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Journal of Sichuan University

The ground state wave function of quasi-2D Bose-condensed gas

Dong Lv

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The quasi-Gauss model is applied to quasi-2D Bose gas.Through solving the Gross-Pitaevskii equation,the quasi-Gauss wave function is obtained,which agrees well with the previous numerical solution and Thomas-Fermi approximation model.In addition,through solving the energy function,we get the ground state energy and the chemical potential.The influence of dimension change to the nature of the system is analyzed.

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The quasi-Gauss model is applied to quasi-2D Bose gas.Through solving the Gross-Pitaevskii equation,the quasi-Gauss wave function is obtained,which agrees well with the previous numerical solution and Thomas-Fermi approximation model.In addition,through solving the energy function,we get the ground state energy and the chemical potential.The influence of dimension change to the nature of the system is analyzed.
Based on the Gross-Pitaevskii(G-P) energy functional and variational method, we present a new method to find the ground state wave function for Bose-condensed gas in a harmonic trap at zero temperature. With this method we are able to find the analytic expression of ground state wave function and explore the relevant quantities, such as energy, chemical potential and so on. These results agree well with previous ground state numerical solutions of the G-P equation given by Dalfovo et al. Under the large number of particles N limit for repulsive interaction, our results and Thomas-Fermi approximation model approach to reaching unanimity. This new method is simple compared to other methods used to solve numerically the G-P equation, and one can obtained the analytic and reliable results.
Taking the gross-pitaevskii（G-P） mean-field energy functional of Bose condensed gas as the objective function, we study the properties of Bose condensed gas in 1D optical lattice system by using the genetic algorithm, and present a new method to find the ground-state wave function of the system. Through the optimized computation, the currently commonly used Thomas-Fermi approximation and Gaussian approximation model are revised and discussed, and the optimal ground state wave function is given.
Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.
The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation of trapped Bose atoms directly by obtaining the stable solutions for the condensate wave function from the 2D Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D system, and also the wave function of the 2D vortex state. In particular, the 2D energy state becomes less stable than the 3D case with the number of trapped atoms. The results of the 2D Bose condensation are also compared with those of the well-known 3D case.