Symmetry examples in open quantum dynamics

TL;DR

This paper investigates dependent symmetries in open quantum dynamics, showing how they influence the form of subsystem evolution and relate to constants of motion, with examples illustrating various scenarios.

Contribution

It introduces the concept of dependent symmetries in open quantum systems and demonstrates how they can simplify the analysis of subsystem dynamics.

Findings

Dependent symmetries determine the form of open quantum dynamics.

Symmetries can be linked to constants of motion in specific situations.

Examples show diverse relationships between symmetries and constants of motion.

Abstract

Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry implies a particular form for the results of the open dynamics. The forms exhibit the symmetries very simply. It is shown directly, without assuming anything about the symmetry, that the dynamics produces the form, but knowing the symmetry and the form it implies can reduce what needs to be done to work out the dynamics; pieces can be deduced from the symmetry rather that calculated from the dynamics. Symmetries can be related to constants of the motion in new ways. A quantity might be a dependent constant of the motion, constant only for particular situations of the subsystem in the larger system. In particular, a generator of dependent symmetries could represent a quantity that is a dependent constant of the motion for the same situations as for the symmetries. The examples present a variety of possibilities. Sometimes a generator of dependent symmetries does represent a dependent constant of the motion. Sometimes it does not. Sometimes no quantity is a dependent constant of the motion. Sometimes every quantity is.