Statistical properties of the Hamiltonian generating phase state derived by using the generalized Hellmann–Feynman theorem

Abstract

We study statistical properties of the Hamiltonian ( H = ω a † a + κ a † N + 1 + κ N + 1 a ) generating phase state. Using the generalized Hellmann–Feynman theorem for ensemble average, we derive its mean energy and find the ratio of the mean energies contributed from the term a † a to that from a † N + 1 + κ N + 1 a . The relation on the entropy-variation with respect to the dynamic parameters ω and κ is also examined.