Nontrivial eigenvalues of the Liouvillian of an open quantum system

TL;DR

This paper develops methods to identify complex eigenvalues of the Liouvillian in open quantum systems, revealing nontrivial eigenvalues not predictable from the Hamiltonian, using a quantum dot model and diagrammatic techniques.

Contribution

It introduces new approaches to find nontrivial Liouvillian eigenvalues by reducing the problem to a two-particle Hamiltonian and analyzing Green's function correlations.

Findings

Identification of nontrivial eigenvalues in a quantum dot model.

Reduction of the eigenvalue problem to a two-particle Hamiltonian.

Diagram expansion reveals correlations between bra and ket states.

Abstract

We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem.