Microscopic description of irreversibility in quantum Lorentz gas by complex spectral analysis of the Liouvillian outside the Hilbert space.

Irreversible process of a weakly coupled one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouvillian. Without any phenomenological operations, such as a coarse-graining of space-time or a truncation of the higher order correlation, we obtained irreversible processes on 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. The list of development of the complex spectral analysis of the Hamiltonian (instead of the Liouvillian) in quantum optical systems and in quantum nano-devices is also presented.