Correlation inequalities for noninteracting Bose gases
Abstract
For a noninteracting Bose gas with a fixed one-body Hamiltonian H0 independent of the number of particles we derive the inequalities <Ni>N < <Ni>N+1, <Ni Nj>N < <Ni>N <Nj>N for i≠ j, ∂ <N0>N/∂ β >0 and <Ni>+N < <Ni>N. Here Ni is the occupation number of the ith eigenstate of H0, β is the inverse temperature and the superscript + refers to adding an extra level to those of H0. The results follow from the convexity of the N-particle free energy as a function of N.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.