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

We study statistical properties of the Hamiltonian 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 . The relation on the entropy-variation with respect to the dynamic parameters ω and κ is also examined.