Related papers: Spectral Form Factor for Chaotic Dynamics in a Wea…
For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
The relativistic approach to electroweak properties of two-particle composite systems developed in Ref. [A.F.Krutov, V.E.Troitsky, Phys.Rev.C. 65 (2002) 045501] is generalized here to the case of nonzero spin. In developed technique the…
We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of…
A new class of Random Matrix Ensembles is introduced. The Gaussian orthogonal, unitary, and symplectic ensembles GOE, GUE, and GSE, of random matrices are analogous to the classical Gibbs ensemble governed by Boltzmann's distribution in the…
Novel magnetic phases are expected to occur in highly frustrated spin systems. Here we study the structurally perfect kagom\'e antiferromagnet CdCu$_3$(OH)$_6$(NO$_3$)$_2\cdot$H$_2$O by magnetization, magnetic torque, and heat capacity…
We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit…
Single-site dynamical mean field theory is used to determine the magnetic and orbital-ordering phase diagram for a model of electrons moving on a lattice with three orbital states per site and with the fully rotationally invariant…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing.…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
Spectral form factor (SFF), one of the key quantity from random matrix theory, serves as an important tool to probe universality in disordered quantum systems and quantum chaos. In this work, we present exact closed-form expressions for the…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation…
Statistical distribution of energy levels for Dirac fermions confined in a quantum dot is studied numerically on the examples of triangular and hexagonal graphene flakes with random electrostatic potential landscape. When increasing the…
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
In order to understand the parameters of the standard model of electroweak and strong interactions (coupling constants, masses, mixing angles) one needs to embed the standard model into some larger theory that accounts for the observed…
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary…