Related papers: On quantum quadratic operators of $\bm_2(\mathbb{C…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
In the present paper, we study infinite dimensional orthogonal preserving quadratic stochastic operators (OP QSO). A full description of OP QSOs in terms of their canonical form and heredity coefficient's values is provided. Furthermore,…
In this paper, we further study the G-dynamics newly emerged in the covariant dynamics defined by the quantum covariant Poisson bracket (QCPB) theory. We propose three new operators based on the G-dynamics, we find that the non-Hermitian…
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…
The present paper focuses on the dynamical systems of the quadratic bistochastic operators (QBO) on the standard simplex. In the paper, we show the character of connection of the dynamical systems of a bistochastic operator with the…
Working within the framework of Loop Quantum Gravity (LQG), we construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration. In doing so, we rely on known properties of operators for…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic…
Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse…
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More…
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 this paper we consider quadratic stochastic operators designed on finite Abelian groups. It is proved that such operators have the property of regularity.
We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum…
In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear…
In this paper we define the Schwartz linear operators among spaces of tempered distributions. These operators are the analogous of linear continuous operators among separable Hilbert spaces, but in the case of spaces endowed with Schwartz…
In present paper we introduce the notion of dissipative quadratic stochastic operator and cubic stochastic operator. We prove necessary conditions for dissipativity of quadratic stochastic operators. Besides, it is studied certain limit…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…