Generalized Invariants and Quantum Evolution of Open Fermionic System

TL;DR

This paper extends the Lewis-Riesenfeld invariant theorem to open quantum fermionic systems, providing explicit solutions for their evolution and analyzing phenomena like fermion pair production.

Contribution

It introduces a generalized invariant framework for open fermionic systems, enabling explicit quantum evolution analysis after second quantization.

Findings

Explicit invariants for time-dependent quadratic fermionic systems derived

Fermion pair production computed under time-dependent conditions

Physical implications of the generalized invariants discussed

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.