ON A CLASS OF EQUILIBRIUM STATES UNDER KUBO-MARTIN-SCHWINGER BOUNDARY CONDITION .I. FERMIONS

Using the Kubo-Martin-Schwinger boundary condition for equilibrium states of quantum statistical mechanics of fermion gas, we prove that for T≠;0 a one-particle evolution (corresponding essentially to bilinear hamiltonians) generally defines a unique equilibrium state, which is quasi-free. Conversely any quasi-free state is the equilibrium state for a single one-particle evolution if it has no Fock part in its product decomposition. Limiting cases where T → 0 and T → ∞ are studied. In the case where T → 0 one shows that the state generally converges to a Fock state linked to the evolution. © 1969 Springer-Verlag.