Related papers: Approximate Solution of the Representability Probl…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…
In this paper we present a solution of the Einstein's boxes paradox by modern Quantum Mechanics in which a notion of density matrix is equivalent to a notion of a quantum state of a system. We use a secondary quantization formalism in the…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and…
In this paper we treat the Jaynes-Cummings model with dissipation and give an approximate solution to the master equation for the density operator {\bf under the general setting} by making use of the Zassenhaus expansion.
This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation, coherent manipulation and characterization of free-electron quantum states. The available measurement consists of electron energy…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
An efficient procedure for constructing quasi-exactly solvable matrix models is suggested. It is based on the fact that the representation spaces of representations of the algebra sl(2,R) within the class of first-order matrix differential…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
In this paper we consider nonlinear problems with an operator depending only on the deformation tensor. We consider the class of operators derived from a potential and with $(p,\delta)$ structure, for $1<p\leq 2$ and for all $\delta\geq0$.…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are…