Scattering of particles in the presence of harmonic confinement perturbed by a complex absorbing potential

2018 ◽  
Vol 32 (09) ◽  
pp. 1850109
Author(s):  
A. Maghari ◽  
M. Mansoori Kermani
Keyword(s):  
Bound States ◽  
Optical Lattices ◽  
Harmonic Trap ◽  
Absorbing Boundary ◽  
Boundary Potential ◽  
Harmonic Confinement ◽  
Atom Interaction ◽  
Interacting Atoms ◽  
Analytical Expressions ◽  
Absorption Probabilities

A system of two interacting atoms confined in 1D harmonic trap and perturbed by an absorbing boundary potential is studied using the Lippmann–Schwinger formalism. The atom–atom interaction potential was considered as a nonlocal separable model. The perturbed absorbing boundary potential was also assumed in the form of Scarf II complex absorbing potential. The model is used for the study of 1D optical lattices that support the trapping of a pair atom within a unit cell. Moreover, it allows to describe the scattering particles in a tight smooth trapping surface and to analyze the bound and resonance states. The analytical expressions for wavefunctions and transition matrix as well as the absorption probabilities are calculated. A demonstration of how the complex absorbing potential affecting the bound states and resonances of particles confined in a harmonic trap is described.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

scholarly journals Bound states and Cooper pairs of molecules in 2D optical lattices bilayer

2016 ◽  
Vol 528 (7-8) ◽  
pp. 580-587 ◽  
Author(s):  
A. Camacho-Guardian ◽  
G. A. Domínguez-Castro ◽  
R. Paredes
Keyword(s):  
Bound States ◽  
Optical Lattices ◽  
Cooper Pairs

Electrostatique de systèmes cylindriques de révolution où le potentiel sur certaines parties de la frontière est un polynôme du second degré de la cote suivant l'axe

1981 ◽  
Vol 59 (2) ◽  
pp. 202-206 ◽  
Author(s):  
Colette Berger
Keyword(s):  
Second Order ◽  
Real System ◽  
Elementary System ◽  
Boundary Potential ◽  
Rapid Calculation ◽  
Order Polynomial ◽  
Analytical Expressions ◽  
Derivatives Of ◽  
Aberration Corrected

The systems studied are equivalent to indefinite cylinders with rotationally symmetrical potentials. The analytical expressions for the derivatives of the axial potential with respect to z are given for two elementary systems called "Electrode" and "Interval." This analysis is also applied to one further elementary system in which the boundary potential is zero except in one region where its dependence on z follows a second-order polynomial. For a complex real system, the analytical expressions of the derivatives of the axial potential are obtained by superposition of elementary systems. This method renders possible a rapid calculation of the field, even for systems with large electrode separations. Furthermore, it may be used for the design of aberration-corrected systems.[Journal translation]

Quantum signature of breathers in 1D ultracold bosons in optical lattices involving next-nearest neighbor interactions

2017 ◽  
Vol 31 (20) ◽  
pp. 1750140 ◽  
Author(s):  
Z. I. Djoufack ◽  
A. Kenfack-Jiotsa ◽  
J.-P. Nguenang
Keyword(s):  
Energy Spectrum ◽  
Optical Lattice ◽  
Bound States ◽  
Optical Lattices ◽  
Nearest Neighbor ◽  
Laser Light ◽  
Energy Spectra ◽  
System Parameters ◽  
Quantum Breathers ◽  
Bosonic Atoms

The dynamics and the energy spectrum of an ultracold gas of bosonic atoms in an optical lattice can be described by a Bose–Hubbard model for which the system parameters can be controlled by laser light. We study by means of the perturbation theory in addition to the numerical diagonalization, the energy spectrum and the related features of the band structures of the ultracold bosons in optical lattices containing a few number of quanta interacting with next-nearest neighbor interactions (NNNI) modeled by the Bose–Hubbard Hamiltonian. The energy spectra of such system display the bound states signature, which are analyzed in the first Brillouin zone for different wave numbers. The finding, i.e., quantum breathers, shows that their probabilities’ weight depends on the wave vector. The influence of NNNI on both the probabilities’ amplitude and the correlation function is also realized in case of a system with a small number of sites, respectively.

Thermodynamics of rotating weakly interacting Bose gases in a harmonic trap

2019 ◽  
Vol 33 (20) ◽  
pp. 1950225 ◽  
Author(s):  
Yushan Li
Keyword(s):  
Particle Number ◽  
Local Density ◽  
Scattering Length ◽  
Harmonic Trap ◽  
Repulsive Interaction ◽  
Density Approximation ◽  
Bose Gases ◽  
Weakly Interacting ◽  
Analytical Expressions ◽  
Particle Current

The analytical expressions of particle number, critical temperature, condensate fraction, total energy, specific heat and spatial distribution of particle current for rotating weakly interacting Bose gases in a harmonic trap are derived by using the local density approximation (LDA). The effects of weakly repulsive interaction on the above thermodynamics are discussed by introducing a positive scattering length. Our results completely coincide with those for the case of rotating ideal Bose gases when the weak interaction disappears.

scholarly journals Exact quasi-relativistic wavefunctions of Hydrogen-like atoms

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Luis Grave de Peralta
Keyword(s):  
Bound States ◽  
Relativistic Quantum ◽  
Quantum Mechanical ◽  
Solid State Physics ◽  
Mechanical Wave ◽  
Atomic Orbitals ◽  
Exact Analytical Expression ◽  
Quantum Particles ◽  
Software Packages ◽  
Analytical Expressions

Abstract Exact solutions of a novel quasi-relativistic quantum mechanical wave equation are found for Hydrogen-like atoms. This includes both, an exact analytical expression for the energies of the bound states, and exact analytical expressions for the wavefunctions, which successfully describe quantum particles with mass and spin-0 up to energies comparable to the energy associated to the mass of the particle. These quasi-relativistic atomic orbitals may be used for improving ab-initio software packages dedicated to numerical simulations in physical-chemistry and atomic and solid-state physics.

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