36 research outputs found
Universality of the Wigner time delay distribution for one-dimensional random potentials
We show that the distribution of the time delay for one-dimensional random
potentials is universal in the high energy or weak disorder limit. Our
analytical results are in excellent agreement with extensive numerical
simulations carried out on samples whose sizes are large compared to the
localisation length (localised regime). The case of small samples is also
discussed (ballistic regime). We provide a physical argument which explains in
a quantitative way the origin of the exponential divergence of the moments. The
occurence of a log-normal tail for finite size systems is analysed. Finally, we
present exact results in the low energy limit which clearly show a departure
from the universal behaviour.Comment: 4 pages, 3 PostScript figure
Distribution of time-constants for tunneling through a 1D Disordered Chain
The dynamics of electronic tunneling through a disordered 1D chain of finite
length is considered. We calculate distributions of the transmission
coefficient T, Wigner delay time and, and the transport time,
. The central bodies of these distributions have a power-law
form, what can be understood in terms of the resonant tunneling through
localised states.Comment: 5 pages, 3 figures, submitted to PR
Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis
We study statistical properties of a class of band random matrices which
naturally appears in systems of interacting particles. The local spectral
density is shown to follow the Breit-Wigner distribution in both localized and
delocalized regimes with width independent on the band/system size. We analyse
the implications of this distribution to the inverse participation ratio, level
spacing statistics and the problem of two interacting particles in a random
potential.Comment: 4 pages, 4 postscript figures appended, new version with minor
change
Topological universality of level dynamics in quasi-one-dimensional disordered conductors
Nonperturbative, in inverse Thouless conductance 1/g, corrections to
distributions of level velocities and level curvatures in quasi-one-dimensional
disordered conductors with a topology of a ring subject to a constant vector
potential are studied within the framework of the instanton approximation of
nonlinear sigma-model. It is demonstrated that a global character of the
perturbation reveals the universal features of the level dynamics. The
universality shows up in the form of weak topological oscillations of the
magnitude ~ exp(-g) covering the main bodies of the densities of level
velocities and level curvatures. The period of discovered universal
oscillations does not depend on microscopic parameters of conductor, and is
only determined by the global symmetries of the Hamiltonian before and after
the perturbation was applied. We predict the period of topological oscillations
to be 4/(pi)^2 for the distribution function of level curvatures in orthogonal
symmetry class, and 3^(1/2)/(pi) for the distribution of level velocities in
unitary and symplectic symmetry classes.Comment: 15 pages (revtex), 3 figure
Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement
Coherent propagation of two interacting particles in weak random
potential is considered. An accurate estimate of the matrix element of
interaction in the basis of localized states leads to mapping onto the relevant
matrix model. This mapping allows to clarify the mechanism of enhancement of
the localization length which turns out to be rather different from the one
considered in the literature. Although the existence of enhancement is
transparent, an analytical solution of the matrix model was found only for very
short samples. For a more realistic situation numerical simulations were
performed. The result of these simulations is consistent with l_{2}/l_1 \sim
l_1^{\gamma} , where and are the single and two particle
localization lengths and the exponent depends on the strength of the
interaction. In particular, in the limit of strong particle-particle
interaction there is no enhancement of the coherent propagation at all ().Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for
publication in Phys. Rev.
Electron-Electron Interaction in Disordered Mesoscopic Systems: Weak Localization and Mesoscopic Fluctuations of Polarizability and Capacitance
The weak localization correction and the mesoscopic fluctuations of the
polarizability and the capacitance of a small disordered sample are studied
systematically in 2D and 3D geometries. While the grand canonical ensemble
calculation gives the positive magnetopolarizability, in the canonical ensemble
(appropriate for isolated samples) the sign of the effect is reversed. The
magnitude of mesoscopic fluctuations for a single sample exceeds considerably
the value of the weak localization correction.Comment: 13 pages Latex, 3 .eps figures included. To appear in Phys. Rev. B.
Minor corrections, in particular in formulae; new references adde
Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances
We derive the explicit expression for the distribution of resonance widths in
a chaotic quantum system coupled to continua via M equivalent open channels. It
describes a crossover from the distribution (regime of isolated
resonances) to a broad power-like distribution typical for the regime of
overlapping resonances. The first moment is found to reproduce exactly the
Moldauer-Simonius relation between the mean resonance width and the
transmission coefficient. This fact may serve as another manifestation of
equivalence between the spectral and the ensemble averaging.Comment: 4 two-column pages, RevTex. text is slightly modified; some misprints
are correcte
Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks
We use the Real Space Renormalization Group (RSRG) method to study extreme
value statistics for a variety of Brownian motions, free or constrained such as
the Brownian bridge, excursion, meander and reflected bridge, recovering some
standard results, and extending others. We apply the same method to compute the
distribution of extrema of Bessel processes. We briefly show how the continuous
time random walk (CTRW) corresponds to a non standard fixed point of the RSRG
transformation.Comment: 24 pages, 5 figure
Eigenfunctions of electrons in weakly disordered quantum dots: Crossover between orthogonal and unitary symmetries
A one-parameter random matrix model is proposed for describing the statistics
of the local amplitudes and phases of electron eigenfunctions in a mesoscopic
quantum dot in an arbitrary magnetic field. Comparison of the statistics
obtained with recent results derived from first principles within the framework
of supersymmetry technique allows to identify a transition parameter with real
microscopic characteristics of the problem. The random-matrix model is applied
to the statistics of the height of the resonance conductance of a quantum dot
in the regime of the crossover between orthogonal and unitary symmetry classes.Comment: 6 pages (latex), 3 figures available upon request, to appear in
Physical Review
Semi-classical Theory of Conductance and Noise in Open Chaotic Cavities
Conductance and shot noise of an open cavity with diffusive boundary
scattering are calculated within the Boltzmann-Langevin approach. In
particular, conductance contains a non-universal geometric contribution,
originating from the presence of open contacts. Subsequently, universal
expressions for multi-terminal conductance and noise valid for all chaotic
cavities are obtained classically basing on the fact that the distribution
function in the cavity depends only on energy and using the principle of
minimal correlations.Comment: 4 pages, 1 .eps figur