277 research outputs found
On Hubbard-Stratonovich Transformations over Hyperbolic Domains
We discuss and prove validity of the Hubbard-Stratonovich (HS) identities
over hyperbolic domains which are used frequently in the studies on disordered
systems and random matrices. We also introduce a counterpart of the HS identity
arising in disordered systems with "chiral" symmetry. Apart from this we
outline a way of deriving the nonlinear -model from the gauge-invariant
Wegner orbital model avoiding the use of the HS transformations.Comment: More accurate proofs are given; a few misprints are corrected; a
misleading reference and a footnote in the end of section 2.2 are remove
Level curvature distribution in a model of two uncoupled chaotic subsystems
We study distributions of eigenvalue curvatures for a block diagonal random matrix perturbed by
a full random matrix. The most natural physical realization of this model is a quantum chaotic system
with some inherent symmetry, such that its energy levels form two independent subsequences,
subject to a generic perturbation which does not respect the symmetry. We describe analytically
a crossover in the form of a curvature distribution with a tunable parameter namely the ratio of
inter/intra subsystem coupling strengths. We find that the peak value of the curvature distribution
is much more sensitive to the changes in this parameter than the power law tail behaviour. This
observation may help to clarify some qualitative features of the curvature distributions observed
experimentally in acoustic resonances of quartz blocks
A conjecture on Hubbard-Stratonovich transformations for the Pruisken-Sch\"afer parameterisations of real hyperbolic domains
Rigorous justification of the Hubbard-Stratonovich transformation for the
Pruisken-Sch\"afer type of parameterisations of real hyperbolic
O(m,n)-invariant domains remains a challenging problem. We show that a naive
choice of the volume element invalidates the transformation, and put forward a
conjecture about the correct form which ensures the desired structure. The
conjecture is supported by complete analytic solution of the problem for groups
O(1,1) and O(2,1), and by a method combining analytical calculations with a
simple numerical evaluation of a two-dimensional integral in the case of the
group O(2,2).Comment: Published versio
On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
Given any fixed positive semi-definite diagonal matrix
we derive the explicit formula for the density of complex eigenvalues for
random matrices of the form } where the random unitary
matrices are distributed on the group according to the Haar
measure.Comment: 10 pages, 1 figur
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)
Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder
We resolve the problem of the violation of single parameter scaling at the
zero energy of the Anderson tight-binding model with diagonal disorder. It
follows from the symmetry properties of the tight-binding Hamiltonian that this
spectral point is in fact a boundary between two adjacent bands. The states in
the vicinity of this energy behave similarly to states at other band
boundaries, which are known to violate single parameter scaling.Comment: revised version, 4 pages, 2 figures, revte
Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
Random banded matrices with linearly increasing diagonal elements are
recently considered as an attractive model for complex nuclei and atoms. Apart
from early papers by Wigner \cite{Wig} there were no analytical studies on the
subject. In this letter we present analytical and numerical results for local
spectral density of states (LDOS) for more general case of matrices with a
sparsity inside the band. The crossover from the semicircle form of LDOS to
that given by the Breit-Wigner formula is studied in detail.Comment: Misprints are corrected and stylistic changes are made. To be
published in PR
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.
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
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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