Related papers: Confined systems associated with the discrete Meix…
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
We find a new quantum system associated with the Wilson Orthogonal Polynomial. In order to establish correspondence between the recent reformulation of quantum mechanic without potential function [1-2] and the convention quantum mechanics,…
We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
Quantum correlations can be used as a resource for quantum computing, eg for quantum state manipulation, and for quantum sensing, eg for creating non-classical states which allow to achieve the quantum advantage regime. This review collects…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schr\"odinger equation. The first part is a quick presentation of some of the…
We study the kinetics of confined carrier-phonon system in a quantum dot under fast optical driving and discuss the resulting limitations to fast coherent control over the quantum state in such systems.
Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We briefly review some examples of confinement which arise in condensed matter physics. We focus on two instructive cases: the off-critical Ising model in a magnetic field, and an array of weakly coupled (extended) Hubbard chains in the…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
The paper is devoted to the further study of the remarkable classes of orthogonal polynomials recently discovered by Bender and Dunne. We show that these polynomials can be generated by solutions of arbitrary quasi - exactly solvable…
Confinement/deconfinement, captivating attributes of high-energy elementary particles, have recently garnered wide attention in quantum simulations based on cold atoms. Yet, the partial confinement, an intermediate state between the…
The problem of confinement of spinless particles in 1+1 dimensions is approached with a linear potential by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling…
We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study…
Confined excitonic complexes in two dimensions, consisting of N_e electrons and N_h holes, are studied by means of Bethe-Goldstone equations. Systems with up to twelve pairs, and asymmetric configurations with N_e \ne N_h are considered.…
The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As…
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.