Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

TL;DR

This paper derives exact expressions for the density matrix elements of a driven, dissipative quantum system with a quadratic Hamiltonian, using a generating function approach based on Heisenberg equations.

Contribution

It introduces a method to compute exact density matrix elements for quadratic Hamiltonian systems in driven dissipative settings, expanding analytical tools in quantum dynamics.

Findings

Exact density matrix elements obtained from generating functions.

Method applicable to various special and limiting cases.

Provides a framework for analyzing driven dissipative quantum systems.

Abstract

For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.