1208.3651 (M. O. C. Pires)

Generalized Wick's theorem at finite temperature for a quadratic
Hamiltonian    [PDF]

M. O. C. Pires

In Gaudin (1960), Michel Gaudin showed the Wick's theorem at finite temperature using a diagonal Hamiltonian. We extend the Gaudin's prove for a statistical density operator which depend on a quadratic Hamiltonian. To illustrate the utility of the theorem, we evaluate the ratio $\sqrt{[<\hat{N}^2>-<\hat{N}>^2]/<\hat{N}>}$ of a homogeneous weakly interacting Bose gas at temperature below the Bose-Einstein condensation temperature. At this condition, the quadratic Hamiltonian approximation is valued and, in this evaluation, we show the sub-Poissonian behaviour of the fundamental state distribution at zero temperature.

View original: http://arxiv.org/abs/1208.3651