Dynamical stabilization and time in open quantum systems

TL;DR

This paper explores how time is defined and behaves in open quantum systems with non-Hermitian Hamiltonians, revealing a dynamical phase transition that stabilizes the system and bounds decay rates.

Contribution

It introduces a framework where the imaginary part of the non-Hermitian Hamiltonian acts as a time operator, and describes a dynamical phase transition causing stabilization.

Findings

Dynamical phase transition occurs at high state density.

Time is bounded from below due to stabilization.

Decay widths do not increase indefinitely.

Abstract

The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process.