arXiv subjects

Yan V. Fyodorov

Publications and source records attributed to Yan V. Fyodorov.

At least 73 records · Page 4Linked to original sources

arXiv2003

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.

cond-mat.mes-hall↗

arXiv2003

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 $τ$ 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 $τ$, and investigate particular cases. Finally, relating $τ$ 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.

cond-mat↗

arXiv2003

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.

cond-mat.stat-mech↗

arXiv2003

An exact formula for general spectral correlation function of random Hermitian matrices

We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential difference from the previously studied correlation functions (of products only) is the appearance of non-polynomial functions along with the orthogonal polynomials. These non-polynomial functions are the Cauchy transforms of the orthogonal polynomials. The result is valid for any ensemble of beta=2 symmetry class and generalizes recent asymptotic formulae obtained for GUE and its chiral counterpart by different methods..

math-ph↗

arXiv2003

On the supersymmetric partition function in QCD-inspired random matrix models

We show that the expression for the supersymmetric partition function of the chiral Unitary Ensemble conjectured recently by Splittorff and Verbaarschot [Phys. Rev. Lett. v. 90, 041601 (2003)] follows from the general expression derived recently by Fyodorov and Strahov [ J. Phys. A: Math.Gen.} {\bf 36}(2003) 3203] .

cond-mat.mes-hall↗

arXiv2003

On random symmetric matrices with a constraint: the spectral density of random impedance networks

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A: Math. Gen. 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi one-dimensional random impedance networks.

cond-mat.dis-nn↗

arXiv2002

Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations

We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as $N \to \infty$. The results agree nontrivially with a recent conjecture of Berry & Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivial predictions obtained using these techniques have been proved.

math-ph↗

arXiv2002

Statistics of transmitted power in multichannel dissipative ergodic structures

We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed counterparts with local-in-space internal dissipation. We concentrate on the regime of broken time-reversal invariance and employ two different analytical approaches: the exact supersymmetry method and a simpler technique that uses RMT eigenstatistics for closed non-dissipative systems as an input. The results of the supersymmetric method were confirmed by numerical simulation. The simpler method is found to be adequate for closed systems with uniform dissipation, or in the limit of a large number of weak local dampers.

cond-mat.mes-hall↗

arXiv2002

Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach

We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal polynomials; b) constructed from Cauchy transforms of the same orthogonal polynomials and finally c) those constructed from both orthogonal polynomials and their Cauchy transforms. These kernels are related with the Riemann-Hilbert problem for orthogonal polynomials. For the correlation functions we obtain exact expressions in the form of determinants of these kernels. Derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via Deift-Zhou steepest-descent/stationary phase method for Riemann-Hilbert problems, and in particular to find negative moments of characteristic polynomials. This reveals the universal parts of the correlation functions and moments of characteristic polynomials for arbitrary invariant ensemble of $β=2$ symmetry class.

math-ph↗

arXiv2001

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.

cond-mat.dis-nn↗

arXiv2000

Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex eigenvalues of generic $N\times N$ random matrices $\hat{A}$ of such a type, corresponding to systems with broken time-reversal invariance. Deviations from unitarity are characterized by rank $M\le N$ and a set of eigenvalues $0 >M,n$ the correlation functions acquire the universal form found earlier for weakly non-Hermitian random matrices.

nlin.CD↗

arXiv2000

Spectra of Random Matrices Close to Unitary and Scattering Theory for Discrete-Time Systems

We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. Deviation from unitarity are characterized by rank $M$ and eigenvalues $T_i, i=1,...,M$ of the matrix $\hat{T}=\hat{\bf 1}-\hat{A}^{\dagger}\hat{A}$. For the case M=1 we solve the problem completely by deriving the joint probability density of eigenvalues and calculating all $n-$ point correlation functions. For a general case we present the correlation function of secular determinants.

nlin.CD↗

arXiv1999

Fluctuations in random $RL-C$ networks: non-linear $σ-$ model description

Disordered $RL-C$ 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 $σ-$ model. This fact provides a direct link to the theory of Anderson localization.

cond-mat↗

arXiv1999

Spectral Properties of Random Reactance Networks and Random Matrix Pencils

Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $λ_n$ of matrix pencils ${\bf H}-λ{\bf W}$, with ${\bf W}$ being positive definite matrix and ${\bf H}$ a random real symmetric one. We first consider spectra of matrix pencils with independent, identically distributed entries of ${\bf H}$. Then we concentrate on an infinite-range ("full-connectivity") version of random $LC$ network. In all cases we calculate the mean eigenvalue density and the two-point correlation function in the framework of Efetov's supersymmetry approach. Fluctuations in spectra turn out to be the same as those provided by Wigner-Dyson theory of usual random matrices.

cond-mat↗

arXiv1999

Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering

We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point correlation functions in the complex plane. As a by-product, we establish the Ginibre-like statistics of resonances for many open channels. Our method is a combination of Itzykson-Zuber integration and a variant of nonlinear $σ-$model and can be applied when the use of orthogonal polynomials is problematic.

cond-mat↗

arXiv1998

The Spectral Autocorrelation Function in Weakly Open Chaotic Systems: Indirect Photodissociation of Molecules

We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework of random matrix theory, and hold more generally for any chaotic quantum system that is weakly coupled to the continuum. The "correlation hole" that characterizes the spectral autocorrelation in the bound molecule diminishes as the typical average total width of a resonance increases.

chao-dyn↗

arXiv1998

S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances

We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hatΓ$, where both $\hat{H}$ and $\hatΓ$ are real symmetric, $\hat{H}$ is random Gaussian and $\hatΓ$ is such that $NTr \hatΓ^2_2\sim Tr \hat{H}_1^2$ when $N\to \infty$. When $\hatΓ\ge 0$ the model can be used to describe the universal statistics of S-matrix poles (resonances) in the complex energy plane. We derive the ensuing distribution of the resonance widths which generalizes the well-known $χ^2$ distribution to the case of overlapping resonances. We also consider a different class of "almost real" matrices when $\hatΓ$ is random and uncorrelated with $\hat{H}$.

chao-dyn↗

arXiv1998

Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on statistics of $Z_i$ for systems with broken time-reversal invariance and verify that it allows to reproduce statistical characteristics of Wigner time delays known from independent calculations. We analyze the ensuing two-point statistical measures as e.g. spectral form factor and the number variance. In addition we find the density of complex eigenvalues of real asymmetric matrices generalizing the recent result by Efetov\cite{Efnh}.

cond-mat↗