Quantum kinetic theory of flux-carrying Brownian particles

TL;DR

This paper develops a quantum kinetic theory for flux-carrying Brownian particles, revealing unique chiral effects like vortex flows and antisymmetric diffusion, expanding understanding of non-standard dissipative quantum fluids.

Contribution

It introduces a quantum kinetic equation for flux-carrying particles, highlighting novel chiral effects and fluid dynamics absent in traditional Brownian motion models.

Findings

Quantum particles exhibit dissipationless vortex flows.

Flux effects act as vorticity sources in fluid dynamics.

Standard Boyle's law holds with a modified kinetic temperature.

Abstract

We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems. This model constitutes an effective description of two-dimensional dissipative particles violating both time-reversal and parity that is consistent with standard thermodynamics. By making use of an appropriate Breit-Wigner approximation, we derive the general form of its quantum kinetic equation for weak system-environment coupling. This encompasses the well-known Kramers equation of conventional Brownian motion as a particular instance. The influence of the underlying chiral symmetry is essentially twofold: the anomalous diffusive tensor picks up antisymmtretic components, and the drift term has an additional contribution which plays the role of an environmental torque acting upon the system particles. These yield an unconventional fluid dynamics that is absent in the standard (two-dimensional) Brownian motion subject to an external magnetic field or an active torque. For instance, the quantum single-particle system displays a dissipationless vortex flow in sharp contrast with ordinary diffusive fluids. We also provide preliminary results concerning the relevant hydrodynamics quantities, including the fluid vorticity and the vorticity flux, for the dilute scenario near thermal equilibrium. In particular, the flux-carrying effects manifest as vorticity sources in the Kelvin's circulation equation. Conversely, the energy kinetic density remains unchanged and the usual Boyle's law is recovered up to a reformulation of the kinetic temperature.