Action Functional for a Particle with Damping

TL;DR

This paper derives an action functional for a damped particle that is invariant under time reversal, connecting it to the Caldeira-Leggett model without assuming weak coupling to a bath.

Contribution

It introduces a novel derivation of the particle's action functional that does not rely on weak coupling assumptions, enhancing understanding of dissipative quantum systems.

Findings

Derived an invariant action functional for damped particles.

Connected the functional to the Caldeira-Leggett model.

Provided a new perspective on dissipation without weak coupling assumption.

Abstract

In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional is exactly the effective action of Caldeira-Leggett model but, in our approach, it is derived without the assumption that the particle is weakly coupled to a bath of infinite harmonic oscillators.