Fluctuations in Some Soluble Models in Quantum Statistical Mechanics

摘要

Following the work on the normality of fluctuations in the Dicke maser model in [1], we study fluctuations and some of their properties in a few solvable models in quantum statistical mechanics which exhibit a phase transition. In part I, which is the main core of this work, fluctuations are studied from the point of view of equilibrium statistical mechanics, as in referencen[l]. In part II, a linear response theory for a class of operators is briefly considered in the B.C.S. model. It is also proven in Appendix C that the infinite volume version of the Ornstein-Zernicke equation of state, relating the infinite-volume limit of the fluctuation of the number oprator, suitably defined, to the integral of a truncated correlation function, is not in general valid for the free Fermi and Bose gases.