  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.
