# An operator derivation of the Feynman-Vernon theory, with applications to the generating function of bath energy changes and to anharmonic baths

## TL;DR

This paper introduces a super-operator based derivation of the Feynman-Vernon theory, enabling direct calculation of bath energy change generating functions and extension to anharmonic baths via cumulant expansion.

## Contribution

It provides a new, more straightforward derivation of the Feynman-Vernon influence functional and extends the framework to anharmonic baths using cumulant expansions.

## Key findings

- Derived a super-operator formulation of Feynman-Vernon theory.
- Established a method to compute energy change generating functions.
- Extended the approach to include anharmonic baths through cumulants.

## Abstract

We present a derivation of the Feynman-Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths. This generating function is given by a Feynman-Vernon-like influence functional, with only time shifts in some of the kernels. We further show that the approach can be extended to anharmonic baths by an expansion in cumulants. Every non-zero cumulant of certain environment correlation functions thus gives a kernel in a higher-order term in the Feynman-Vernon action.