The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry

TL;DR

This paper derives a formal influence superoperator for Fermionic systems, enabling improved simulation of their dynamics and spectra by accounting for arbitrary parity symmetry and deriving generalized master equations.

Contribution

It introduces a canonical derivation of an influence superoperator for Fermionic environments, extending existing methods to arbitrary parity symmetry conditions.

Findings

Derived a generalized-Lindblad master equation in the Markovian limit.

Developed a generalized hierarchical equations of motion for Fermionic systems.

Provided a formalism for accurate evaluation of system correlation functions and spectra.

Abstract

We present a canonical derivation of an influence superoperator which generates the reduced dynamics of a Fermionic quantum system linearly coupled to a Fermionic environment initially at thermal equilibrium. We use this formalism to derive a generalized-Lindblad master equation (in the Markovian limit) and a generalized version of the hierarchical equations of motion valid in arbitrary parity-symmetry conditions, important for the correct evaluation of system correlation functions and spectra.