Ideal Bose gas in steep one-dimensional traps
Andrij Rovenchak and Yuri Krynytskyi
Professor Ivan Vakarchuk Department for Theoretical Physics, Ivan Franko National University of Lviv Lviv 79005, Ukraine
Received June 15, 2021, published online November 25, 2021
We study thermodynamic properties of a one-dimensional ideal Bose gas trapped by a steep potential of an exponential type U(q) = U0[e(2q/a)b-1]. Fugacity, energy, and heat capacity of such a system are calculated for various combinations of the potential parameters as well for several values of the number of particles N. Both the thermodynamic limit and finite N are considered. Estimations for the single-particle spectrum asymptotics are obtained in the analytical form involving the Lambert W function. In the thermodynamic limit, the Bose–Einstein condensation is predicted for 0 < b <2. We associate such behavior with an effective temperature-dependent space dimensionality arising due to the influence of the external potential of the analyzed type.
Key words: Bose–Einstein condensation, one-dimensional traps, specific heat, quasiclassical approximation, exponential potential, Lambert W function.