Kinetics of a bose gas in harmonic traps: nonergodic behavior
Abstract
The quantum Boltzmann equation describes kinetics of a degenerate quantum gas. For applications to a trapped Bose gas, it takes the following form *be1 fracdn_idt&=& sum_j,k,lδ (ɛi +ɛj -ɛk -ɛl )*g(i,j,k,l) &&(; n_k*n_l*(1+n_i)*(1+n_j)-n_i*n_j*(1+n_l)*(1+n_k)) * with ni the average number of particles in the state i of the three dimension al harmonic trap labelled by quantum numbers (i_x,i_y,i_z). The delta function ensures energy conservation and the matrix element g(i,j,k,l) is a two-body scattering matrix element which includes an overlap integral of the fou r harmonic oscillator eigenstates associated with the states i,j,k and l. Previous studies of this equation (M.Holland, J.Williams, K.Coakley, J.Cooper, Phys.Rev.A,55,3670, (1996)), (C W Gardiner and P Zoller, Phys.Rev.A(1997)) assume an ergodic approximation (degenerate energy states have equal particle numbers) in order to simplify numerical simula tions. In this study we include a limited number of low lying states without making the ergodic assumption. Interesting nonergodic effects will be reported, and comparisons between the ergodic and nonergodic kinetics will be made.
- Publication:
-
APS Southeastern Section Meeting Abstracts
- Pub Date:
- November 1997
- Bibcode:
- 1997APS..SES..AD08G