Related papers: Composition of quantum operations and products of …
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
In Liouville formalism the expression for density matrix, determining the time evolution of unstable $\pi^{\pm}$ - meson in the framework of unified formulation of quantum and kinetic dynamics is defined. The eigenvalues problem is…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
The Ginibre unitary ensemble (GinUE) consists of $N \times N$ random matrices with independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre, who showed that the eigenvalues form a determinantal point process with…
Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By…
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary…
Let $\Psi_n$ be a product of $n$ independent, identically distributed random matrices $M$, with the properties that $\Psi_n$ is bounded in $n$, and that $M$ has a deterministic (constant) invariant vector. Assuming that the probability of…
We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects then Hamiltonians. In this paper we study an evolution operator for the one-dimensional integrable q-deformed Bose gas with…
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 show that as $n$ changes, the characteristic polynomial of the $n\times n$ random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to P\'olya's urn scheme. As a result, we get a random…
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…
We find stochastic equations governing eigenvalues and eigenvectors of a dynamical complex Ginibre ensemble reaffirming the intertwined role played between both sets of matrix degrees of freedom. We solve the accompanying…
We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we…