Strongly coupled matter field and nonanalytic decay rate of dipole molecules in a waveguide

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.

Quasibound states in the continuum in a two channel quantum wire with an adatom

We report the prediction of quasibound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for certain systems in which the continuum is formed by two overlapping energy bands. We illustrate this effect using a quantum wire system with two channels and an attached adatom. When the energy bands of the two channels overlap, a would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second such state lays above the lower energy band). Unlike the bound states in continuum predicted by von Neumann and Wigner, these states occur for a wide region of parameter space.

Exact Markovian kinetic equation for a quantum Brownian oscillator

We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincaré's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast, for nonintegrable systems, the invariant subspaces follow a dynamics with broken time symmetry, involving generalized functions. This result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces. We comment on the relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.