Dynamics of the phase transition in the weakly interacting Bose gas

Evgeny Levich, Victor Yakhot

Hoang Van Quyet

Yu. Kagan, Boris V. Svistunov, Gora V. Shlyapnikov

Jian-hui Wang, Yong-li Ma

We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.

B. Ya. Balagurov, Валентин Григорьевич Вакс

Bernhard Irsigler, Axel Pelster

We investigate the dimensionally induced phase transition from the normal to the Bose-Einstein-condensed phase for a weakly interacting Bose gas in an optical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popov theory, where we include numerically exact hopping energies and effective interaction strengths. At first we determine the critical chemical potential, where we find a much better agreement with recent experimental data than a pure Hartree-Fock treatment. This finding originates from an important correction due to quantum fluctuations, which are enhanced in lower dimensions. Furthermore, we determine for the one-dimensional to three-dimensional transition the power-law exponent of the critical temperature for two different noninteracting Bose gas models yielding the same value of 1/2, which indicates that they belong to the same universality class. For the weakly interacting Bose gas we find for both models that this exponent is robust with respect to finite interaction strengths.