Generalized partition function for Bose statistics and thermodynamic functions

摘要

Based on the density operator's coherent state representation [Phys. Lett. A252, 281(1999)], we extend the well-known Bose distribution's partition function #XI# #XI# = exp(-1/2 #beta#h#omega#) (1 - exp(-#beta#h#omega#))~(-1) for ideal photon gas (H = h#omega#(a~(dagger)a + 1/2)) to that of an assembly of photon gas interacting with nonlinear medium described by the Hamiltonian H = 1/2 (A~(dagger), A)#OMEGA#(_A-tilde~(A-tilde~(dagger))), where A = (a_1, a_2, ...,a_n), #OMEGA# is a symmetric matrix, and we report that the corresponding partition function is #XI# = ((-1)~n det[I - exp(-#beta# #OMEGA# #PI#)])~(1/2), #PI# ident to [_(I 0)~(0 -I)]. As a result, the generalized Bose distribution and thermodynamic functions are derived.