Field theory reformulated without self-energy parts. Kinetic extension for the Lee model

Michel De Haan

Michel De Haan

Michel De Haan

The intuitive description of atomic levels requires the use of renormalized objects, with lifetime and dressed atomic levels. The reformulation of field theory for avoiding self-energy parts in the dynamical evolution enables us to provide such a description outside the scope of the usual quantum mechanics. That approach is illustrated here on a two-level system, interacting with a field, inside and outside the rotating wave approximation (RWA). A kinetic extension of the description is reached, enabling a statistical mixture to change its composition with time. The original reversible description is embedded in the new one and is recovered now from a restricted class of initial conditions. After dressing, the structure of the kinetic operators inside and outside the RWA is now common.

Dieter Schütte

Tomio Yamakoshi Petrosky

Kinetic theory in nonequilibrium statistical physics is discussed in terms of the complex spectral representation of the Liouvillian for quantum systems. We show that the collision operator appearing in the kinetic equation is the “self-energy part” of the Liouvillian. Solving the dispersion equation associated to the “self-energy part”, one can construct the resonance states of the Liouvillian which have complex eigenvalues. The imaginary part of the eigenvalue gives a decay rate in irreversible process in nonequilibrium statistical physics. As illustrations of the resonance states of the Liouvillian we consider two examples; one is a one-dimensional system in which a polaron is weakly interacting with a thermal reservoir consisting of an acoustic phonon field, and the other is a molecular chain that is described by the Davydov Hamiltonian, which has been introduced as a simple model that describes a protein chain. We show that the imaginary part of the spectrum of the Liouvillian in these systems has rich structures showing band structure, an accumulation point, and a fractal structure reminiscent of Hofstadter's butterfly.

Edward B. Manoukian, Nattapong Yongram