Brownian motion and magnetism (original) (raw)
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Ann. Phys.(Leipzig), 2004
In systems possessing a spatial or dynamical symmetry breaking thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro-and even on the nano-scale. This theme is known as "Brownian motor" concept. The constructive role of (the generally overdamped) Brownian motion is exemplified for a noise-induced transport of particles within various set-ups. We first present the working principles and characteristics with a proof-of-principle device, a diffusive temperature Brownian motor. Next, we consider very recent applications based on the phenomenon of signal mixing. The latter is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors. The subtleties and also the potential for Brownian motors operating in the quantum regime are outlined and some state-of-the-art applications, together with future roadways, are presented.
Classical and quantum Brownian motion in an electromagnetic field
Fortschritte der Physik, 2016
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and Caldeira-Leggett framework for the quantum problem. We study the time evolution in configuration space of the probability distribution of an initial pure state represented by an asymmetrical Gaussian wave function and show that it can be described as the superposition of (a) the classical motion of the center of mass, (b) a rotation around the mean position, and (c) a spreading processes along the principal axes.
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We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integro-differential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.
SpringerBriefs in Physics, 2019
In the previous chapter we described the main theoretical attempts to treat the grains motion detected by Robert Brown. These theories are purely classical and rely on phenomenological equations, i.e. equations that are not derived in a Hamiltonian framework, but are proposed starting from experimental results that one aims to interpret.
Fundamental aspects of quantum Brownian motion
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2005
With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary nonequilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.
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Dynamics of a magnetic active Brownian particle under a uniform magnetic field
Physical Review E, 2017
The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment that reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α. In this work, the time-dependent active diffusivity and the crossover time (τ cross)-from ballistic to diffusive regimes-are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α, the particle undergoes a directional (or ballistic) propulsive motion at very short times (t ≪ τ cross). In this regime the correlation function decreases linearly with time and the active diffusivity increases with it. It the opposite time limit (t ≫ τ cross), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α = 0), the crossover time is equal to the characteristic timescale for rotational diffusion, τrot. In the presence of a magnetic field (α > 0), the correlation function, the active diffusivity, and the crossover time decrease with increasing α. The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τ cross ≪ τrot. In the limit of weak fields (α ≪ 1), the crossover time decreases quadratically with α, while in the limit of strong fields (α ≫ 1) it decays asymptotically as α −1. The results are in excellent agreement with those obtained by Brownian dynamics simulations.
Quantum Brownian motion in a magnetic field: Transition from monotonic to oscillatory behaviour
Physica A: Statistical Mechanics and its Applications
We investigate the Brownian motion of a charged particle in a magnetic field. We study this in the high temperature classical and low temperature quantum domains. In both domains, we observe a transition of the mean square displacement from a monotonic behaviour to a damped oscillatory behaviour as one increases the strength of the magnetic field. When the strength of the magnetic field is negligible, the mean square displacement grows linearly with time in the classical domain and logarithmically with time in the quantum domain. We notice that these features of the mean square displacement are robust and remain essentially the same for an Ohmic dissipation model and a single relaxation time model for the memory kernel. The predictions stemming from our analysis can be tested against experiments in trapped cold ions.