Related papers: Higher Order Correlations in Quantum Chaotic Spect…
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum…
Guztwiller's Trace Formula is central to the semiclassical theory of quantum energy levels and spectral statistics in classically chaotic systems. Motivated by recent developments in Random Matrix Theory and Number Theory, we elucidate a…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
We investigate spatial reflection and associated nonlocal order in spin chain quantum systems. The proposed string order parameters, e.g., reflected via operations of the spatial reflection or combinations of it with spin reflection, are…
A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies…
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by Random Matrix Theory. Scattering resonances…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show…
It has been long recognized that the task of semiclassical evaluation of quantum spectra for the classically nonintegrable systems is fundamentally more complex than for the classically integrable ones. Below it is argued that the quantum…
We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor $K(t)$ analytically and numerically, we show that…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states.…
We review recent studies about the resonance spectrum of quantum scattering systems, in the semiclassical limit and assuming chaotic classical dynamics. Stationary quantum properties are related to fractal structures in the classical phase…
Higher order parametric level correlations in disordered systems with broken time-reversal symmetry are studied by mapping the problem onto a model of coupled Hermitian random matrices. Closed analytical expression is derived for parametric…
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
The spectral form factor is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or OPE coefficients in conformal field theories.…
Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…