311 research outputs found
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
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.
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)
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
The decay of photoexcited quantum systems: a description within the statistical scattering model
The decay of photoexcited quantum systems (examples are photodissociation of
molecules and autoionization of atoms) can be viewed as a half-collision
process (an incoming photon excites the system which subsequently decays by
dissociation or autoionization). For this reason, the standard statistical
approach to quantum scattering, originally developed to describe nuclear
compound reactions, is not directly applicable. Using an alternative approach,
correlations and fluctuations of observables characterizing this process were
first derived in [Fyodorov YV and Alhassid Y 1998 Phys. Rev. A 58, R3375]. Here
we show how the results cited above, and more recent results incorporating
direct decay processes, can be obtained from the standard statistical
scattering approach by introducing one additional channel.Comment: 7 pages, 2 figure
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
Fluctuations in random networks: non-linear model description
Disordered networks are known to be an adequate model for describing
fluctuations of electric fields in a random metal-dielectric composite. We show
that under appropriate conditions the statistical properties of such a system
can be studied in the framework of the Efetov's non-linear model.
This fact provides a direct link to the theory of Anderson localization.Comment: 4 pages, latex, no figure
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