Correlation inequalities for noninteracting Bose gases

Abstract

For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities <N_i>_N < <N_i>_{N+1}, <N_i N_j>_N < <N_i>_N <N_j>_N for i\neq j, \partial <N_0>_N/\partial β>0 and <N_i>^+_N < <N_i>_N. Here N_i is the occupation number of the ith eigenstate of H^0, βis the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.

a further inequality added

Cited by in corpus (4)

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