Bose systems in linear traps: Exact calculations versus effective space dimensionality

Abstract

Systems of noninteracting bosons trapped by linear potentials V(r) = αr, where r = |r|, are studied in one and three dimensions. For the latter problem, an interpolation formula is suggested for energy levels between n, ℓ ∼ 10 and the WKB limit. Thermodynamic functions are calculated for N = 10, … ,104 particles using discrete energy spectrum. The specific heat and fugacity are compared to the results of the quasiclassical approach, in which the external potential effectively increases the space dimensionality. As expected, the comparison demonstrates that the thermodynamic functions obtained using the discrete spectra rapidly approach the quasiclassical ones in a space with the effectively tripled space dimensionality as N increases.