420 research outputs found
Spectral Statistics: From Disordered to Chaotic Systems
The relation between disordered and chaotic systems is investigated. It is
obtained by identifying the diffusion operator of the disordered systems with
the Perron-Frobenius operator in the general case. This association enables us
to extend results obtained in the diffusive regime to general chaotic systems.
In particular, the two--point level density correlator and the structure factor
for general chaotic systems are calculated and characterized. The behavior of
the structure factor around the Heisenberg time is quantitatively described in
terms of short periodic orbits.Comment: uuencoded file with 1 eps figure, 4 page
Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance
We study long-range correlations of equilibrium current densities in a
two-dimensional mesoscopic system with the time reversal invariance broken by a
random or homogeneous magnetic field. Our result is universal, i.e. it does not
depend on the type (random potential or random magnetic field) or correlation
length of disorder. This contradicts recent sigma-model calculations of
Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well
as for the renormalization of the conductivity. We show explicitly that the new
term in the sigma-model derived by TS&E and claimed to lead to delocalization
does not exist. The error in the derivation of TS&E is traced to an incorrect
ultraviolet regularization procedure violating current conservation and gauge
invariance.Comment: 8 pages, 3 figure
The leading Ruelle resonances of chaotic maps
The leading Ruelle resonances of typical chaotic maps, the perturbed cat map
and the standard map, are calculated by variation. It is found that, excluding
the resonance associated with the invariant density, the next subleading
resonances are, approximately, the roots of the equation , where
is a positive number which characterizes the amount of stochasticity
of the map. The results are verified by numerical computations, and the
implications to the form factor of the corresponding quantum maps are
discussed.Comment: 5 pages, 4 figures included. To appear in Phys. Rev.
Ballistic electron motion in a random magnetic field
Using a new scheme of the derivation of the non-linear -model we
consider the electron motion in a random magnetic field (RMF) in two
dimensions. The derivation is based on writing quasiclassical equations and
representing their solutions in terms of a functional integral over
supermatrices with the constraint . Contrary to the standard scheme,
neither singling out slow modes nor saddle-point approximation are used. The
-model obtained is applicable at the length scale down to the electron
wavelength. We show that this model differs from the model with a random
potential (RP).However, after averaging over fluctuations in the Lyapunov
region the standard -model is obtained leading to the conventional
localization behavior.Comment: 10 pages, no figures, to be submitted in PRB v2: Section IV is
remove
Quantum interference and the formation of the proximity effect in chaotic normal-metal/superconducting structures
We discuss a number of basic physical mechanisms relevant to the formation of
the proximity effect in superconductor/normal metal (SN) systems. Specifically,
we review why the proximity effect sharply discriminates between systems with
integrable and chaotic dynamics, respectively, and how this feature can be
incorporated into theories of SN systems. Turning to less well investigated
terrain, we discuss the impact of quantum diffractive scattering on the
structure of the density of states in the normal region. We consider ballistic
systems weakly disordered by pointlike impurities as a test case and
demonstrate that diffractive processes akin to normal metal weak localization
lead to the formation of a hard spectral gap -- a hallmark of SN systems with
chaotic dynamics. Turning to the more difficult case of clean systems with
chaotic boundary scattering, we argue that semiclassical approaches, based on
classifications in terms of classical trajectories, cannot explain the gap
phenomenon. Employing an alternative formalism based on elements of
quasiclassics and the ballistic -model, we demonstrate that the inverse
of the so-called Ehrenfest time is the relevant energy scale in this context.
We discuss some fundamental difficulties related to the formulation of low
energy theories of mesoscopic chaotic systems in general and how they prevent
us from analysing the gap structure in a rigorous manner. Given these
difficulties, we argue that the proximity effect represents a basic and
challenging test phenomenon for theories of quantum chaotic systems.Comment: 21 pages (two-column), 6 figures; references adde
Quantum Disorder and Quantum Chaos in Andreev Billiards
We investigate the crossover from the semiclassical to the quantum
description of electron energy states in a chaotic metal grain connected to a
superconductor. We consider the influence of scattering off point impurities
(quantum disorder) and of quantum diffraction (quantum chaos) on the electron
density of states. We show that both the quantum disorder and the quantum chaos
open a gap near the Fermi energy. The size of the gap is determined by the mean
free time in disordered systems and by the Ehrenfest time in clean chaotic
systems. Particularly, if both times become infinitely large, the density of
states is gapless, and if either of these times becomes shorter than the
electron escape time, the density of states is described by random matrix
theory. Using the Usadel equation, we also study the density of states in a
grain connected to a superconductor by a diffusive contact.Comment: 20 pages, 10 figure
Dyonic BIon black hole in string inspired model
We construct static and spherically symmetric particle-like and black hole
solutions with magnetic and/or electric charge in the
Einstein-Born-Infeld-dilaton-axion system, which is a generalization of the
Einstein-Maxwell-dilaton-axion (EMDA) system and of the Einstein-Born-Infeld
(EBI) system. They have remarkable properties which are not seen for the
corresponding solutions in the EMDA and the EBI system.Comment: 13 pages, 15 figures, Final version in PR
Superconductive proximity effect in interacting disordered conductors
We present a general theory of the superconductive proximity effect in
disordered normal--superconducting (N-S) structures, based on the recently
developed Keldysh action approach. In the case of the absence of interaction in
the normal conductor we reproduce known results for the Andreev conductance G_A
at arbitrary relation between the interface resistance R_T and the diffusive
resistance R_D. In two-dimensional N-S systems, electron-electron interaction
in the Cooper channel of normal conductor is shown to strongly affect the value
of G_A as well as its dependence on temperature, voltage and magnetic field. In
particular, an unusual maximum of G_A as a function of temperature and/or
magnetic field is predicted for some range of parameters R_D and R_T. The
Keldysh action approach makes it possible to calculate the full statistics of
charge transfer in such structures. As an application of this method, we
calculate the noise power of an N-S contact as a function of voltage,
temperature, magnetic field and frequency for arbitrary Cooper repulsion in the
normal metal and arbitrary values of the ratio R_D/R_T.Comment: RevTeX, 28 pages, 18 PostScript figures; added and updated reference
Interface effects on the shot noise in normal metal- d-wave superconductor Junctions
The current fluctuation in normal metal / d-wave superconductor junctions are
studied for various orientation of the crystal by taking account of the spatial
variation of the pair potentials. Not only the zero-energy Andreev bound states
(ZES) but also the non-zero energy Andreev bound states influence on the
properties of differential shot noise. At the tunneling limit, the noise power
to current ratio at zero voltage becomes 0, once the ZES are formed at the
interface. Under the presence of a subdominant s-wave component at the
interface which breaks time-reversal symmetry, the ratio becomes 4eComment: 13 pages, 3 figure
Weak Localization and Integer Quantum Hall Effect in a Periodic Potential
We consider magnetotransport in a disordered two-dimensional electron gas in
the presence of a periodic modulation in one direction. Existing quasiclassical
and quantum approaches to this problem account for Weiss oscillations in the
resistivity tensor at moderate magnetic fields, as well as a strong
modulation-induced modification of the Shubnikov-de Haas oscillations at higher
magnetic fields. They do not account, however, for the operation at even higher
magnetic fields of the integer quantum Hall effect, for which quantum
interference processes are responsible. We then introduce a field-theory
approach, based on a nonlinear sigma model, which encompasses naturally both
the quasiclassical and quantum-mechanical approaches, as well as providing a
consistent means of extending them to include quantum interference corrections.
A perturbative renormalization-group analysis of the field theory shows how
weak localization corrections to the conductivity tensor may be described by a
modification of the usual one-parameter scaling, such as to accommodate the
anisotropy of the bare conductivity tensor. We also show how the two-parameter
scaling, conjectured as a model for the quantum Hall effect in unmodulated
systems, may be generalized similarly for the modulated system. Within this
model we illustrate the operation of the quantum Hall effect in modulated
systems for parameters that are realistic for current experiments.Comment: 15 pages, 4 figures, ReVTeX; revised version with condensed
introduction; two figures taken out; reference adde
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