Effective area and expansion energy of trapped Bose gas in a combined magnetic–optical potential

Finite Size Correction to The Thermo-Magnetic Properties of Charged Bose Gas

“…The q-potential for Bose gas using the eigenvalues (4) given by, Expanding the logarithm to express the q potential as a sum over Bose-Einstein distribution and using the semiclassical approximation in which the summation over n is converted into an integral weighted by an the DOS [8] we have where qo = − ln(1 − z) is the contribution of the ground states, z = e −β(E0−µ) is the effective fugacity and β = 1/kT . Substituting by , the thermodynamic potential (4) reads…”

Thermodynamic properties of a rotating Bose--Einstein condensation in a deep optical lattice

“…Two slight modifications for the DOS in [29,30,31,32] are considered by one of the authors for rotating condensate [15] and trapped boson gas in a combined magnetic-optical potential [11]. However, for the spectrum in Eq.…”

“…Generalization to a many particle system is straightforward. Following the method outlined in our previous paper [11,15], the DOS for the many particle system in a fast rotation regime, i.e. Ω ∼ ω ⊥ , is given by…”

“…These effects can be seen more clearly by calculating the critical temperature. The latter is obtained as usual [11,30,32] by setting N 0 /N in Eq. (19) equal to zero, thus…”

“…While the preceding papers elaborate the thermodynamic properties of a BEC in an optical lattice [11,12,13,14] and a rotating BEC in harmonic potential [15,16,17] , the present paper investigates the thermodynamic properties of a rotating BEC in a deep optical lattice [18]. Separately, fast rotation or the deepness of the optical potential is affected significantly by the thermodynamic properties of the system [19,20] compared to the pure harmonically BEC.…”