Equilibrium States in Open Quantum Systems

Area of Science:

• Quantum Mechanics
• Open Quantum Systems
• Non-Hermitian Hamiltonians

Background:

• Open quantum systems interact with their environments, influencing their dynamics.
• Non-Hermitian Hamiltonians describe systems with gain or loss, often exhibiting complex behaviors like exceptional points.
• Understanding equilibrium states is crucial for characterizing the long-term behavior of quantum systems.

Purpose of the Study:

• To determine the existence of equilibrium states in open quantum systems coupled to multiple environments.
• To investigate the role of exceptional points and external mixing in these systems.
• To analyze the properties of wavefunctions for these equilibrium states.

Main Methods:

• Utilizing a non-Hermitian Hamilton operator to model the open quantum system.
• Analyzing the influence of exceptional points (EPs) and external mixing (EM) from the environment on system states.
• Examining the eigenfunctions of the Hamiltonian.

Main Results:

• Equilibrium states have been shown to exist in open quantum systems, provided they are sufficiently far from exceptional points.
• These equilibrium states differ from those found in corresponding closed quantum systems.
• The wavefunctions of these equilibrium states are orthogonal, despite the non-Hermitian nature of the Hamiltonian.

Conclusions:

• Equilibrium states can be established in open quantum systems interacting with multiple environments.
• The presence of exceptional points can disrupt the formation of equilibrium states.
• The orthogonality of wavefunctions in non-Hermitian systems under these conditions is a significant finding.