232 research outputs found
Ehrenfest-time dependence of weak localization in open quantum dots
Semiclassical theory predicts that the weak localization correction to the
conductance of a ballistic chaotic cavity is suppressed if the Ehrenfest time
exceeds the dwell time in the cavity [I. L. Aleiner and A. I. Larkin, Phys.
Rev. B {\bf 54}, 14424 (1996)]. We report numerical simulations of weak
localization in the open quantum kicked rotator that confirm this prediction.
Our results disagree with the `effective random matrix theory' of transport
through ballistic chaotic cavities.Comment: 4 pages, 2 figure
Point perturbations of circle billiards
The spectral statistics of the circular billiard with a point-scatterer is
investigated. In the semiclassical limit, the spectrum is demonstrated to be
composed of two uncorrelated level sequences. The first corresponds to states
for which the scatterer is located in the classically forbidden region and its
energy levels are not affected by the scatterer in the semiclassical limit
while the second sequence contains the levels which are affected by the
point-scatterer. The nearest neighbor spacing distribution which results from
the superposition of these sequences is calculated analytically within some
approximation and good agreement with the distribution that was computed
numerically is found.Comment: 9 pages, 2 figure
Directed flow in non-adiabatic stochastic pumps
We analyze the operation of a molecular machine driven by the non-adiabatic
variation of external parameters. We derive a formula for the integrated flow
from one configuration to another, obtain a "no-pumping theorem" for cyclic
processes with thermally activated transitions, and show that in the adiabatic
limit the pumped current is given by a geometric expression.Comment: 5 pages, 2 figures, very minor change
Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
We study the spectral statistics of the Dirac operator on a rose-shaped
graph---a graph with a single vertex and all bonds connected at both ends to
the vertex. We formulate a secular equation that generically determines the
eigenvalues of the Dirac rose graph, which is seen to generalise the secular
equation for a star graph with Neumann boundary conditions. We derive
approximations to the spectral pair correlation function at large and small
values of spectral spacings, in the limit as the number of bonds approaches
infinity, and compare these predictions with results of numerical calculations.
Our results represent the first example of intermediate statistics from the
symplectic symmetry class.Comment: 26 pages, references adde
On the theory of cavities with point-like perturbations. Part II: Rectangular cavities
We consider an application of a general theory for cavities with point-like
perturbations for a rectangular shape. Hereby we concentrate on experimental
wave patterns obtained for nearly degenerate states. The nodal lines in these
patterns may be broken, which is an effect coming only from the experimental
determination of the patterns. These findings are explained within a framework
of the developed theory.Comment: 14 pages, 3 figure
Classical limit of transport in quantum kicked maps
We investigate the behavior of weak localization, conductance fluctuations,
and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved
numerical results, obtained by truncating the time-evolution of a kicked
quantum map after a certain number of iterations, are compared to semiclassical
theory. Considering how the appearance of quantum effects is delayed as a
function of the Ehrenfest time gives a new method to compare theory and
numerical simulations. We find that both weak localization and shot noise agree
with semiclassical theory, which predicts exponential suppression with
increasing Ehrenfest time. However, conductance fluctuations exhibit different
behavior, with only a slight dependence on the Ehrenfest time.Comment: 17 pages, 13 figures. Final versio
On the eigenvalue spacing distribution for a point scatterer on the flat torus
We study the level spacing distribution for the spectrum of a point scatterer
on a flat torus. In the 2-dimensional case, we show that in the weak coupling
regime the eigenvalue spacing distribution coincides with that of the spectrum
of the Laplacian (ignoring multiplicties), by showing that the perturbed
eigenvalues generically clump with the unperturbed ones on the scale of the
mean level spacing. We also study the three dimensional case, where the
situation is very different.Comment: 25 page
Lower bounds on dissipation upon coarse graining
By different coarse-graining procedures we derive lower bounds on the total
mean work dissipated in Brownian systems driven out of equilibrium. With
several analytically solvable examples we illustrate how, when, and where the
information on the dissipation is captured.Comment: 11 pages, 8 figure
Semiclassical Approach to Chaotic Quantum Transport
We describe a semiclassical method to calculate universal transport
properties of chaotic cavities. While the energy-averaged conductance turns out
governed by pairs of entrance-to-exit trajectories, the conductance variance,
shot noise and other related quantities require trajectory quadruplets; simple
diagrammatic rules allow to find the contributions of these pairs and
quadruplets. Both pure symmetry classes and the crossover due to an external
magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version
Exact formula for currents in strongly pumped diffusive systems
We analyze a generic model of mesoscopic machines driven by the nonadiabatic
variation of external parameters. We derive a formula for the probability
current; as a consequence we obtain a no-pumping theorem for cyclic processes
satisfying detailed balance and demonstrate that the rectification of current
requires broken spatial symmetry.Comment: 10 pages, accepted for publication in the Journal of Statistical
Physic
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