title: Unified projection operator formalism in nonequilibrium statistical mechanics.
abstract: The method of projection operators, which plays an important role in the field of nonequilibrium statistical mechanics, has been established with the use of the Liouville-von Neumann equation for a density matrix to eliminate irrelevant information from a whole system. We formulate a unified and general projection operator method for dynamical variables. The main features of our formalism parallel those for the Liouville-von Neumann equation. (1) Two types of basic equations, time-convolution and time-convolutionless decompositions, are systematically obtained without specifying a projection operator. (2) Expansion formulas for both decompositions are also obtained. (3) Problems incorporating a time-dependent Liouville operator can be flexibly treated. We apply the formulas to problems in random frequency modulation and low field resonance. In conclusion, our formalism yields a more direct and easier means of determining the average time evolution of an operator than the one for the Liouville-von Neumann equation.
authors.affiliation: Department of Electronic Engineering, Faculty of Engineering, Yamanashi University, Takeda-4, Yamanashi 400, Japan.
authors.forename: C
authors.initials: C
authors.lastname: Uchiyama
authors.forename: F
authors.initials: F
authors.lastname: Shibata