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

Abstract

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.

Statistical physics of flux-carrying Brownian particles

“…α, λ = 1, 2). The open quantum system dynamics is captured by the recently introduced dissipative MCS description [25,31], which is consistent with the (non-relativistic) MCS electrodynamics in the long-wavelength (i.e. dipole approximation [48]) and low-energy regime (i.e.…”

“…As anticipated in the introduction, this description essentially distinguishes from the standard Brownian motion [26][27][28] in the fact that a dynamical pseudomagnetic flux tube is attached to each system particle, which must not be confused with the ordinary flux notion from the standard Maxwell electrodynamics. We also note that the treatment in [25,31] differs from the one discussed in Refs. [21,22]: the flux tube in the latter is self-induced by an emergent (external) gauge field within the classical Fröhlich-Bogoliubov theory (which is a particular instance of the standard Maxwell electrodynamics), while in our case the flux attachment is a primary constraint built upon the microscopic Lagrangian description of the coupled systemenvironment complex (see A for further details on the microscopic Lagrangian).…”

“…Motivated by the relevance of the flux attachment notion in the treatment of 2D quantum many-particle systems, the CS theory was recently applied to open quantum systems in [25]. More precisely, by just demanding space-time locality as well as local U(1)-gauge invariance, the authors devised a rather fundamental microscopic description of the 2D Brownian motion (dubbed flux-carrying Brownian motion) in the context of the nonrelativistic Maxwell-Chern-Simons (MCS) electrodynamics.…”

“…The main goal of our paper is to address the quantum kinetic theory characteristic of the flux-carrying Brownian description [25,31] by following a perturbative approach of the flux attachment effects. Interestingly, the latter make it significantly distinct from the kinetic theory based on the conventional Brownian motion [30,[38][39][40][41][42].…”

New point-like sources and a conducting surface in Maxwell–Chern–Simons electrodynamics

“…One of the most important class of models of this kind is the so called Maxwell-Chern-Simons electrodynamics [2], or Abelian topological massive gauge theory [3], which is relevant because it is simultaneously massive and gauge invariant. Theoretical aspects of Maxwell-Chern-Simons electrodynamics have been investigated in Casimir effect [4][5][6][7][8][9], quantum dissipation of harmonic systems [10], quantum electrodynamics (QED 3 ) [11][12][13][14][15], dynamical mass generation [16,17], condensed matter physics (see, for instance, Ref. [18] and references therein), description of graphene properties [19][20][21][22][23][24], noncommutativity [25][26][27][28], strings theory [29], dynamics of vortices [30,31], and with a planar boundary [32][33][34][35][36], to mention just a few.…”