Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

TL;DR

This paper develops a microscopic model for dissipative dynamics of 2D harmonic oscillators using Maxwell-Chern-Simons theory, revealing vortex-like Brownian motion and second-order corrections to traditional models.

Contribution

It introduces a novel first-principles description of 2D dissipative systems based on topological gauge theory, extending conventional Brownian motion models.

Findings

Reveals vortex-like Brownian dynamics due to topological gauge effects.

Identifies second-order corrections to standard damped harmonic oscillator.

Shows intrinsic dissipative phenomena linked to system dimensionality.

Abstract

The conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of two-dimensional harmonic oscillators that contains the conventional Brownian motion as a particular instance. This description is derived from first principles in the framework of the so-called Maxwell-Chern-Simons electrodynamics, or also known, Abelian topological massive gauge theory. Disregarding backreaction effects and endowing the system Hamiltonian with a suitable renormalized potential interaction, the conceived description is equivalent to a minimal-coupling theory with a gauge field giving rise to a fluctuating force that mimics the Lorentz force induced by a particle-attached magnetic flux. We show that the underlying symmetry structure of the theory (i.e. time-reverse asymmetry and parity violation) yields an interacting vortex-like Brownian dynamics for the system particles. An explicit comparison to the conventional Brownian motion in the quantum Markovian limit reveals that the proposed description represents a second-order correction to the well-known damped harmonic oscillator, which manifests that there may be dissipative phenomena intrinsic to the dimensionality of the interesting system.