Related papers: Higher Order Correlations in Quantum Chaotic Spect…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We calculate the S-matrix correlation function for chaotic scattering on quantum graphs and show that it agrees with that of random--matrix theory (RMT). We also calculate all higher S-matrix correlation functions in the Ericson regime.…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
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 argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…
Quantum mechanics requires that identical particles are treated as indistinguishable. This requirement leads to correlations in the fluctuating properties of a system. Theoretical predictions are made for an experiment on a multi-lead…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
In multimode optical systems, the spectral covariance matrix encodes all the information about quantum correlations between the quadratures of Gaussian states. Recent research has revealed that, in scenarios that are more common than…
Out-of-time-order correlators (OTOC) being explored as a measure of quantum chaos, is studied here in a coupled bipartite system. Each of the subsystems can be chaotic or regular and lead to very different OTOC growths both before and after…
Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…
We wish to report an experimental observation of anti-correlation from first-order incoherent classical chaotic light. We explain why the classical statistical theory does not apply and provide a quantum interpretation. In quantum theory,…
It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain…
This article aims at popularizing some aspects of "quantum chaos", in particular the study of eigenmodes of classically chaotic systems, in the semiclassical (or high frequency) limit.
Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new `dual' types of correlations. Such ordering leads to novel collective…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…