A semiclassical approximation for an evolving density operator, driven by a “closed” hamiltonian operator and “open” markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the hamiltonian operator is a quadratic function and the Lindblad operators ...

In the present work we show that joint probability distribution of eigenvalues can be expressed in terms a differential operator acting on some other matrix quantities. Those quantities might diagonal or pseudo-diagonal entries as it is case for Hermitian matrices. These representations are called derivative principles. We them additive spaces Hermitian, antisymmetric, anti-self-dual, and compl...

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator, or equivalently, as the index of Neuberger’s lattice Dirac operator, is shown to have analogous properties to Lüscher’s geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum lim...

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit infinite (but still incomplete) sets of exact (algebraic) solutions. The hamiltonians of these models are hermitian operators of the form H = −∆ +V1(r)+ (s · l)V2(r)+ (...

This technical note supplies an affirmative answer to a question raised in a recent pre-print in the context of a “matrix recovery” problem. Assume one samples m Hermitian matrices X1, . . . , Xm with replacement from a finite collection. The deviation of the sum X1+ · · ·+Xm from its expected value in terms of the operator norm can be estimated by an “operator Chernoff-bound” due to Ahlswede a...

The unitary-model-operator approach (UMOA), a kind of the correlation operator method, is discussed in the framework of the general theory of effective interaction. The two-body effective interaction ṽ12, introduced as a basic element in the UMOA, has some desirable properties of being E-independent, Hermitian and decoupled between a model space and its complement. The UMOA is applied to the ca...

A unitary family is a family of unitary operators U(x) acting on a finite dimensional hermitian vector space, depending analytically on a real parameter x. It is monotone if 1 i U (x)U(x) is a positive operator for each x. We prove a number of results generalizing standard theorems on the spectral theory of a single unitary operator U0, which correspond to the ’commutative’ case U(x) = eU0. Als...