Related papers: Spectral form factor in a random matrix theory
We prove a uniform spectral gap for complex transfer operators near the critical line associated to overlapping $C^2$ iterated function systems on the real line satisfying a Uniform Non-Integrability (UNI) condition. Our work extends that…
An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean…
We study the limiting behavior of singular values of a lag-$\tau$ sample auto-correlation matrix $\bf{R}_{\tau}^{\epsilon}$ of error term $\epsilon$ in the high-dimensional factor model. We establish the limiting spectral distribution (LSD)…
We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the…
A spectral average which generalises the local spacing distribution of the eigenvalues of random $ N\times N $ hermitian matrices in the bulk of their spectrum as $ N\to\infty $ is known to be a $\tau$-function of the fifth Painlev\'e…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly-correlated photon pairs in an…
In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix…
We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…
The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the…
We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic…
Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
To describe longitudinal fine structure like microbunching within a particle beam, a classical approach is to define a bunching factor which is the Fourier transform of the particle longitudinal density distribution. Such a 1D definition of…