title: Microscopic description of quantum Lorentz gas and extension of the Boltzmann equation to entire space-time scale.
abstract: Irreversible processes of weakly coupled one-dimensional quantum perfect Lorentz gas are studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann operator. Without any phenomenological operations, such as a coarse-graining of space-time, or a truncation of the higher order correlation, we obtained irreversible processes in a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free length. Based on this solution, a limitation of the usual phenomenological Boltzmann equation, as well as an extension of the Boltzmann equation to entire space-time scale, is discussed.
authors.affiliation: Graduate School of Interdisciplinary Research, University of Yamanashi, Kofu 400-8511, Japan.
authors.forename: K
authors.initials: K
authors.lastname: Hashimoto
authors.affiliation: Department of Physical Science, Osaka Prefecture University, Sakai 599-8531, Japan.
authors.forename: K
authors.initials: K
authors.lastname: Kanki
authors.affiliation: Department of Physical Science, Osaka Prefecture University, Sakai 599-8531, Japan.
authors.forename: S
authors.initials: S
authors.lastname: Tanaka
authors.affiliation: Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: T
authors.initials: T
authors.lastname: Petrosky