Generalized Invariants and Quantum Evolution of Open Fermionic System

Abstract

Open systems acquire time-dependent coupling constants through interaction with an external field or environment. We generalize the Lewis-Riesenfeld invariant theorem to open system of quantum fields after second quantization. The generalized invariants and thereby the quantum evolution are found explicitly for time-dependent quadratic fermionic systems. The pair production of fermions is computed and other physical implications are discussed.

LaTex, 10 pages, no figures; replaced by the version to be published in Phys. Lett. A; the validity of the Liouville-von Neumann approach is clarified for non-normalizable and degenerate states; references added