Related papers: Gaussian ensembles distributions from mixing quant…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
There exists a Hamiltonian formulation of the factorisation problem which also needs the definition of a factorisation ensemble (a set to which factorable numbers, $N'=x'y'$, having the same trivial factorisation algorithmic complexity,…
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study…
The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each…
For random matrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribution to a Gaussian process whose covariance matrix is…
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…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…
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…
The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in…
Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…
We consider the frequency at which avoided crossings appear in an energy level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings…
The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…