Non-Hermitian Quantum Physics of Open Systems

TL;DR

This paper discusses the theoretical framework of open quantum systems using non-Hermitian Hamiltonians, highlighting eigenfunction fluctuations and their high efficiency in systems like photosynthesis.

Contribution

It reviews the projection operator formalism for open quantum systems and emphasizes the importance of eigenfunctions and their fluctuations in non-Hermitian Hamiltonians.

Findings

Eigenfunction fluctuations occur with nearly 100% efficiency in gain and loss systems.

Non-Hermitian Hamiltonians are crucial for describing open quantum systems.

Applications include understanding photosynthesis processes.

Abstract

Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical description of open quantum systems by means of a projection operator formalism elaborated many years ago, and applied by now to the description of different open quantum systems. The Hamiltonian describing the open quantum system is non-Hermitian. Most studied are the eigenvalues of the non-Hermitian Hamiltonian of many-particle systems embedded in one environment. We point to the unsolved problems of this method when applied to the description of realistic many-body systems. We then underline the role played by the eigenfunctions of the non-Hermitian Hamiltonian. Very interesting results originate from the fluctuations of the eigenfunctions in systems with gain and loss of excitons. They occur with an efficiency of nearly 100\%. An example is the photosynthesis.