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We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant…
We exploit the rich algebraic structure of the interacting boson model to explain the notion of partial dynamical symmetry (PDS), and present a procedure for constructing Hamiltonians with this property. We demonstrate the relevance of PDS…
Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. In the present paper we consider the quantum differential equations resulting from position dependent…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces $\DC P^N$, as well as on their non-compact counterparts, i. e. the $N-$dimensional Lobachewski spaces ${\cal L}_N$. We find the…
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\"odinger picture in which the analogs of the Schr\"odinger operators of the particle…
The model under consideration is the two-dimensional (2D) one-component plasma of pointlike charged particles in a uniform neutralizing background, interacting through the logarithmic Coulomb interaction. Classical equilibrium statistical…
We construct static solutions to a SU(2) Yang--Mills (YM) dilaton model in 4+1 dimensions subject to bi-azimuthal symmetry. The YM sector of the model consists of the usual YM term and the next higher order term of the YM hierarchy, which…
We provide exact analytical solutions for a two dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the…
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations…
We construct an infinite family of one-dimensional equilibrium solutions for purely magnetized quantum plasmas described by the quantum hydrodynamic model. The equilibria depends on the solution of a third-order ordinary differential…
The dynamical behavior of quantum state properties under intrinsic decoherence models can be modified by the presence of external magnetic fields. Although generically external magnetic fields are detrimental to preserve quantumness in the…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on the energy levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction. The extension…
Using a solvable model, the two-dimensional two-component plasma, we study a Coulomb gas confined in a disk and in an annulus with boundaries that can adsorb some of the negative particles of the system. We obtain explicit analytic…
Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably…
A new method for generating exactly solvable Schr\"odinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schr\"odinger equations, which can be dealt with by using a supersymmetric quantum…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
In this paper we treat the 2--level system interacting with external fields without the rotating wave approximation and construct some approximate solutions in the strong coupling regime.