Related papers: Distribution of matrix elements of random operator…

We present a reduced density operator for electronically open molecules by explicitly averaging over the environmental degrees of freedom of the composite Hamiltonian. Specifically, we include the particle-number non-conserving…

We introduce and study `matricial circular systems' of operators which play the role of matricial counterparts of circular operators. They describe the asymptotic joint *-distributions of blocks of independent block-identically distributed…

For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…

The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are…

The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…

It is known that a unitary matrix can be decomposed into a product of reflections, one for each dimension, and the Haar measure on the unitary group pushes forward to independent uniform measures on the reflections. We consider the sequence…

Operator scrambling denotes the evolution of a simple operator into a complicated one (in the Heisenberg picture), which characterizes quantum chaos in many-body systems. More specifically, a simple operator evolves into a linear…

Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively…

The random matrix ensembles (RMT) 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…

The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.

We characterise the probability distributions that arise from quantum circuits all of whose gates commute, and show when these distributions can be classically simulated efficiently. We consider also marginal distributions and the…

We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of…

The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…

We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…

A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute…

We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum…

We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…

We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…

Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…