Related papers: Harmonic Oscillator Trap and the Phase-Shift Appro…
We investigate a system of bosons in a two-dimensional harmonic trap. In the limit of strong attractive interactions, the bosons make a droplet insensitive to external confinement. For weak interactions, in contrast, the ground state is…
We solve the problem of a Bose or Fermi gas in $d$-dimensions trapped by $% \delta \leq d$ mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific…
As a limiting case of ultracold atoms trapped in deep optical lattices, we consider two interacting atoms trapped in a general anisotropic harmonic oscillator potential, and obtain exact solutions of the Schrodinger equation for this…
We derive solutions of the Schr\"{o}dinger equation for the isotropic van der Waals interaction in a symmetric harmonic trap, with the recent approach [arXiv:2207.09377 (2022)] to handle the multi-scale long-range potential. Asymptotic…
We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground state energy and chemical potential, and obtain simple…
Electron orbits are calculated in solitary two-dimensional axisymmetric electrostatic potential structures, typical of plasma electron holes, in order to establish the conditions for the particles to remain trapped. Analytic calculations of…
A phase operator formulation for a recent model of interacting one-dimensional fermions in a harmonic trap is developed. The resulting theory is similar to the corresponding approach for the Luttinger model with open boundary conditions…
We consider a dilute gas of dipole moments in an arbitrary harmonic trap and treat both the short-range, isotropic delta-interaction and the long-range, anisotropic dipole-dipole interaction perturbatively. With this we calculate the…
Using the Euler-Maclaurin summation we calculate analytically the internal energy for non-interacting bosons confined within a harmonic oscillator potential. The specific heat shows a sharp $\lambda$-like peak indicating a condensation into…
An exact solution of the energy shift in each quantum mechanical energy levels in a one dimensional symmetrical linear harmonic oscillator has been investigated. The solution we have used here is firstly derived by manipulating Schrodinger…
We consider two bosonic atoms interacting with a short-range potential and trapped in a spherically symmetric harmonic oscillator. The problem is exactly solvable and is relevant for the study of ultra-cold atoms. We show that the energy…
We study the quantum spin-1/2 Heisenberg model in two dimensions, interacting through a nearest-neighbor antiferromagnetic exchange ($J$) and a ferromagnetic dipolar-like interaction ($J_d$), using double-time Green's function, decoupled…
By using Supersymmetric Quantum Mechanics and Semiclassical Quantization, one may argue that the low-lying excited states of any quantum system can be modeled by a set of harmonic oscillators. In the present paper, we fit the experimental…
We derive the ground-state energy for a small number of ultracold atoms in an isotropic harmonic trap using effective quantum field theory (EFT). Atoms are assumed to interact through pairwise energy-independent and energy-dependent…
We consider two ultracold particles confined in spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact…
The quantum problem of four particles in $\mathbb{R}^d$ ($d\geq 3$), with arbitrary masses $m_1,m_2,m_3$ and $m_4$, interacting through an harmonic oscillator potential is considered. This model allows exact solvability and a critical…
We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law…
I revisit the problem of the interaction between two dissimilar atoms with one atom in an excited state, recently addressed by the authors of Refs.[1-3], and for which precedent approaches have given conflicting results. In the first place,…
Using the conformable fractional calculus, a new formulation of the Bohr Hamiltonian is introduced. The conformable fractional energy spectra of free- and two- parameters anharmonic oscillator potentials are investigated. The energy…
We consider chains of $N$ harmonic oscillators in two dimensions coupled to two Langevin heat reservoirs at different temperatures - a classical model for heat conduction introduced by Lebowitz, Lieb, and Rieder \cite{RLL67}. We extend our…