418 research outputs found
Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements
The random banded matrices (RBM) whose diagonal elements fluctuate much
stronger than the off-diagonal ones were introduced recently by Shepelyansky as
a convenient model for coherent propagation of two interacting particles in a
random potential. We treat the problem analytically by using the mapping onto
the same supersymmetric nonlinear model that appeared earlier in
consideration of the standard RBM ensemble, but with renormalized parameters. A
Lorentzian form of the local density of states and a two-scale spatial
structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky
are confirmed by direct calculation of the distribution of eigenfunction
components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.
Correlation functions of impedance and scattering matrix elements in chaotic absorbing cavities
Wave scattering in chaotic systems with a uniform energy loss (absorption) is
considered. Within the random matrix approach we calculate exactly the energy
correlation functions of different matrix elements of impedance or scattering
matrices for systems with preserved or broken time-reversal symmetry. The
obtained results are valid at any number of arbitrary open scattering channels
and arbitrary absorption. Elastic enhancement factors (defined through the
ratio of the corresponding variance in reflection to that in transmission) are
also discussed.Comment: 10 pages, 2 figures (misprints corrected and references updated in
ver.2); to appear in Acta Phys. Pol. A (Proceedings of the 2nd Workshop on
Quantum Chaos and Localization Phenomena, May 19-22, 2005, Warsaw
Induced vs Spontaneous Breakdown of S-matrix Unitarity: Probability of No Return in Quantum Chaotic and Disordered Systems
We investigate systematically sample-to sample fluctuations of the
probability of no return into a given entrance channel for wave
scattering from disordered systems. For zero-dimensional ("quantum chaotic")
and quasi one-dimensional systems with broken time-reversal invariance we
derive explicit formulas for the distribution of , and investigate
particular cases. Finally, relating to violation of S-matrix unitarity
induced by internal dissipation, we use the same quantity to identify the
Anderson delocalisation transition as the phenomenon of spontaneous breakdown
of S-matrix unitarity.Comment: This is the published version, with a few modifications added to the
last par
Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
The explicit analytical expression for the distribution function of
parametric derivatives of energy levels ("level velocities") with respect to a
random change of scattering potential is derived for the chaotic quantum
systems belonging to the quasi 1D universality class (quantum kicked rotator,
"domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.
Inhomogeneous losses and complexness of wave functions in chaotic cavities
In a two-dimensional microwave chaotic cavity Ohmic losses located at the contour of the cavity result in different broadenings of different modes. We provide an analytic description and establish the link between such an inhomogeneous damping and the complex (non-real) character of biorthogonal wave functions. This substantiates the corresponding recent experimental findings of Barthélemy et al. (Europhys. Lett., 70 (2005) 162)
Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
We study fluctuations of the local density of states (LDOS) on a tree-like
lattice with large branching number . The average form of the local spectral
function (at given value of the random potential in the observation point)
shows a crossover from the Lorentzian to semicircular form at ,
where , is the typical value of the hopping matrix
element, and is the width of the distribution of random site energies. For
the LDOS fluctuations (with respect to this average form) are
weak. In the opposite case, , the fluctuations get strong and the
average LDOS ceases to be representative, which is related to the existence of
the Anderson transition at . On the localized side
of the transition the spectrum is discrete, and LDOS is given by a set of
-like peaks. The effective number of components in this regime is given
by , with being the inverse participation ratio. It is shown that
has in the transition point a limiting value close to unity, , so that the system undergoes a transition directly from the deeply
localized to extended phase. On the side of delocalized states, the peaks in
LDOS get broadened, with a width being exponentially small near the
transition point. We discuss application of our results to the problem of the
quasiparticle line shape in a finite Fermi system, as suggested recently by
Altshuler, Gefen, Kamenev, and Levitov.Comment: 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section
VII added. Accepted for publication in Phys. Rev.
On absolute moments of characteristic polynomials of a certain class of complex random matrices
Integer moments of the spectral determinant of complex
random matrices are obtained in terms of the characteristic polynomial of
the Hermitian matrix for the class of matrices where is a
given matrix and is random unitary. This work is motivated by studies of
complex eigenvalues of random matrices and potential applications of the
obtained results in this context are discussed.Comment: 41 page, typos correcte
Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry
Employing the chiral Unitary Ensemble of random matrices we calculate the
probability distribution of the local density of states for zero-dimensional
("quantum chaotic") two-sublattice systems at the point of chiral symmetry E=0
and in the presence of uniform absorption. The obtained result can be used to
find the distributions of the reflection coefficent and of the Wigner time
delay for such systems.Comment: 4 pages, 3 figure
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