Integro-differential equation for Bose-Einstein condensates

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.053635· OSTI ID:21528715

Adam, R M ^[1]; Sofianos, S A ^[2]

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1. South African Nuclear Energy Corporation, P.O. Box 582, Pretoria 0001 (South Africa)
2. Physics Department, University of South Africa, P.O. Box 392, Pretoria 0001 (South Africa)

We use the assumption that the potential for the A-boson system can be written as a sum of pairwise acting forces to decompose the wave function into Faddeev components that fulfill a Faddeev type equation. Expanding these components in terms of potential harmonic (PH) polynomials and projecting on the potential basis for a specific pair of particles results in a two-variable integro-differential equations suitable for A-boson bound-state studies. The solution of the equation requires the evaluation of Jacobi polynomials P{sub K}{sup {alpha},{beta}}(x) and of the weight function W(z) which give severe numerical problems for very large A. However, using appropriate limits for A{yields}{infinity} we obtain a variant equation which depends only on the input two-body interaction, and the kernel in the integral part has a simple analytic form. This equation can be readily applied to a variety of bosonic systems such as microclusters of noble gasses. We employ it to obtain results for A(set-membership sign)(10-100) {sup 87}Rb atoms interacting via interatomic interactions and confined by an externally applied trapping potential V{sub trap}(r). Our results are in excellent agreement with those previously obtained using the potential harmonic expansion method (PHEM) and the diffusion Monte Carlo (DMC) method.

• OSTI ID: 21528715
• Journal Information: Physical Review. A, Vol. 82, Issue 5; Other Information: DOI: 10.1103/PhysRevA.82.053635; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOSE-EINSTEIN CONDENSATION
BOSONS
BOUND STATE
HARMONIC POTENTIAL
INTEGRO-DIFFERENTIAL EQUATIONS
KERNELS
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
PARTICLES
POLYNOMIALS
RUBIDIUM 87
TWO-BODY PROBLEM
WAVE FUNCTIONS
WEIGHTING FUNCTIONS
BETA DECAY RADIOISOTOPES
BETA-MINUS DECAY RADIOISOTOPES
CALCULATION METHODS
EQUATIONS
FUNCTIONS
INTERMEDIATE MASS NUCLEI
ISOTOPES
MANY-BODY PROBLEM
NUCLEAR POTENTIAL
NUCLEI
ODD-EVEN NUCLEI
POTENTIALS
RADIOISOTOPES
RUBIDIUM ISOTOPES
YEARS LIVING RADIOISOTOPES