independent
perturbation theory.

\section{Level crossing and quantum coherence}
\label{sec:four}

The effects of dissipative interactions on macroscopic quantum
tunneling have been extensively analyzed in the path integral
formalism~\cite{13} and also in the canonical (field theoretical)
formalism~\cite{14}. It is generally accepted that the Ohmic
dissipation suppresses the macroscopic quantum coherence; in fact,
an attractive idea of a dissipative phase transition has been
suggested~\cite{13}.

It is plausible that the effects of potential curve crossing with
nearby potentials influence the quantum coherence of the two
degenerate ground states. We here analyze the general features of the
effects of potential crossing on quantum coherence on the basis of
time-independent perturbation theory, which was confirmed in the
preceding section to be reliable in the both limits of weak and strong
potential curve crossing interaction. We assume
$V_2(x)=V_1(-x)$ and $V_2'(0)<0$.

\noindent
We thus analyze this problem from two different view points.

\subsection{Strong potential curve crossing interaction $g\gg1$
(diabatic picture)}

We start with the diabatic picture in~Fig.~\ref{fig4} and incorporate
the effects of the potential crossing interaction~$\sigma_{1}/g$.
Namely, we (approximately) diagonalize the total Hamiltonian in the
diabatic picture. By treating the last term of~(\ref{eq:two.one}) as
a perturbation for~$g\gg1$, we obtain the energy eigenvalues of the
two lowest lying states as (with~$E_0$ the zeroth order degenerate
energy eigenvalue)
\begin{equation}
   E_{\pm}^{(1)}=E_0\mp{1\over g}\int_{-\infty}^\infty dx\,
   \psi_L(x)\psi_R(x),
\label{eq:five.one}
\end{equation}
with the corresponding eigenfunctions
\begin{eqnarray}
   &&\Psi_+(x)
   \simeq{1\over\sqrt{2}}\pmatrix{\psi_L(x)\cr-\psi_R(x)\cr}
   \equiv{1\over\sqrt{2}}[e_+\psi_L(x)-e_-\psi_R(x)],
\nonumber\\
   &&\Psi_-(x)
   \simeq{1\over\sqrt{2}}\pmatrix{\psi_L(x)\cr\psi_R(x)\cr}
   \equiv{1\over\sqrt{2}}\bigl[e_+\psi_L(x)+e_-\psi_R(x)\bigr].
\label{eq:five.two}
\end{eqnarray}
Namely, both of these two states~$\Psi_\pm(x)$ choose
\begin{eqnarray}
   &&\hbox{$e_+\psi_L(x)$ in the region of left valley},
\nonumber\\
   &&\hbox{$e_-\psi_R(x)$ in the region of right valley}.
\label{eq:five.three}
\end{eqnarray}
The ``spin'' eigenstates~$e_\pm$ and the ``space'' eigenstates
$\psi_L(x)$ or~$\psi_R(x)$ are strongly correlated. Note that one can
conveniently think of the two potentials as spin-up and spin-down
states. Originally, before we incorporate the
perturbation~$\sigma_1/g$ in~(\ref{eq:five.one}), we have
energetically degenerate two states with energy~$E_0$ defined by
\begin{equation}
   \Psi_L(x)=\pmatrix{\psi_L(x)\cr0\cr}\equiv e_+\psi_L(x),
\label{eq:five.four}
\end{equation}
which is always a spin-up state, and
\begin{equation}
   \Psi_R(x)=\pmatrix{0\cr\psi_R(x)\cr}\equiv e_-\psi_R(x),
\label{eq:five.five}
\end{equation}
which is always a spin-down state.

In the strong potential crossing limit, $g\rightarrow\infty$, we have
{\it no effect\/} of the conventional quantum tunneling in addition
to the mixing in~(\ref{eq:five.two}), since the conventional
tunneling goes through the interaction~$\sigma_1/g$
in~(\ref{eq:two.one}), and thus higher order effects in~$1/g$.

We can find the $O(1/g)$~energy splitting in the WKB approximation.
The left wave function~$\psi_L(x)$ is given
by~(\ref{eq:three.twentynine}) with~$C_1=\sqrt{2m\omega/\pi}$
(For a sufficiently low energy state such as the ground state,
$\omega$~can be regarded as the curvature of the potential energy
at the minimum.) The right wave function~$\psi_R(x)$ is given
by
\begin{equation}
   \psi_R(x)=\cases{
   \displaystyle
   {C_2\over2\sqrt{|p_2(x)|}}
   \exp\left[-{1\over\hbar}\int_x^{a_2}dx\,|p_2(x)|\right]
   &for $x<a_2$,\cr
   \displaystyle
   {C_2\over\sqrt{p_2(x)}}
   \cos\left[{1\over\hbar}\int_{a_2}^xdx\,p_2(x)
   -{\pi\over4}\right]&for $x>a_2$.\cr}\nonumber
\end{equation}
 with~$C_2=\sqrt{2m\omega/\pi}$. In the saddle
point approximation, we have the overlap integral
\begin{eqnarray}
   &&\int dx\,{1\over\sqrt{|p_1(x)||p_2(x)|}}
   \exp\left[-{1\over\hbar}\int_{a_1}^xdx\,|p_1(x)|
             +{1\over\hbar}\int_{a_2}^xdx\,|p_2(x)|\right]
\nonumber\\
   &&\simeq{\sqrt{2\pi\hbar}
      \over\sqrt{m[V_1'(0)-V_2'(0)]}(-2mE)^{1/4}}
   \exp\left[-{1\over\hbar}\int_{a_1}^0dx\,|p_1(x)|
             +{1\over\hbar}\int_{a_2}^0dx\,|p_2(x)|\right],
\label{eq:five.six}
\end{eqnarray}
which yields the energy splitting,
\begin{eqnarray}
   &&E_-^{(1)}-E_+^{(1)}
\nonumber\\
   &&\simeq
   {\sqrt{2\hbar}\over g\sqrt{\pi[V_1'(0)-V_2'(0)]}}
   \left({m\over-2E_0}\right)^{1/4}
   \exp\left\{-{1\over\hbar}
   \int_{a_1}^{a_2}dx\,\sqrt{2m[\overline V(x)-E_0]}\right\}.
\label{eq:five.seven}
\end{eqnarray}
In the above expression, we have defined~$\overline V(x)$ as the
following ``$\Lambda$-shape'' potential:
\begin{equation}
   \overline V(x)=\cases{V_1(x)&for $x<0$\cr
               V_2(x)&for $x>0$.\cr}
\label{eq:five.eight}
\end{equation}
We recall that, when the upper adiabatic potential~$U_1(x)$ is absent,
the standard WKB formula gives the energy splitting of lowest
levels~\cite{4},
\begin{equation}
   E_--E_+\simeq
   {\hbar\omega\over\pi}
   \exp\left\{-{1\over\hbar}
   \int_{-a}^adx\,\sqrt{2m[U_2(x)-E_0]}\right\}.
\label{eq:five.nine}
\end{equation}
Comparing this with~(\ref{eq:five.seven}), we find that the quantum
coherence is actually suppressed by two elements; the overall
small coefficient~$1/g\ll1$ and the exponential suppression factor;
$\overline V(x)$~is always larger than the lower potential,
$\overline V(x)>U_2(x)$.

\subsection{Weak potential curve crossing interaction $g\ll1$
(adiabatic picture)}

In this case, we can use the gauge transformed adiabatic picture
defined by~(\ref{eq:two.six}). In this scheme, the low lying
eigenstates for~$H_0'$ are described by the nearly degenerate two
states in the lower potential curve~$U_2(x)$. See~Fig.~\ref{fig5}.
For a small~$g$, the two potential curves $U_1(x)$ and~$U_2(x)$ are
widely separated. We thus take the ground states of the spin-down
sector (i.e., the nearly degenerate two ground states of the lower
potential curve),
\begin{equation}
   \Phi_+(x)=\pmatrix{0\cr\varphi_{2+}(x)\cr},
   \quad
   \Phi_-(x)=\pmatrix{0\cr\varphi_{2-}(x)\cr}
\label{eq:five.ten}
\end{equation}
as the zeroth order approximation of the lowest lying states. These
two states correspond to the conventional symmetric and anti-symmetric
tunneling eigenstates of the double well potential~$U_2(x)$, whose
energy splitting gives the {\it order parameter\/} of the quantum
coherence~\cite{13}. To the second order of the gauge
field~$\partial_x\theta(x)$, the energy eigenvalue is perturbed to
\begin{eqnarray}
   E_\pm^{(2)}&=&
   E_\pm+\langle\Phi_\pm|H_I'|\Phi_\pm\rangle
   -\sum_n{|\langle\Phi_{1,n}|H_I'|\Phi_\pm\rangle|^2
           \over E_{1,n}-E_\pm}
\nonumber\\
   &=&E_\pm+{\hbar^2\over8m}\int dx\,
      [\partial_x\theta(x)]^2\varphi_{2\pm}(x)^2
\nonumber\\
   &&-{\hbar^2\over16m^2}\sum_n{1\over E_{1,n}-E_\pm}
   \left|\int dx\,\varphi_{1,n}(x)
   \left[\hat p\partial_x\theta(x)
         +\partial_x\theta(x)\hat p\right]\varphi_{2\pm}(x)\right|^2,
\label{eq:five.eleven}
\end{eqnarray}
where $\Phi_{1,n}(x)$ [and $\varphi_{1,n}(x)$] is the $n$th energy
eigenstate of the upper potential~$U_1(x)$.

It is generally difficult to conclude the suppression or enhancement
of the quantum coherence solely from the perturbation
formula~(\ref{eq:five.eleven}). The reason is that the effect of
intermediate state sum can depend on the details of the upper
potential curve. Nevertheless, when the well of the upper potential is
narrow enough, we can show that the quantum coherence is always
suppressed.

We first assume that the lowest lying parity even and parity odd
states are given respectively by a linear combination of the ground
states in left and right wells:
\begin{equation}
   \varphi_{2\pm}(x)={1\over\sqrt{2}}
   [\varphi_{2L}(x)\pm\varphi_{2R}(x)],
\label{eq:five.twelve}
\end{equation}
where in the WKB approximation in the classically forbidden region,
\begin{equation}
   \varphi_{2L}(x)=\varphi_{2R}(-x)=
   {C_2\over2\sqrt{|p_2(x)|}}
   \exp\left[-{1\over\hbar}\int^xdx\,|p_2(x)|\right].
\label{eq:five.thirteen}
\end{equation}
The normalization constant is given by~$C_2=\sqrt{2m\omega/\pi}$.

We next assume that the upper potential~$U_1(x)$ is narrow enough
and can be well approximated by a square well potential with the
width~$a$. The eigenfunctions in the upper potential are therefore
given by
\begin{equation}
   \varphi_{1,n}(x)=\sqrt{2\over a}
   \sin\left[{n\pi\over a}(x+{a\over2})\right],\quad
   n=1,2,\cdots.
\label{eq:five.fourteen}
\end{equation}
Moreover, since the gauge field~$\partial_x\theta(x)$ defined
in~(\ref{eq:two.ten}) is non-zero only within this narrow region,
we may make the following replacements in the
integral~(\ref{eq:five.eleven}):
\begin{eqnarray}
   &&\varphi_{2+}(x)\rightarrow\varphi_{2+}(0),\quad
   \varphi_{2-}(x)\rightarrow0,
\nonumber\\
   &&\hat p\,\varphi_{2+}(x)\rightarrow0,\quad
   \hat p\,\varphi_{2-}(x)\rightarrow i|p_2(0)|\varphi_{2+}(0),
\label{eq:five.fifteen}
\end{eqnarray}
and
\begin{equation}
   \hat p\,\varphi_{1,n}(x)\rightarrow
   -i|p_{1,n}|\sqrt{2\over a}
   \cos\left[{n\pi\over a}\left(x+{a\over2}\right)\right],
   \quad |p_{1,n}|\equiv\hbar{n\pi\over a}.
\label{eq:five.sixteen}
\end{equation}

Under these assumptions, the energy shift~(\ref{eq:five.eleven}) is
estimated for the parity even state,
\begin{eqnarray}
   E_+^{(2)}&=&
   E_++{\hbar^2\over8m}\int dx\,
   [\partial_x\theta(x)]^2\varphi_{2+}(0)^2
\nonumber\\
   &&-{\hbar^2\over16m^2}\sum_{n=1}^\infty
   {|p_{1,n}|^2\over E_{1,n}-E_+}
   \left|\int dx\,\sqrt{2\over a}
   \cos\left[{n\pi\over a}\left(x+{a\over2}\right)\right]
   \partial_x\theta(x)\right|^2\varphi_{2+}(0)^2.
\label{eq:five.seventeen}
\end{eqnarray}
By noting $|p_{1,n}|^2=2m[E_{1,n}-U_1(0)]$ and $U_1(0)>E_+$,
we see that
\begin{equation}
   {\hbar^2\over16m^2}{|p_{1,n}|^2\over E_{1,n}-E_+}=
   {\hbar^2\over8m}{E_{1,n}-U_1(0)\over E_{1,n}-E_+}<
   {\hbar^2\over8m},
\label{eq:five.twenty}
\end{equation}
and thus
\begin{eqnarray}
   E_+^{(2)}&>&
   E_++{\hbar^2\over8m}\int dx\,
   [\partial_x\theta(x)]^2\varphi_{2+}(0)^2
\nonumber\\
   &&-{\hbar^2\over8m}\sum_{n=0}^\infty
   \left|\int dx\,\sqrt{2\over a}
   \cos\left[{n\pi\over a}\left(x+{a\over2}\right)\right]
   \partial_x\theta(x)\right|^2\varphi_{2+}(0)^2
\nonumber\\
   &=&E_+,
\label{eq:five.twentyone}
\end{eqnarray}
where we have added $n=0$~mode to make the cosine functions a complete
set. Therefore the perturbation always increases the ground state
energy.

On the other hand, eq.~(\ref{eq:five.eleven}) gives for the parity
odd state,
\begin{equation}
   E_-^{(2)}=E_-
   -{\hbar^2\over16m^2}\sum_{n=1}^\infty
   {|p_2(0)|^2\over E_{1,n}-E_-}
   \left|\int dx\,
   \varphi_{1,n}(x)\partial_x\theta(x)\right|^2\varphi_{2+}(0)^2.
\label{eq:five.eighteen}
\end{equation}
Since the second term of~(\ref{eq:five.eighteen}) is negative
definite, we see that the perturbation always lowers the odd state
energy,
\begin{equation}
   E_-^{(2)}<E_-.
\label{eq:five.nineteen}
\end{equation}

The perturbative corrections in (\ref{eq:five.seventeen})
and~(\ref{eq:five.eighteen}) are proportional to the wave
function at the origin, which satisfies
$\varphi_{2+}(0)^2\simeq m(E_--E_+)/[\hbar|p_2(0)|]$~\cite{4}, and
therefore the correction to the energy splitting itself is
proportional to the zeroth order energy splitting, $E_--E_+$. Since
the correction cannot excess the zeroth order value in a reliable
region of perturbation theory, we should have $E_-^{(2)}-E_+^{(2)}>0$.
By combining (\ref{eq:five.twentyone}) and~(\ref{eq:five.nineteen}),
therefore we find
\begin{equation}
   0<E_-^{(2)}-E_+^{(2)}<E_--E_+,
\label{eq:five.twentytwo}
\end{equation}
which shows that the quantum coherence is suppressed.

Although we derived the suppression of quantum coherence for the very
special configuration in the weak coupling adiabatic picture, we
expect that this suppression of quantum coherence is more general
at least for small~$g$. This is based on the following physical
picture: When a particle tunnels the barrier in the lower potential
curve, it has a small probability to cross to the upper potential
curve. This potential curve crossing means that the particle enters
deep inside the tunneling region of the upper potential curve and
repelled back by the upper potential (as is expected in the diabatic
picture), which in turn leads to the suppression of quantum tunneling
of the particle. This argument leads to the general suppression of
quantum coherence by potential crossing. This is also consistent with
the suppression of barrier transmission in the scattering process by
the non-adiabatic potential crossing effect~\cite{8}.

Our explicit analyses both in the weak and strong potential crossing
interactions suggest the general suppression of quantum coherence by
potential crossing, which is analogous to the effect of Ohmic
dissipation on quantum coherence~\cite{13,14}. In this connection, we
may note that the formula~(\ref{eq:five.eleven}) and the Ohmic
dissipation in the Caldeira-Legget model~\cite{13} both correspond to
the dipole approximation. However, an analysis of the basically
non-perturbative tunneling effect in the second order perturbation
theory needs a great care; for this reason, we were able to explicitly
analyze the very specific case in
(\ref{eq:five.fourteen})--(\ref{eq:five.sixteen}). This suppression
phenomenon of quantum coherence may become important in the future
when one takes the effects of the environment into account in the
analysis of potential curve crossing in physical and chemical
processes.

\section{Discussion and Conclusion}

Motivated by the presence of interesting weak and strong duality in
the model Hamiltonian~(\ref{eq:two.one}) of potential curve crossing,
we analyzed a perturbative approach to potential crossing phenomena.
We have shown that straightforward perturbation theory combined with
the zeroth order WKB wave functions provides a reliable description
of general potential crossing phenomena. Our analysis is based on the
local data as much as possible without referring to global Stokes
phenomena~\cite{12}. Formulated in this manner, perturbation theory
becomes more flexible to cover a wide range of problems. From a
perturbative view point, the treatment of the Landau-Zener formula
in the adiabatic picture is most complicated since it does not contain
the coupling constant in the prefactor. We pointed out that this
absence of the coupling constant in the prefactor is related to the
presence of an interesting kink-like topological object in the present
formulation of adiabatic picture. The absence of the coupling constant
in the prefactor is thus perfectly consistent with perturbation
theory, provided that a more precise criterion of perturbation
theory~(\ref{eq:two.eleven}) is satisfied. In effect, we explained
why the prefactor of the Landau-Zener formula should come out to be
very close to unity in perturbation theory.

The suppression of quantum coherence by potential curve crossing,
which to our knowledge has not been discussed before in this context,
has also been neatly formulated in our treatment, in the both limits
of very strong and very weak potential crossing interactions.

{}From a view point of general gauge theory, it is not unlikely that
the electric-magnetic duality in conventional gauge theory is also
related to some generalized form of potential crossing in the
so-called moduli space~\cite{11}. We hope that our work may turn out
to be relevant from this view point also.

Finally, we gratefully acknowledge H. Nakamura for critical comments
which greatly helped improve the present work.

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Sarah Millican is back with a bobby dazzler of a comedy show touring to Derby and Sheffield
TV comedian Sarah Millican will tour her new show Bobby Dazzler to Derby and Sheffield, with tickets going on sale this week.
By Gay Bolton
Thursday, 26th November 2020, 5:30 am
Sarah Millican will tour to Sheffield and Derby in 2022.
Tickets go on general sale at 10am tomorrow (Friday, November 27) for shows at Derby Arena on Friday, October 29, 2021 and Sheffield City Hall on Wednesday, October 5 and Thursday, October 6, 2022,
In this, her sixth international tour, you'll learn about what happens when your mouth seals shut, trying to lose weight but only losing the tip of your finger and how truly awful a floatation tank can actually be.
Sarah established herself as one of the leading talents of the British comedy scene by winning the best newcomer award at the 2008 Edinburgh Fringe. In subsequent years, she has gone on to host three series of her critically acclaimed BBC2 series The Sarah Millican Television Programme, and has become a familiar face on primetime shows for the BBC such as QI, Live at the Apollo and The Royal Variety Performance. Her last tour, Control Enthusiast, was seen by more than 245,000 people in the UK and Ireland.
Tickets for Derby cost £29.50; pre-sale tickets for existing Derby LIVE customers will be released today (Thursday) at 10am; go to www.derbylive.co.uk
Tickets for her Sheffield shows cost £31.95, go to www.sheffieldcityhall.co.uk.
READ THIS: Ross Noble tours Humournoid show to Buxton.
Chesterfield now and then photos show changing face of Markham Road over the years
Take a look at these memorable photos of Derbyshire pitmen and mining communities of times past
Can you spot yourself in our 90s Chesterfield clubbing photo gallery
Dancers turn back time in 10 memorable photos from Chesterfield and beyond
10 memorable photos to take you back to Chesterfield in 2007
Spot anyone you know among these teenagers at Chesterfield's Saltergate Youth Club in 1948?
Derbyshire livestock farmer to star in new series of Quest reality show Born Mucky
Looking back at Chesterfield's Scarsdale Hospital down the years
£1.9million Peak District dairy farm put up for sale for first time in 80 years
Archive photos show life in Chesterfield in the 70s and 80s


This entry was posted in Race Previews and tagged Drumstick Dash, Milwaukee Races, Race Previews, Running in MKE, Upcoming Events. Bookmark the permalink.
Wouldnt it be great if race promoters who use "great causes" to promote their races would actually donate funds to "their" causes? personal opinion.


The site of Kagran is unique in that it is characterized by complete infrastructural separation, forming an island of building types that operate at a scale closer to urbanism than of architecture.
Simultaneously, however, the site is highly connected to regional infrastructures, allowing it to attract both a local and regional public. Our proposal begins by adding a civic architectural type —the arcade— to reconcile the two scales of inhabitation — architectural and urban — through a strategy of consolidating domestic programs into infrastructure that utilize the arcades below to produce a local rhythm and organization. Seven bars run through the site to both operate at the scale of the surrounding infrastructures as well as organize the local scale of the neighborhoods. These bars contain nine housing types to cater to differing demographics and touch down on the site lightly to activate the arcaded public realm below in a precise manner.
Ten different scales of arches are employed within the bars to mediate between the scales of public and private. These range from four to thirty meters, providing for intimate as well as monumental civic spaces. The arches touch down lightly on the site to provide access to the housing and roof terraces above, contain 'activator' programs related to the surface below, and offer areas to store micro-infrastructures for the multi-programmed surface. By touching minimally on the surface below, a highly level of flexibility is achieved through programming. What emerges is a field condition that is unified yet provides a diverse range of scales and publics that can form naturally.
The question of adaptability in the site is addressed through the notion of time and the spatial type of the surface. A large surface operates as a multi-programmed public realm that is timeshared through a schedule - to allow a more diverse and larger set of public programs. The surface is coded through differing materials and paint to provide flexible, soft organizational strategies that are activated by the bars above. For instance, the same space can be used for greenhouses, parking, a market, and basketball courts at different times of the day, week, and year. The schedule is malleable to the needs of current and future residents, adapting for seasonal festivals, cultural events, and needs that cannot be anticipated. The surface is broadly organized into programs that share the similar surface characteristics — recreational, commercial, and community. Regions of overlap between these sectors allow for hybrid uses. For instance, a school's playground can be used in a broader recreational sense when the school is closed, or market areas can be converted to informal night theaters. Five subtle surface variations provide diversity while still allowing for flexible programming. Pools of water and landscape enable sustainable water collection and promote microclimates to alleviate the large paved surfaces in the broader strategic site. The malleable surface and schedule is structures through the arches above, forming a symbiotic arrangement as well a unique architectural scenario wherein form runs east-west through the site to connect across infrastructure while space runs north-south to connect with the larger strategic site. This weave between form and space is structured through the public realm and surface below.
A singular road loop enters the site from the North, and provides access and service to the site without ordering the entire site as most examples of contemporary urbanism. A running track sits above the bars to allow connection between the arcades above grade. Void spaces between the bars and outside of the running track are densely planted with coniferous and deciduous trees to act as air and acoustic filters. The rooftops of the bars in these zones are dedicated to private uses — terraces, gardens, and courtyards. The roof tops within the region defined by the running track are zoned with public programs — restaurants, bars, community gardens, etc. Thus, the bars reconcile the scale of the public and private in plan and section. The strategic site is addressed with a similar methodology as the site, but is structured by space running east-west and form running north-south. This inverted use of space/form allows for an ease of phasing and implementation with regards to the existing buildings. The strategic site is phased to consolidated parking and return the vast surface to public uses. The north edge of the site phased for a natural remediation techniques — aeration, phyto-remediation and steam remediation. In time, this land is zoned for a denser development of housing.
The arcaded public realm works in conjunction with the surface that adheres to the monumentality of the infrastructure and surrounding architecture while breaking down into local supports to promote soft neighborhood units. By connecting this island to the surrounding developments and infrastructure, a multivalent public realm is achieved in a dynamic field condition.
Contributors: Carly Dean, Alicia Hergenroeder, De Yi, Jonathan Negron, Wei Zhao.


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Olorunrinu tasks Asiwaju over mandate restoration in Amuwo Odofin LGA
2023: Why I Will Win Presidential Election — Bola Tinubu
BREAKING: Tinubu Visits Masari In Katsina
22-Year-Old Lady Asked To Choose Between Her Boyfriend And Scholarship Abroad
Over 72 Hours After Lifting Twitter Ban, No Tweets From Buhari, Osinbajo Yet
By Gabriel Agbeja
The Nigeria Civil Aviation Authority (NCAA) has shutdown main switch centre of Globacom Limited at Wuse 2, Abuja over non-payment of outstanding debt of N4.7 billion.
The NCAA Director–General, Capt. Musa Nuhu, carried out the exercise on Wednesday, under the supervision of the Minister of Aviation, Sen. Hadi Sirika.
Nuhu told the newsmen after locking up the tower that the facility would be switched off until outstanding debt was paid.
He said the company had paid only N500 million out of the N5.2 billion it was owing, pointing out that the outstanding debt was N4.7 billion.
According to him, all the other telecommunications service providers are paying except the Globacom, which has failed to meet up since 2007.
"My Agency is under tremendous pressure by the Federal Government of Nigeria and we will do our best within the power vested on us to make sure the debt is settled.
"The action we took is for the safety of aviation in Nigeria. As a matter of fact, any masts after a certain of height, we are supposed to regulate it to ensure that it is properly covered.
"We do fly aircraft, we do flight helicopter, and it could be drone among others things we fly. Not necessary regular passenger flight. Police, PHCN and all those people; they do patrol all over the country.
"I am sure, you have seen their helicopters, that is why it is important for us to ensure we have all these in road map and put them in action," he said.
Nuhu said it was the regulation of NCAA that whoever erected the masts would pay for the process that would carried out by NCAA.
According to the director-general, 15 letters have been sent to glo in the past without any tangible reply since his assumed office.
He said that generally in the past, they only paid some amount and walked away.
"Of recent, when I came, then we sat down we have been speaking silently.
"They have paid some money but they still have almost N4.7 billion debt remaining. None of the communication services providers has that amount of a due for payment.
"That started in 2007. We don't like shutting down things but we have to take this drastic action because we are having financial issues and we pressures from different sectors of government, " he said.
Nuhu listed sectors of government pressuring NCAA to include; Committees from the National Assembly, Federal Ministry of Aviation as the supervising ministry, Agencies such as Fiscal Revenue Commission, and Auditor General Office of the Federation and Accountant General Office of the Federation.
I'm Now Ready To Reconcile With Ganduje – Kwankwaso
Why Buhari deserves rousing welcome to Borno, by Zulum
Piqued by the various frantic efforts to champion All Progressives Congress (APC) course in Amuwo-Odofin Local Government Area of Lagos…
Bola Tinubu, a presidential candidate, has stated that he believes he would win the 2023 election. Tinubu predicted that he…
Tinubu during the visit to Governor Masari in Katsina (Photo: Tinubu support group) Asiwaju Bola Tinubu, the national leader of…
Piqued by the various frantic efforts to champion All Progressives Congress (APC) course in Amuwo-Odofin Local Government Area of…
Bola Tinubu, a presidential candidate, has stated that he believes he would win the 2023 election. Tinubu predicted that…
Tinubu during the visit to Governor Masari in Katsina (Photo: Tinubu support group) Asiwaju Bola Tinubu, the national leader…
Nigerians have taken to social media to react to the story of a 22-year-old lady who was asked to…
Over 72 hours after the Federal Government announced the lifting of the ban on Twitter, the President, Muhammadu Buhari,…
Small Boys Killing Girls Just To Drive Benz – Actor, Okon Lagos Laments As He Calls For Urgent Fixing Of The Boy-Child
Imeh Okon, the comic actor, who is also known as Okon Lagos, has called on Nigerians to pay attention…
Wow! 51-Year-Old Nigerian Woman Gives Birth To Twins After Over 20 Years Of Waiting
The happy woman's colleague, Felicia Simon Odey, shared the good news on Saturday, January 15. Mrs Justina Bassey,…
BREAKING: Ganduje Visits Kano APC Chairman Over Brother's Death
This was disclosed by Ganduje's aide on New Media, Abubakar Ibrahim, who revealed that the Governor was accompanied on…
Serious Panic As Residents Of Kaduna Community Flee Their Homes After Terrorists' Invasion
File photo According to a report by SaharaReporters, scores of residents of Damari community in Birnin Gwari Local Government…
2face Idibia Shares Heartwarming Video Of Himself And His Son, Nino, As He Turns 16
One of Nigeria's most successful singers ever, 2face Idibia is celebrating his son, Nino, who turned 16 years old.…
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50 Homosexuals Arrested During Orgy In Kano
Malami Writes Heads Of Courts Amid COVID-19…This Is What He Asked Them To About Time-Bound Cases


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At the region's newest public garden, you won't see ruler-straight rows of color-coordinated petunias, or trees pruned into perfect proportions, or hedges of boxwood trimmed high and tight.
At Stoneleigh, native plants get preference, and trees have spent the past century growing wild, unshaped by orchard saws and pruning shears. That's just what the former owners, the wealthy Haas family, wanted—and Natural Lands Trust, the property's current steward, will keep it that way.
This laissez-faire approach to arboriculture means towering, uniquely gnarled specimens, many more than 100 years old.
An outsized, asymmetrical sycamore welcomes visitors as they approach the property's main house. The arbor vitae trees that ring the massive, open Circle Garden aren't the tightly clipped, Christmas-tree-shaped ones you've seen edging a suburban lawn—they're sprawling, multi-trunked specimens, with huge evergreen branches extending along the ground and swooping up dramatically, giving this outdoor space an insular, enclosed feel. Stoneleigh's massive ironwood, with a damaged trunk that gives it the look of one of the ancient heart trees from "Game of Thrones," is the largest of its kind in Pennsylvania.
At 42 acres, the Main Line estate-turned-public-garden, which opens to visitors on Mother's Day weekend, may seem petite compared to the sprawling grounds of Longwood. Its open spaces and knotted trunks may look rather minimalist next to a manicured, perpetually blooming garden such as Chanticleer. But that's all the better to show off the space's striking, unique beauty.
Stoneleigh's former owners, John and Chara Haas, lived in the main house, raised a family and took care of the property starting in 1964. John's father, Otto Haas—one of the founders of chemical company Rohm and Haas—originally purchased it in 1932. While the property was the estate of one of the Main Line's wealthiest families, John and especially Chara wanted the grounds to reflect the natural world as much as possible, using only native plants and letting long-established trees grow freely and wild.
The site also features examples of historically significant landscape-architecture practices. When United Gas Improvement Co. head Samuel Bodine bought Stoneleigh around the turn of the 20th century, he brought in prestigious Olmstead Brothers firm, owned by the sons of celebrated landscape architect Frederick Law Olmstead—they'd bring in plantings, shape pathways and add decorative structures such as lychgates and pergolas around the property for the next 50 years.
Like many other titans of industry in the region, the Haases valued green, natural spaces; John and Chara chose to establish their family home—already something of a nature preserve—as a place where anyone could enjoy the natural world. In 1996, they placed the property under a conservation easement to preserve it in perpetuity; in 2016, their children officially turned the property over to Natural Lands.
"The story of Stoneleigh will be the story of what happens when a land conservancy takes over a garden," said Axelrod. The organization holds easements on more than 23,000 acres of preserved land in Pennsylvania and New Jersey, from woods to meadow to pastureland. But Stoneleigh is its first public garden.
Natural Lands has spent the past two years readying the property for the public—Kauffman estimates that 70 contractors a day worked on the property during the past 12 months, upgrading facilities and infrastructure—but much of the landscape remains untouched.
Stoneleigh also provides a well-preserved example of early 20th century Main Line architecture; at the time, the area was a magnet for magnates, attracting industry tycoons to build sprawling estates outside of the city. Most have been sold off or transformed, but the Stoneleigh remains.
Months of renovations went into restoring the main house's dark wood interior; the inside of the building is closed to the public apart from special tours, but it's rentable as an event-and-meeting space. The Richmond, Va.-based Organ Historical Society—another beneficiary of the Haas family, as son Fred is a passionate player—has transported its archives to the second floor of the house.
In addition to its manageable size—it's easy for a family to roam the entire property over just a few hours—Stoneleigh is meant to be accessible in more ways than one. Admission is free, and the property is only about a five minutes' walk from the Villanova regional rail stop. Ramps have been built and gravel pathways paved so that those with wheelchairs or walkers can visit all parts of the garden. This, Natural Lands Trust hopes, will attract garden-goers from all over the region, not just the Main Line.
While natural beauty takes center stage, Stoneleigh isn't just about aesthetics. A big part of the garden's mission is to promote reverence for, not just access to, the natural world.
With workshops, tours and the property itself, part of Stoneleigh's programs will teach visitors about sustainable landscape practices such as stormwater mitigation, soil erosion, planting for biodiversity and using native plants, as well as raising awareness about the work of Natural Lands Trust.
For example, there are 14 acres of turf on the property, but Kauffman has plans to reduce that number. A portion is designated to become a meadow, designed to increase habitat for insects, migrating birds and small mammals. The garden is already a vibrant habitat for wildlife: Kauffman has spotted five different species of snake in addition to red foxes, coyotes, raccoons, chipmunks, squirrels, groundhogs, salamanders, toads, rare species of birds, even a bald eagle—and deer, of course.
But they'll also, er, cut down on how often they mow portions of the lawn.
"We'll stylize it, but we want to let it grow long—you don't have to use machines to cut your grass so often," Kauffman explained. And when workers do tighten up the grass, they'll use greener, battery-powered mowers and shears rather than heavy, gas-powered machinery.
Stoneleigh uses other sustainable landscaping practices, too. Leaving plants standing in the winter rather than cutting them down, for example, provides places for bees and nesting ground birds to overwinter. The staff plants native species in the landscape, sourced from local and regional nurseries when possible, instead of commonly used non-natives—American euonymus instead of a privet, for example, or pinkberry instead of boxwood. They'll source leaf mulch from local contractors and manage compost on site, with a goal of never having to take waste off of the property.
The Stoneleigh staff will keep programming light for their first season, but there are already ways to get involved; monthly volunteer days will give folks the chance to help out in Stoneleigh's gardens. They'll hold classes for adults around sustainability in the garden, bird walks and big tree walks, and collaborations with the Organ Historical Society, which is installing an instrument in the house's basement. For garden members, they'll offer evening events for picnicking in the summer and a special silent film screening featuring the organ's music in the fall.
When Stoneleigh opens its doors to the public for the first time on May 12, this space, once beloved by a single family, will enter a new chapter as a place where thousands can benefit from its vibrant life and natural beauty. Natural Lands Trust will enter a new phase of essential conservation work along with it.
The organization has had experience managing garden spaces on preserved lands, Axelrod notes, but Stoneleigh is its first public garden.


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Fire Risk Assessments are required in order to ensure compliance to the Regulatory Reform (Fire Safety) Order 2005. Our consultants cover the UK and across all sectors.
Legionella Risk Assessments are required under C.O.S.H.H regulations and our experienced and qualified consultants can perform assessments to the approved code of practice (L8) standards including provision of marked schematics and written schemes.
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On March 26, 2019, all charges against Jussie Smollett were dropped even though it was clear that he staged a hate crime. In the hate crime he fabricated, he claimed that two men wearing MAGA hats yelled racist and homophobic slurs, put a noose around his neck, and poured what appeared to be bleach on him, among other things.
This story aligns well with the general claim of the left that Trump and his supporters are racist, hence why it included two men wearing MAGA hats. But the claim that America is racist goes back even before Trump won the presidency. Recall that the Black Lives Matter movement bloomed after a series of incidents involving black men being beaten and sometimes murdered as a result of police brutality. It was then widely believed that white policemen in America are racist and are disproportionately targeting black citizens. This belief was coupled with the belief that America was systemically racist. A popular perception on the political left is that this racism was empowered and amplified after Trump was elected.
Let's start off with the basics that any sane person can agree to.
There are racist people in the world, including America.
There are racist police who have abused their power.
There are racist Trump supporters.
There are non-racist people who voted for Donald Trump for reasons that they believe to be significant enough to overlook his obnoxious character.
Now that we've hopefully established that not all Trump supporters are racist or condone racism, let's assess the claim that America is a systemically racist country.
Ever since the uproar from Black Lives Matter, I haven't seen police brutality against black people dominate the news. That, to me, is a hint that the police force as a whole is not racist. If it was a systemically racist arm of the government, the brutality would've gone on like in the days of Martin Luther King Jr.
Allow me to refer to an interview hosted by Dave Rubin of The Rubin Report. Dave Rubin is gay and is liberal, and the guest is a black man by the name of Larry Elder. This background should hopefully dispel any suspicion that this is a biased interview. In the clip, Dave argues that police are more likely to shoot a black man than a white man. What follows is a dialogue about the extent to which that is true.
As for me, I observe from what I see in my own experiences in the city I live in, and I hear news from mainstream media and social media, and I just don't see police brutality against black people as an epidemic. Here I take the police force out of the picture of systemic racism.
Judging by the numerous positions in high levels of government I've seen over the years, I believe that black citizens have just as open a path as citizens of other ethnicities.
The most striking example is Barack Obama. What kind of systemically racist country allows a black man to be elected as its president? For two terms? With the popular vote in both terms?
We've had extensive inclusion of black people in power in cities like Baltimore and Chicago, and I would venture to say many more cities as well as state governments.
Other individuals I can remember include Condoleezza Rice and Colin Powell. Many more black people in prominent government positions can be read about here: 25 Most Influential African Americans In Politics.
Sports is open to people of all sorts of color. Black athletes dominate the NFL with 70% and 80% of athletes in the NBA are people of color. These are major sports leagues where players and coaches earn tens and hundreds of millions of dollars. I don't see how a systemically racist country would allow black and minority athletes to enjoy such opportunities.
Colin Kaepernick, former QB for the 49'ers, famously and controversially kicked off the trend of kneeling while the national anthem is playing. He has claimed that America is racist and has worn socks depicting police officers as pigs. Would a systemically racist system of government let a black man freely protest like that? Nothing has happened to him. He has instead signed a deal with Nike and privately settled with the NFL to put closure to his accusation that the NFL discriminated against him after his kneeling fiasco, allegedly preventing him from again being employed in the league.
If Kaepernick really believes in something, namely that the system is against him and black people as a whole, and he is willing to sacrifice everything, why did he settle privately with the NFL and, reportedly, received an undisclosed amount of money to hush up? Shouldn't he continue the good fight since black people are oppressed?
Circling back to Jussie Smollett, who works in the entertainment industry and is a cast in Empire, Smollett himself is the de facto example of a black man who enjoys such title and position and support from the media that even staging a hate crime and being caught with a mountain of evidence along with 16 counts of felony can be let off the hook for $10,000 in bonds and community service.
The entire cast of Empire is black. This should eradicate all skepticism about whether black people are an oppressed group in this country. Black people are well represented in the movie industry, with mega stars like Denzel Washington, Samuel Jackson, and Morgan Freeman. Black Panther was a movie with a black-dominated cast. Looking around the entertainment industry should make it obvious that black people are well represented.
The fact that Jussie Smollett can stage a racist hate crime, draw national attention in the media and the public, be charged with 16 counts of felony, and still be released under obscure circumstances, should be more than enough to put to rest the idea that this country is racist. A truly racist America would not leave Jussie Smollett in such a forgiving ending. Normal citizens would not have come anywhere close to being treated as such.
Smollett stirred up even more the idea that America and Trump and his supporters are racist and furthered the political divide in America.
Smollett undermined and devalued real cases of hate crimes against LGBT and black persons.
Smollett made a joke of the integrity of the Chicago Police Department specifically and law enforcement as a whole.
Smollett created a perception that he is above the law, and that staging hate crimes is something that can be done with minimal consequences.
The treatment Smollett received compares glaringly favorable to the treatment the public and media gave to Nick Sandman, who is white, in which they rushed to condemn him, even though he was thereafter cleared of any wrong-doing. Between the gay black man and the white teenager, who was given better treatment in this so-called racist America?
To wrap up this case (pun intended), I will let the superintendent in the Chicago Police Department, who is black, and the mayor speak on my behalf and on behalf of all Americans who are infuriated by the appalling injustice that was displayed for all to see.


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RORY MAGUIRE (HMP/YOI Ashfield)
COMMENDEE 2012-13: Substance Misuse Manager: for contributions to the Duke of Edinburgh scheme at HMP/YOI Ashfield.
Rory Maguire, Substance Misuse Manager at HMP and YOI Ashfield, receives a commendation for 'contributions to the Duke of Edinburgh award scheme' at his establishment.
Rory has been Awards Manager for Ashfield's Duke of Edinburgh Award programme since 2008, with his hard work and enthusiasm helping to build it into a widely recognised example of good practice. The award is designed to give young people 'the chance to develop skills for work and life, fulfil their potential and have a brighter future,' and the scheme runs four 18-week programmes a year at Ashfield.
The groups – made up of eight young people in each – meet once or twice a week, with additional fourday training walks helping to boost physical fitness, team working and communication skills. As well as gaining skills that allow them to make better decisions and move away from offending behaviour, participants also learn important lessons about health and nutrition. The scheme is also invaluable in building trust and selfesteem, and the awards are recognised by employers throughout the world.
Overnight camps are initially organised on the prison grounds to reassure Rory that he can trust the young people before allowing them to take part in camping outside. Although some establishments deliver the service entirely within the confines of the establishment walls, Rory is a firm believer that participants need to feel trusted in order for the scheme to be fully successful. Outside activities also give them the chance to experience the sense of achievement that comes with successfully planning and completing an expedition.
Staff and young people complete the programme together, with many of the latter going on to act as mentors. Dropouts from the scheme are rare, and tend to occur only when someone leaves the establishment, although many who have yet to finish their award when they are released have then been allowed back to complete it. Fifty-two young people achieved bronze or silver awards between 2009 and early 2012, and reoffending rates among them remain low.
As well as obtaining core funding from outside agencies to help improve the programme, Rory managed to secure Ashfield its own Duke of Edinburgh Award operating licence and is also responsible for all of the administration work that goes along with running the programme. He has also made imaginative use of ROTL (release on temporary licence) – which involves comprehensive risk assessments and approval from a number of agencies – to maximise the benefits of the participants' experience.
Finally, and crucially, the fact that both young people and staff take part in the awards means that each comes to learn more about the other as they interact in a different environment. 'These interactions carry back to the wings where both parties learn to see from a different perspective,' said Rory. 'This has much wider implications than a prison wing and is something a young person will always carry with them.'
For more information: contact HMP/YOI Ashfield


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Q: Is there a way to split a HTML file without losing all the formatting within each segment? So... the split command allows me to split a file into pieces. The problem with that, though, is that only one of the files is going to contain the HTML headers, and only one of them is going to contain the HTML footers.
(this is probably relevant for a lot of other files that contain header/footer information)

A: You could first extract and remove the header/footer of the source file, split it and add the extracted header/footer to each split.
You could use xpath or sed to do the editing of the source file.
For example this command line strips the header footer of a file:
$ sed -e '0,/<body>/d' -e '/<\/body>/,$d input.html

Where sed is the GNU one and it is assumed that a body tag is on its own line.

A: Most unix tools, like split, are file format agnostic. To split files that use a specific format (like HTML) into smaller validly formatted files, use specific tools. For HTML splitting, htmldoc is the first I found looking quickly on the web. It has been packaged (at least in debian, ubuntu, fedora, gentoo, etc…).
Do not use sed-ish tricks that make troublesome assumptions on the files, as it would backfire one day or the other.

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« Time to Replace Your Mac?
Some time back, a few people decided to post some Tweets and blogs erroneously claiming that I expected Apple to stop building the Mac Pro then and there, or in the not-too-distant future. As regular readers of these columns realize, I've said no such thing. While I have addressed a possible future end to Apple's professional desktop workstation, I don't expect that Apple will do that unless or until sales dip significantly.
Sure, the vast majority of sales of new Macs these days are note-books. The refreshed MacBook Pros, along with the MacBook Air — which is expected to also receive an upgrade soon — have dominated the market. The new iMac may move that scale someone back towards desktops, but a lot more is going on here.
Today's Mac Pro contains Intel Xeon chips, which are widely used in Web servers because of their reliability. They can work 24/7 for months on end without need of repair. In addition, the Xeon uses expensive ECC memory, defined this way, according to the Wiki on the subject: "RAM with ECC or Error Correction Code can detect and correct errors." While ECC RAM, in theory, means greater reliability at the expense of somewhat slower performance, I'm not sure that real world memory problems occur that often. If you have a computer with bad memory, that will manifest itself with increased crashes and other untoward behavior easily fixed by replacing the defective component.
By making quad-core Intel Sandy Bridge processors standard on the 2011 iMac, and on many MacBook Pro configurations, Apple has seriously raised the performance bar. They claim from 30% to 70% faster than last year's iMac. You'll also find high-performance graphics hardware, and the growing availability of solid state drives.
But the icing on the cake is Thunderbolt, the speedy peripheral port Apple and Intel designed, which, in essence, adds external PCI Express support. That means that some peripherals that would have been designed to be placed inside a Mac Pro can be reengineered in external cases to support a far greater number of products. At first, you'll be seeing RAID drives, but, in theory, anything that can take advantage of 10 gigabits per second input and output speeds. The 27-inch iMacs have two of them, and multiple peripherals can be daisy chained. What's more, two 30-inch displays are supported, in addition to the internal monitor. Imagine the possibilities.
So do you see where Apple is taking you?
What this means is that more and more Mac users can do heavy-duty 3D graphics and other content creation chores on regular desktop-class Macs. They do not need to invest thousands more in a fully outfitted Mac Pro. This doesn't mean the iMac is a direct replacement. Certainly, there is the benefit of two six-core processors, which gives the Mac Pro a leg up. But that's the sort of advantage only a small number of customers will care about.
A fully decked out customized 27-inch iMac adds just a few hundred dollars to the standard $1,999 purchase price. Once you pay for the dual Xeon "Westmere" processors on a Mac Pro, the price starts at $4,999 with 6GB of RAM. It's very easy to check a few options, such as extra internal drives, a RAID card, and other extras, and boost the price to well beyond $10,000. Productivity has to improve by an awful lot to justify that sort of investment, though I expect Hollywood special effects artists will regard the expense as trivial compared to the tens of millions they waste in filming a summer blockbuster.
Future Intel consumer chips will add extra cores, and I wouldn't dismiss the prospects of putting two of them on a single logic board, something that's the province of the Xeon these days. But that luxury will be less useful when eight or more cores are standard issue on a single affordable chip.
Up until two years ago, I would never have given serious consideration to using an iMac as a direct replacement for a Mac Pro. But Apple's David Moody is telling you that they expect more and more professional users to abandon their Mac towers during their next computer upgrade cycle.
But before you take that as evidence that I expect a near-term demise for the Mac Pro, consider the published reports of a forthcoming 3U refresh, thinner and lighter, which will fit perfectly into a server rack. That, and continued sales from professional customers who require the fastest desktop workstations on the planet, will assure a continued existence for the Mac Pro.
But if you could get 98% of the capability of a Mac Pro for less than 25% the price, why would you spend the extra cash? Serious business customers have to think twice as to how paying so much more for a Mac Pro will provide a better return on their investment. I'll be revisiting this subject from time to time, but, once again, I would be the last to declare the impending death of the Mac Pro.
This article was posted on Wednesday, May 4th, 2011 at 12:00 AM and is filed under News and tagged with: 3d Graphics, Apple, Apple Inc., Graphics Hardware, Graphics Processors, iMac, Intel, Intel Xeon, Mac Pro, Macbook, Macintosh, Personal Computers, quad-core, RAM, Sandy Bridge processors, Web Servers, Xeon.
i agree with you on the horse power stakes, but the drawback with all-in-ones has always been that when you're working on a project at 4 in the morning and your hdd dies, you don't want to be digging it out of a imac to swap in a back-up. plus the lack of a sata speed swap disk. and you have to either keep your clients non disclosure projects on an external, or send them to an applestore on the internal drive for repair. i guess thunderbolt may well change the game, especially if we can get some definite info on if these new imacs can boot off a thunderbolt hdd/ssd.
Thunderbolt will change the game and I'm sure you can boot the new Macs off a TB drive.
Although I'm fully invested in PCIe and eSATA devices, I welcome our new single port I/O overlords. I can't wait to be fully solid state. Blackmagic Designs, AJA, and others announcing product at The NAB Show is exciting. However, I'm hesitant at the initial cost of moving to Thunderbolt devices. I've had great luck with traditional HDDs, but chasing the dragon of RAID through-put for uncompressed HD has been expensive. Thankfully my current 16TB RAID only cost me $2,500 when all was said and done. I cringe at what this RAID would have cost just ten years ago.
In my estimation, its going to be about five years before SSDs even begin to be as affordable as today's HDDs. Particularly in the capacities we are accustomed to.
I think there will be a iMac Pro in my future. I like that future. In the meantime a slimmer lighter Mac Pro will do.
I see the new iMac as an incredible amount of power for the price, with Thunderbolt solving the storage speed and expansion issues of prior iMac models. In fact, its only the glossy-only display that takes this down from what I consider the perfect desktop.
Glossy or not, I just ordered a 21.5″.
The MacPro also serves a strategic purpose. Not only is it a test bed for the fastest, most reliable hardware that Apple can get, it also keeps them in touch with their serious power users and the software developers who sell to them. Apple realizes that today's MacPro will be tomorrow's iMac and MacBook Pro in terms of processing and data transfer and storage capabilities. If Apple abandons having a high end system, they will lose this window into the future, and when a new class of applications moves down-processor, they won't have the software and support system in place for it.
I think this is another reason why the MacPro will undergo a serious redesign within a year to correct some of these issues. With Thunderbolt, you really don't need four drive bays, for example. A smaller form factor, which could be optionally rack mounted, would lower the cost and fill the X-Serve void. Perhaps they could offer a workstation version using standard memory and a rackmount version using the ECC RAM. I could definitely see Apple designing a custom rack sled just like they designed the iPad cover.
BTW, apparently OS X Lion will include OS X server. There will be no separate OS X server software.
While I think there is a place for a "small tower" as you describe, I do not see it as a replacement for a full size tower. Even with TB, distance does matter. If there are future high speed connections or even just iterations of TB, there will be a class of user who does not want to be constrained by a comparatively long external connection.
This not to say that an even higher speed external storage system would not be welcome in the near future (fibre channel users are not going to abandon their systems tomorrow), but the SSD evolution can benefit from a short high speed connection. There are several PCIe SSD systems now trying to speed things up. As processing power continues to increase, the ability to feed the monster will need to be optimized.
The problem with a small tower is that Steve simply does not like the idea and so the vote continues to be one to nothing.
Raging personal opinion: I think you will see the Mac Pro and Xserve merge into the next generation Mac Pro. 3U, rack-mountable (but also sold with a stand or with a BTO option for a stand) and available with E3 Xeon CPUs in 8 and 10 core configurations. It will be announced at WWDC and will be available around the same time that Lion is released.
I see it more a glass half full: people will be able to do more with an iMac, hence be more productive with a ~$1500 computer than before. people have always wanted a mac pro lite, i.e. a tower with a slower, cheaper proc but expandable ala computers in the 90's. iMac aren't quite that, but they are more productive than the original imacs. I think tis just a testament to the power/cost factor of computers: smart phones/tables replacing laptops, laptops replacing desktops and desktops replacing towers. However, people being what they are, there's no such thing as a computer thats too fast/powerful. And I think the Tower, aka mac pro, is built specifically for high end needs, which is different than an iMac; where one component failure can make it useless. Thats what you pay extra for in a mac pro and there's where your market is. also think of it as apple's way of branding: ios = accessibility by masses, ibook = value, macbook pro = portable power, imac = scalable value/productivity, mac pro = professional. Why dilute that? If a professional is going to need a professional workstation, they will always choose a mac pro.. I doubt that will ever change, all without taking anything away from the value and productivity of an iMac.
ThunderBolt could change this, but Mac Pro supporting hardware RAID for 600Mb/sec speeds and port aggregation or 10Gb/sec Ethernet, is a strong argument for now, for the PCIe slot equipped Mac Pro. And with Lion offering server software, which should include file locking lacking in Personal file Sharing, I'm looking forward to that for my performance minded clients.


This week Cara enthusiastically talks about hacking flow, an optimal state of energy and aliveness, and how she trains to experience flow, tap inner intelligence and sustain presence. She explores natural genius, our essence, and how training the body, mind, and breath opens us up to intelligence, grace and flow.
PrevPreviousIf you need to solve a problem, go out for a walk.


text:
15 year old boy killed by the army at south Gaza Strip border
by Saed Bannoura
Maan/IMEMC/Haaretz
http://www.maannews.net/eng/ViewDetails.aspx?ID=272733
http://www.imemc.org/article/58323
http://www.haaretz.com/hasen/spages/1159950.html
Gaza – Ma`an – A boy was shot and killed by Israeli forces east of the Yasser Arafat International Airport in Rafah on Tuesday, medics said.
Muawiya Hassanein, director of ambulance and emergency services in Gaza, said Muhammad Zen Ismail Al-Farmawi, 15, was shot dead near the southeasterly border by Israeli forces.
Hassanein said ambulances had been unable to retrieve the body because of ongoing clashes in the area.
An Israeli military spokesman told Ma`an that `from an examination the IDF [the Israeli army] is not familiar with a Palestinian being injured or killed by IDF fire in Rafah today.`
Locals said dozens of Palestinians sustained injuries when Israeli forces opened fire on a number of marches across Gaza heading to the borders, marking the 34th anniversary of Land Day in which six Palestinians with Israeli citizenship were killed by Israeli forces during demonstrations protesting land confiscation.
Witnesses said Israeli troops opened fire directly at protesters east of Khan Younis and the Al-Maghazi refugee camp in southern Gaza.
The marches were organized by the Popular Committee Against the Buffer Zone in Rafah and Khan Younis in southern Gaza, and Beit Hanoun and Beit Lahiya to the north.
An Israeli military spokesman told Ma`an he would look into the reports.
Mahmud Az-Zaq, coordinator of the Popular Committee Against the Buffer Zone, said six peaceful marches were launched at the same time across all Gaza districts, heading toward Israel.
`We are 200 meters from the border, with groups of young men heading the marches, waving Palestinian flags,` he said.
Walid Al-Awad, member of the Palestine People`s Party`s politburo, said hundreds of Palestinians participated in the march to confirm that the Palestinian people are united against Israel`s occupation.
Original title: `Child Killed By Army Fire In Rafah`
Palestinian medical sources in the Gaza Strip reported Tuesday morning that a boy was shot and killed by Israeli military fire in Rafah, in the southern part of the Gaza Strip.
The boy was identified as Mohammad Zeid Al Farmawi, 15, from Qishtat neighborhood in Rafah.
Local sources reported that the boy was shot by Israeli soldiers after he crossed through the border fence, east of the Gaza International Airport.
Medics rushed to the scene but the boy was already dead when they arrived; his body was moved to Abu Yousef Al Najjar in Rafah.