Statistical physics of flux-carrying Brownian particles

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.

Quantum kinetic theory of flux-carrying Brownian particles

“…The reason to follow this route are twofold: first, it will provide us valuable intuition to understand the consequences of the flux attachment upon the quantum kinetics and hydrodynamics, and second, the path integral formalism has played a major role in the description of quantum Brownian systems [27,28,30,31]. Thanks to the separability property of the initial state, the nonequilibrium generating functional characteristic of the flux-carrying Brownian particles can be readily obtained from the partition function provided in [32] after performing the Wick rotation [27]. Once this is done, we then switch to the phase-space Wigner framework by following the prescription presented in [41,45,46].…”

“…The open quantum system dynamics is captured by the recently introduced MCS description [25,32], which essentially distinguishes from the standard Brownian motion [27][28][29] in the fact that a dynamical pseudomagnetic flux tube is attached to each system particle. This must not be confused with the ordinary flux notion from the standard Maxwell electrodynamics (e.g.…”

“…According to basic electrodynamics, one may expect that the presence of a magneticlike flux gives rise to a magneticlike vector potential (for instance, static charges are able to generate simultaneously electric and magneticlike fields in MCS electrodynamics [56]). Indeed, the authors in [32] show that flux-carrying Brownian particles are subject to a dynamical pseudomagnetic field at the microscopic level, so they can be thought of as 'dressed' dissipative particles in much the same fashion as composite particles in condensed matter physics. Here, it is important to emphasize that such pseudomagnetic field completely arises from the coupling with the environment, rather than from an external source as occurs in the conventional Brownian motion in presence of an auxiliary magnetic field.…”

“…As stated in the introduction, our starting point is the partition function derived from (5) when the coupled system-environment complex, composed of the 2D harmonic particles and the environmental MCS field, is in a canonical equilibrium state at inverse β = 1/k B T (that is e −β ĤSys−MCS up to normalization, with ĤSys−MCS being the Hamiltonian obtained from (5) by the Legendre transform). This was computed in [32] and it permitted to extensively analyse the free energy, internal energy, the entropy and the heat capacity of the flux-carrying Brownian motion. Let us stress that the motivation here is substantially distinct from [32], since the present work is in the line to study the open quantum dynamics when the coupled system-environment complex is initially in a tensor-product state ρ0 ⊗ ρβ : the particle system is in an arbitrary state ρ0 , while the environment is supposed to be in a canonical equilibrium state ρβ characterized by the inverse temperature β (that is e −β ĤMCS up to normalization, with ĤMCS being the Hamiltonian obtained from (7) by the Legendre transform after ignoring the system-environment coupling).…”

“…the microscopic constituents behave as 'chiral' particles). Remarkably enough, the flux-carrying Brownian particle exhibits magneticlike properties beyond the celebrated Landau diamagnetism theory [32], so that it may shed further light on the influence of chirality on the kinetics and hydrodynamics of 2D quantum fluids. Let us stress that this novel microscopic description is significantly distinct from most previous treatments within open quantum system theory to the best of our knowledge [27,30], in particular, those related to the search for observable signatures of the Berry curvature [33,34] or spatial noncommutative effects [35][36][37][38].…”