Related papers: Chaotic maps and flows: Exact Riemann-Siegel looka…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed.…
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
We study the universal fluctuations of the Wigner-Smith time delay for systems which exhibit chaotic dynamics in their classical limit. We present a new derivation of the semiclassical relation of the quantum time delay to properties of the…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
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…
Recently, with Mussardo we defined a quantum mechanical problem of a single particle scattering with impurities wherein the quantized energy levels $E_n (\sigma)$ are exactly equal to the zeros of the Riemann $\zeta (s)$ where $\sigma = \Re…
The spacing intervals of adjacent Riemann zeta zeros(non-trivial) exhibit fractal(irregular) fluctuations generic to dynamical systems in nature such as fluid flows, heart beat patterns, stock market price index, etc., and are associated…
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…
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…
We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a distinguished token in the presence of a contextual measure…