Stationary state in Brownian systems with Lorentz force

Abdoli, Iman; Vuijk, Hidde Derk; Wittmann, René; Sommer, Jens‐Uwe; Brader, Joseph M.; Sharma, Abhinav

doi:10.1103/physrevresearch.2.023381

Cited by 22 publications

(30 citation statements)

References 30 publications

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“…(3) and ( 4) show the generation of a disipationless vortex flow in the single-particle scenario. This stands in contrast to the conventional Brownian motion in presence of an external magnetic field, in which there is no fluxes at thermal equilibrium [43,44,47]. We notice that the small strength of both the steady flow density and the fluid vorticity is in agreement with the subsidiary condition (45), which establishes that the flux-carrying effects must remain perturbative in comparison with the dissipative effects (otherwise the quantum kinetics (58) would deviate from the low-lying description provided by (1) [25,31]).…”

Section: Quantum Hydrodynamics At Late Timesmentioning

confidence: 65%

“…For sake of simplicity, we consider a radially symmetric initial Gaussian state with a simple covariance matrix V (0) = I 4 (this corresponds to the extensively studied coherent state in quantum optics). The reason to focus the attention on this kind of states is because it retrieves a purely diffusive flow (which is parallel to the particle density gradient) in the case of the conventional Brownian motion subject to an uniform magnetic field [43,44]. Hence, the vortex flow shown here is exclusive to the flux-carrying Brownian motion [25] (it is a direct consequence of the broken time reversal and parity symmetries).…”

Section: Quantum Hydrodynamics At Late Timesmentioning

confidence: 99%

“…Compared with the well-known Kramers equation from the conventional Brownian motion, the kinetic equation here displays an additional collision term encoding a diffusive matrix (as well as stress tensor) with antisymmetric components, and a rotational drift which arises out of an environmental torque acting upon the fluxcarrying Brownian particles. We argue that this equation encompasses a wide class of previously treated chiral-fluid effects: for instance, the rotational drift resemblances the active torque in chiral active fluids [11][12][13][14], whereas the antrysimetric diffusive coefficients are responsible for a nondiffusive flow which is common to conventional Brownian particles subject to a Lorentz force [43,44]. However, we further showed that the flux-carrying effects give rise to an unconventional fluid dynamics at equilibrium conditions, in contrast to most instances of parity violating or time-reversal breaking fluids [2,3,47].…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

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Statistical physics of flux-carrying Brownian particles

Valido

2020

Annals of Physics

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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.

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Section: Quantum Hydrodynamics At Late Timesmentioning

confidence: 65%

Section: Quantum Hydrodynamics At Late Timesmentioning

confidence: 99%

Section: Summary and Concluding Remarksmentioning

confidence: 99%

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Statistical physics of flux-carrying Brownian particles

Valido

2020

Annals of Physics

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“…This generates a non-zero probability current in the system and eventually a non-equilibrium steady state is attained [18][19][20][21][22][23][24][25]. Steady state properties under resetting have also been studied in a wide spectrum of stochastic processes namely anomalous diffusion [26,27], underdamped process [28], random acceleration process [29], scaled Brownian motion [30], continuous time random walk [31,32], Lévy flights [33], telegraphic process [34], run and tumble motion [35,36], and others [37][38][39][40][41][42]. Steady state properties under resetting were also studied in many-body interacting systems such as fluctuating interfaces [43] and exclusion processes [44,45].…”

Section: Introductionmentioning

confidence: 99%

Resetting with stochastic return through linear confining potential

Gupta,

Pal,

Kundu

2020

Preprint

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We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred location (say, the origin), here we consider a finite time resetting process facilitated by an external linear potential V (x) = λ|x| (λ > 0). When resetting occurs, the trap is switched on and the particle experiences a force −∂ x V (x) which helps the particle to return to the resetting location. The trap is switched off as soon as the particle makes a first passage to the origin. Subsequently, the particle resumes its free diffusion motion and the process keeps repeating. In this set-up, the system attains a non-equilibrium steady state. We study the relaxation to this steady state by analytically computing the position distribution of the particle at all time and then analysing this distribution using the spectral properties of the corresponding Fokker-Planck operator. As seen for the instantaneous resetting problem, we observe a 'cone spreading' relaxation with travelling fronts such that there is an inner core region around the resetting point that reaches the steady state, while the region outside the core still grows ballistically with time. Notably, our method, based on spectral properties, complements the existing renewal formalism and reveals the intricate mathematical structure responsible for such relaxation phenomena. We verify our analytical results against extensive numerical simulations.

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“…Even in overdamped systems, the hallmark signature of Lorentz force -deflection of trajectories in the direction perpendicular to the velocity -is manifested. This deflection gives rise to additional Lorentz fluxes perpendicular to the typical diffusive fluxes [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Correlations in multithermostat Brownian systems with Lorentz force

Abdoli,

Kalz,

Vuijk

et al. 2020

Preprint

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We study the motion of a Brownian particle subjected to Lorentz force due to an external magnetic field. Each spatial degree of freedom of the particle is coupled to a different thermostat. We show that the magnetic field results in correlation between different velocity components in the stationary state. Integrating the velocity autocorrelation matrix, we obtain the diffusion tensor that enters the Fokker-Planck equation for the probability density. The eigenvectors of the tensor do not match with the temperature axes. We further show that in the presence of an isotropic confining potential, an unusual, flux-free steady state emerges which is characterized by a non-Boltzmann density distribution, which can be rotated by reversing the magnetic field. The nontrivial steady state properties of our system result from the Lorentz force induced coupling of the spatial degrees of freedom which cease to exist in equilibrium corresponding to a single-temperature system.

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Stationary state in Brownian systems with Lorentz force

Cited by 22 publications

References 30 publications

Statistical physics of flux-carrying Brownian particles

Statistical physics of flux-carrying Brownian particles

Resetting with stochastic return through linear confining potential

Correlations in multithermostat Brownian systems with Lorentz force

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