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This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…
This paper, about a fluid-like system of spatially confined particles, reveals the analytic structure for both, the canonical and grand canonical partition functions. The studied system is inhomogeneously distributed in a region whose…
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and…
In this work it will be shown how quark confinement appears when wave equations derived in curved spaces are considered. First, the equations and their solutions for Coulomb-like potentials will be presented, and then, how this theory leads…
We present a comprehensive spectral analysis of cylindrical quantum heterostructures by considering effective electronic carriers with position-dependent mass for five different kinetic-operator orderings. We obtain the bound energy…
The multivariate Meixner polynomials are shown to arise as matrix elements of unitary representations of the $SO(d,1)$ group on oscillator states. These polynomials depend on $d$ discrete variables and are orthogonal with respect to the…
In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the corresponding matrix recursion coefficients. The…
We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
A superintegrable, discrete model of the quantum isotropic oscillator in two-dimensions is introduced. The system is defined on the regular, infinite-dimensional $\mathbb{N}\times \mathbb{N}$ lattice. It is governed by a Hamiltonian…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These…
I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system…