N-boson time-dependent problem:: A reformulation with stochastic wave functions
Year: 2001
Authors: Carusotto I., Castin Y., Dalibard J.
Autors Affiliation: Ecole Normale Super, Lab Kastler Brossel, F-75231 Paris 05, France; Scuola Normale Super Pisa, I-56126 Pisa, Italy; INFM, I-56126 Pisa, Italy.
Abstract: We present a numerically tractable method to solve exactly the evolution of a N boson system with binary interactions. The density operator of the system rho is obtained as the stochastic average of particular operators psi (1)][psi (2) of the system. The states psi (1,2)] are either Fock states N:phi (1,2)] or coherent states [coh: phi (1,2)] With each particle in the state phi (1,2)(x). We determine the conditions on the evolution of phi (1,2), which involves a stochastic element, under which we recover the exact evolution of rho. We discuss various possible implementations of these conditions. The well known positive P representation arises as a particular case of the coherent state ansatz. We treat numerically two examples: a two-mode system and a one-dimensional harmonically confined gas. These examples, together with an analytical estimate of the noise, show that the Fock state ansatz is the most promising one in terms of precision and stability of the numerical solution.
Journal/Review: PHYSICAL REVIEW A
Volume: 63 (2) Pages from: 23606-1 to: 23606-14
KeyWords: Einstein Condensation; Quantum Dynamics; Gas; Evolution; Symmetry; Equation; NumberDOI: 10.1103/PhysRevA.63.023606Citations: 72data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)