Related papers: Quantum anharmonic oscillator and quasi-exactly so…
Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath.…
Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES).…
The ability of semi-classical transport models to correctly simulate Pauli blocking and Bose enhancement is discussed. In the context of simple quantum mechanical systems, it is shown that using $(1 \pm f)$ enhancements is inadequate to…
Adiabatic approximations are a powerful tool for simplifying nonlinear quantum dynamics, and are applicable whenever a system exhibits a hierarchy of time scales. Current interest in small nonlinear quantum systems, such as few-mode…
We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a…
We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions interacting with a small potential with a positive Fourier transform. We compute the imaginary part of the phononic excitation spectrum in the lowest…
We construct a family of triatomic models for heteronuclear and homonuclear molecular Bose-Einstein condensates. We show that these new generalized models are exactly solvable through the algebraic Bethe ansatz method and derive their…
Bose-condensed systems with broken global gauge symmetry are considered. The description of these systems, as has been shown by Hohenberg and Martin, possesses an internal inconsistency, resulting in either nonconserving theories or…
This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level…
In a first order approximation, the Bose-Hubbard Hamiltonian with on site interaction is obtained from the free Hamiltonian (U=0) and generalized commutation relation for the annihilation-creation operators. Similar generalized commutation…
The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems…
We study theoretically the non-equilibrium dynamics of a two-dimensional (2D) uniform Bose superfluid following a quantum quench, from its short-time (prethermal) coherent dynamics to its long-time thermalization. Using a quantum…
The equivalence is established between the one-dimensional (1D) Bose-system with a finite number of particles and the system obeying the fractional (intermediate) Gentile statistics, in which the maximum occupation of single-particle energy…
The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of…
A general procedure is presented to construct conditionally solvable (CES) potentials using the techniques of supersymmetric quantum mechanics.The method is illustrated with potentials related to the harmonic oscillator problem.Besides…
Supersymmetrical intertwining relations of second order in derivatives allow to construct a two-dimensional quantum model with complex potential, for which {\it all} energy levels and bound state wave functions are obtained analytically.…
We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the context of quasi-exactly solvable spectral problems. This Hamiltonian is expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical expressions…
We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact…