par Fujita, Shigeji
Référence Physica, 27, 10, page (940-956)
Publication Publié, 1961-10
Article révisé par les pairs
Résumé : The generalized master equation for a quantum gas due to Résibois is analysed with the aid of new diagrams, which are intimately related to operator diagrams invented by Prigogine and Résibois. It is shown that part of this equation, which is important for the derivation of generalized Boltzmann equation, has a form analogous to the Pauli equation with the probability of quantum statistical transition between many-body states, the probability being expressible in terms of a matrix A formally identical to the so-called transition matrix defined in the modern theory of potential scattering. By use of the technique devised by the author for developping the binary collision expansion of the quantum statistical pair propagator, many-body elements of A are expanded in terms of two-body elements of A. The generalized Boltzmann equation or the reduced equation for the average occupation number of a single-particle momentum state is derived in a usual manner from the generalized master equation. It is pointed out that the Uehling-Uhlenbeck equation for a hard-sphere Fermi gas is valid only in the lowest order a2, a being diameter of a hard sphere, at the very low temperatures. The new equation valid up to the order a2(apFh-1>pF being the Fermi momentum of an ideal Fermi gas and h Planck's constant is given explicitely in the text. Any higher order corrections could easily be calculated in the frame work of the theory. © 1957.