A note on Fermi lattice systems with bilinear hamiltonians

The dynamics of a v-dimensional Fermi lattice system with a bilinear hamiltonian is derived in a very simple and natural way. Moreover the thermodynamics of this linear system is treated by means of the so-called K.M.S.-equilibrium condition. Some words are devoted to ergodicity. As an example these general results are applied to an XY model and finally, for this concrete situation, attention is paid to the effect of boundary conditions on the elementary excitation spectrum in the thermodynamic limit.