Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in
d dimension and the equivalence of trapped quantum gases
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in
d=3 and
d=2. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap the gases under harmonic potential in
d=1. This result suggests the equivalence between Bose and Fermi gases which is already established for
d=1 by M M Faruk (J Stat Phys, DOI 10.1007/s10955-015-1344-4). Surprisingly our investigation also shows that the virial coefficients of two dimensional free quantum gases are identical to the virial coefficients of one dimensional harmonically trapped quantum gases.
Abstract Exchange symmetry affects the occupation of allowed states in quantum gases. If the density of the gas is very low, we can ignore this and forget about exchange symmetry; this is what we do for gases at room temperature. But if the density is high, the effects of exchange symmetry become very important and it really starts to matter whether the particles you are considering are fermions or bosons. This chapter considers quantum gases in detail. It considers non-interacting fermion and boson gases, and discusses Bose-Einstein condensation.