# Action principle and weak invariants

## TL;DR

This paper explores the relationship between weak invariants and the action principle in master equations, revealing that auxiliary operators can be viewed as weak invariants, thus connecting two fundamental concepts in quantum dynamics.

## Contribution

It demonstrates that auxiliary operators in the action principle for master equations can be interpreted as weak invariants, providing new insights into their roles in quantum evolution.

## Key findings

- Weak invariants have time-varying spectra but conserved expectation values.
- Auxiliary operators in the action principle are equivalent to weak invariants.
- The relationship enhances understanding of quantum master equations.

## Abstract

A weak invariant associated with a master equation is characterized in such a way that its spectrum is not constant in time but its expectation value is conserved under time evolution generated by the master equation. Here, an intriguing relationship between the concept of weak invariants and the action principle for master equations based on the auxiliary operator formalism is revealed. It is shown that the auxiliary operator can be thought of as a weak invariant.

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Source: https://tomesphere.com/paper/1903.02302