Fizika Nizkikh Temperatur: Volume 48, Number 1 (January 2022), p. 23-29    ( to contents , go back )

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
E-mail: andrij.rovenchak@gmail.com
yurikryn@gmail.com

pos Анотація:861

Received June 15, 2021, published online November 25, 2021

Abstract

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.

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