3 research outputs found
Thermodynamics of ideal quantum gas with fractional statistics in D dimensions
We present exact and explicit results for the thermodynamic properties
(isochores, isotherms, isobars, response functions, velocity of sound) of a
quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1
connecting bosons (g=0) and fermions (g=1). In D=1 the results are equivalent
to those of the Calogero-Sutherland model. Emphasis is given to the crossover
between boson-like and fermion-like features, caused by aspects of the
statistical interaction that mimic long-range attraction and short-range
repulsion. The full isochoric heat capacity and the leading low-T term of the
isobaric expansivity in D=2 are independent of g. The onset of Bose-Einstein
condensation along the isobar occurs at a nonzero transition temperature in all
dimensions. The T-dependence of the velocity of sound is in simple relation to
isochores and isobars. The effects of soft container walls are accounted for
rigorously for the case of a pure power-law potential.Comment: 15 pages, 31 figure
Thermodynamics of statistically interacting quantum gas in D dimensions
We present the exact thermodynamics (isochores, isotherms, isobars, response
functions) of a statistically interacting quantum gas in D dimensions. The
results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear
Schroedinger model, a gas with repulsive two-body contact potential. In all
dimensions the ideal boson and fermion gases are recovered in the weak-coupling
and strong-coupling limits, respectively. For all nonzero couplings ideal
fermion gas behavior emerges for D>>1 and, in the limit D->infinity, a phase
transition occurs at T>0. Significant deviations from ideal quantum gas
behavior are found for intermediate coupling and finite D.Comment: 12 pages and 19 figure