Passive quasi-free states of the noninteracting Fermi gas (Q1063212)

Let \((A,\alpha)\) be the \(C^*\)-dynamical system describing the noninteracting Fermi gas with a one-particle hamiltonian H having no point spectrum. Then \(\omega\) is a state of A corresponding to a Fermi- Dirac distribution (or a limit of them) if and only if it is quasi-free and passive in the sense of \textit{W. Pusz} and \textit{S. L. Woronowicz} [Commun. Math. Phys. 58, 273-290 (1978)]. The conditions under which the ''no point spectrum'' hypothesis can be weakened are examined. Besides a proof of the Fermi-Dirac distribution, this result emphasizes the role of the passivity condition in the study of equilibrium states.