176 research outputs found
Semiclassical universality of parametric spectral correlations
We consider quantum systems with a chaotic classical limit that depend on an
external parameter, and study correlations between the spectra at different
parameter values. In particular, we consider the parametric spectral form
factor which depends on a scaled parameter difference . For
parameter variations that do not change the symmetry of the system we show by
using semiclassical periodic orbit expansions that the small expansion
of the form factor agrees with Random Matrix Theory for systems with and
without time reversal symmetry.Comment: 18 pages, no figure
Vortex dissipation and level dynamics for the layered superconductors with impurities
We study parametric level statistics of the discretized excitation spectra
inside a moving vortex core in layered superconductors with impurities. The
universal conductivity is evaluated numerically for the various values of
rescaled vortex velocities from the clean case to the dirty limit
case. The random matrix theoretical prediction is verified numerically in the
large regime. On the contrary in the low velocity regime, we observe
which is consistent with the theoretical
result for the super-clean case, where the energy dissipation is due to the
Landau-Zener transition which takes place at the points called ``avoided
crossing''.Comment: 10 pages, 4 figures, REVTeX3.
Persistent Currents in Quantum Chaotic Systems
The persistent current of ballistic chaotic billiards is considered with the
help of the Gutzwiller trace formula. We derive the semiclassical formula of a
typical persistent current for a single billiard and an average
persistent current for an ensemble of billiards at finite temperature.
These formulas are used to show that the persistent current for chaotic
billiards is much smaller than that for integrable ones. The persistent
currents in the ballistic regime therefore become an experimental tool to
search for the quantum signature of classical chaotic and regular dynamics.Comment: 4 pages (RevTex), to appear in Phys. Rev. B, No.59, 12256-12259
(1999
Environment-independent decoherence rate in classically chaotic systems
We study the decoherence of a one-particle system, whose classical
correpondent is chaotic, when it evolves coupled to a weak quenched
environment. This is done by analytical evaluation of the Loschmidt Echo, (i.e.
the revival of a localized density excitation upon reversal of its time
evolution), in presence of the perturbation. We predict an exponential decay
for the Loschmidt Echo with a (decoherence) rate which is asymptotically given
by the mean Lyapunov exponent of the classical system, and therefore
independent of the perturbation strength, within a given range of strengths.
Our results are consistent with recent experiments of Polarization Echoes in
nuclear magnetic resonance and preliminary numerical simulations.Comment: No figures. Typos corrected and minor modifications to the text and
references. Published versio
Universality in quantum parametric correlations
We investigate the universality of correlation functions of chaotic and
disordered quantum systems as an external parameter is varied. A new, general
scaling procedure is introduced which makes the theory invariant under
reparametrizations. Under certain general conditions we show that this
procedure is unique. The approach is illustrated with the particular case of
the distribution of eigenvalue curvatures. We also derive a semiclassical
formula for the non-universal scaling factor, and give an explicit expression
valid for arbitrary deformations of a billiard system.Comment: LaTeX, 10 pages, 2 figures. Revised version, to appear in PR
Universal Predictions for Statistical Nuclear Correlations
We explore the behavior of collective nuclear excitations under a
multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements
have the form , with a
parametric correlation of the type . The studies are done in both the regular and chaotic regimes of the
Hamiltonian. Model independent predictions for a wide variety of correlation
functions and distributions which depend on wavefunctions and energies are
found from parametric random matrix theory and are compared to the nuclear
excitations. We find that our universal predictions are observed in the nuclear
states. Being a multi-parameter theory, we consider general paths in parameter
space and find that universality can be effected by the topology of the
parameter space. Specifically, Berry's phase can modify short distance
correlations, breaking certain universal predictions.Comment: Latex file + 12 postscript figure
Non-universal corrections to the level curvature distribution beyond random matrix theory
The level curvature distribution function is studied beyond the random matrix
theory for the case of T-breaking perturbations over the orthogonal ensemble.
The leading correction to the shape of the level curvature distribution is
calculated using the nonlinear sigma-model. The sign of the correction depends
on the presence or absence of the global gauge invariance and is different for
perturbations caused by the constant vector-potential and by the random
magnetic field. Scaling arguments are discussed that indicate on the
qualitative difference in the level statistics in the dirty metal phase for
space dimensionalities .Comment: 4 pages, Late
Effect of deconfinement on resonant transport in quantum wires
The effect of deconfinement due to finite band offsets on transport through
quantum wires with two constrictions is investigated. It is shown that the
increase in resonance linewidth becomes increasingly important as the size is
reduced and ultimately places an upper limit on the energy (temperature) scale
for which resonances may be observed.Comment: 6 pages, 6 postscript files with figures; uses REVTe
Measuring the Lyapunov exponent using quantum mechanics
We study the time evolution of two wave packets prepared at the same initial
state, but evolving under slightly different Hamiltonians. For chaotic systems,
we determine the circumstances that lead to an exponential decay with time of
the wave packet overlap function. We show that for sufficiently weak
perturbations, the exponential decay follows a Fermi golden rule, while by
making the difference between the two Hamiltonians larger, the characteristic
exponential decay time becomes the Lyapunov exponent of the classical system.
We illustrate our theoretical findings by investigating numerically the overlap
decay function of a two-dimensional dynamical system.Comment: 9 pages, 6 figure
"Level Curvature" Distribution for Diffusive Aharonov-Bohm Systems: analytical results
We calculate analytically the distributions of "level curvatures" (LC) (the
second derivatives of eigenvalues with respect to a magnetic flux) for a
particle moving in a white-noise random potential.
We find that the Zakrzewski-Delande conjecture is still valid even if the
lowest weak localization corrections are taken into account. The ratio of mean
level curvature modulus to mean dissipative conductance is proved to be
universal and equal to in agreement with available numerical data.Comment: 12 pages. Submitted to Phys.Rev.
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