14,555 research outputs found
On the propagation of semiclassical Wigner functions
We establish the difference between the propagation of semiclassical Wigner
functions and classical Liouville propagation. First we re-discuss the
semiclassical limit for the propagator of Wigner functions, which on its own
leads to their classical propagation. Then, via stationary phase evaluation of
the full integral evolution equation, using the semiclassical expressions of
Wigner functions, we provide the correct geometrical prescription for their
semiclassical propagation. This is determined by the classical trajectories of
the tips of the chords defined by the initial semiclassical Wigner function and
centered on their arguments, in contrast to the Liouville propagation which is
determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the
one set to print and differs from the previous one (07 Nov 2001) by the
addition of two references, a few extra words of explanation and an augmented
figure captio
Uniform approximation for the overlap caustic of a quantum state with its translations
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is
known to have a caustic along the corresponding classical closed phase space
curve in the case of a single degree of freedom. Its Fourier transform, the
semiclassical chord function, also has a caustic along the conjugate curve
defined as the locus of diameters, i.e. the maximal chords of the original
curve. If the latter is convex, so is its conjugate, resulting in a simple fold
caustic. The uniform approximation through this caustic, that is here derived,
describes the transition undergone by the overlap of the state with its
translation, from an oscillatory regime for small chords, to evanescent
overlaps, rising to a maximum near the caustic. The diameter-caustic for the
Wigner function is also treated.Comment: 14 pages, 9 figure
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
Experimental Observation of Environment-induced Sudden Death of Entanglement
We demonstrate the difference between local, single-particle dynamics and
global dynamics of entangled quantum systems coupled to independent
environments. Using an all-optical experimental setup, we show that, while the
environment-induced decay of each system is asymptotic, quantum entanglement
may suddenly disappear. This "sudden death" constitutes yet another distinct
and counter-intuitive trait of entanglement.Comment: 4 pages, 4 figure
Spin-glass behaviour on random lattices
The ground-state phase diagram of an Ising spin-glass model on a random graph
with an arbitrary fraction of ferromagnetic interactions is analysed in the
presence of an external field. Using the replica method, and performing an
analysis of stability of the replica-symmetric solution, it is shown that
, correponding to an unbiased spin glass, is a singular point in the
phase diagram, separating a region with a spin-glass phase () from a
region with spin-glass, ferromagnetic, mixed, and paramagnetic phases
()
Decoherence of Semiclassical Wigner Functions
The Lindblad equation governs general markovian evolution of the density
operator in an open quantum system. An expression for the rate of change of the
Wigner function as a sum of integrals is one of the forms of the Weyl
representation for this equation. The semiclassical description of the Wigner
function in terms of chords, each with its classically defined amplitude and
phase, is thus inserted in the integrals, which leads to an explicit
differential equation for the Wigner function. All the Lindblad operators are
assumed to be represented by smooth phase space functions corresponding to
classical variables. In the case that these are real, representing hermitian
operators, the semiclassical Lindblad equation can be integrated. There results
a simple extension of the unitary evolution of the semiclassical Wigner
function, which does not affect the phase of each chord contribution, while
dampening its amplitude. This decreases exponentially, as governed by the time
integral of the square difference of the Lindblad functions along the classical
trajectories of both tips of each chord. The decay of the amplitudes is shown
to imply diffusion in energy for initial states that are nearly pure.
Projecting the Wigner function onto an orthogonal position or momentum basis,
the dampening of long chords emerges as the exponential decay of off-diagonal
elements of the density matrix.Comment: 23 pg, 2 fi
Universal quantum signature of mixed dynamics in antidot lattices
We investigate phase coherent ballistic transport through antidot lattices in
the generic case where the classical phase space has both regular and chaotic
components. It is shown that the conductivity fluctuations have a non-Gaussian
distribution, and that their moments have a power-law dependence on a
semiclassical parameter, with fractional exponents. These exponents are
obtained from bifurcating periodic orbits in the semiclassical approximation.
They are universal in situations where sufficiently long orbits contribute.Comment: 7 page
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