Effective Calculation of thermodynamic properties of finite Bose-Einstein systems

Duan-Liang Xiao, Meng-Yun Lai, Xiao‐Yin Pan

We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties, particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N → ∞ .

K. Matsuda

Peter Borrmann, Jens Harting, Oliver Mülken +1 more

We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in some approximation, e.g., like Bose-Einstein condensates in magnetic traps. The numerical effort of our computation scheme grows only linearly with the number of particles. As an example, we calculate the relative ground-state fluctuations and specific heats for ideal Bose gases with a finite number of particles enclosed in containers of different shapes.

K. Matsuda

T. Haugset, H. Haugerud, F. Ravndal

Hend A. Abdel-Gany, Ali Y. ELLITHI, Abdelhamid Abdelhak Galal +1 more

In this paper, we suggest a conventional semiclassical approximation to calculate several thermodynamic quantities of a rotating Bose-Einstein condensation in a deep optical lattice. Expressions for the condensation fraction, critical temperature, and heat capacity are derived analytically. These expressions are obtained by considering the standard harmonic approximation of the deep optical lattice potential. The suggested approach is able to include the the finite size and the positive chemical potential effects simultaneously. The advantage of our suggested approach is in its simplicity, in comparison to the quantum-mechanical calculations (Bose-Hubbard model). Moreover, its generality allows the treatment of a finite temperature regime