Non-linear Brownian motion: the problem of obtaining the thermal Langevin equation for a non-Gaussian bath

Dubkov, A. A.; Hänggi, Peter; Goychuk, Igor

doi:10.1088/1742-5468/2009/01/p01034

Cited by 24 publications

(29 citation statements)

References 33 publications

(46 reference statements)

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“…the detailed-balance condition and the Gibbs form of the thermal equilibrium condition lead to the speeddependent random force F rand = ψ(v) 2/dt N , where N is a normally distributed random force with zero mean and unit variance, and [21] …”

Section: E Langevin Simulationsmentioning

confidence: 99%

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Individual Tracer Atoms in an Ultracold Dilute Gas

et al. 2017

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Understanding the motion of a tracer particle in a rarefied gas is of fundamental and practical importance. We report the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study the nonequilibrium relaxation of the initial nonthermal state and detect the effect of single collisions which has eluded observation so far. We show that after few collisions, the measured spatial distribution of the light tracer atoms is correctly described by a generalized Langevin equation with a velocity-dependent friction coefficient, over a large range of Knudsen numbers.

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Section: E Langevin Simulationsmentioning

confidence: 99%

“…To our knowledge, the predictions of the Langevin equation with speed-dependent damping coefficient (3) have never been verified experimentally so far. We also note that owing to the detailed-balance condition, the nonlinear friction (3) implies a multiplicative, velocity-dependent fluctuating force [19,21].…”

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confidence: 99%

Individual Tracer Atoms in an Ultracold Dilute Gas

et al. 2017

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“…(6) satisfies the detailed balance condition, the system can be regarded as associated with thermal fluctuation (See Ref. [52], where thermal non-Gaussian noise is studied from the viewpoint of the detailed balance). On the other hand, inherent properties of athermal fluctuation originate from the violation of the detailed balance.…”

Section: Setupmentioning

confidence: 99%

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

et al. 2015

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We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper (Kanazawa et al. in Phys Rev Lett 114:090601-090606, 2015). We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.

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“…within linear FDT, but not necessarily otherwise [66]. In the following, V(x, t) = U(x) À xf(t), includes some periodic spatial potential U(x) = U(x + L) with period L. It is modulated in time by an external force f(t).…”

Section: Introductionmentioning

confidence: 99%

Subdiffusive Brownian ratchets rocked by a periodic force

Goychuk

2010

Chemical Physics

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This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to the realm of antipersistent non-Markovian subdiffusion in viscoelastic media. A periodically forced subdiffusion in a parity-broken ratchet potential is considered within the non-Markovian generalized Langevin equation (GLE) description with a power-law memory kernel $\eta(t)\propto t^{-\alpha}$ ($0<\alpha<1$). It is shown that subdiffusive rectification currents, defined through the mean displacement and subvelocity $v_{\alpha}$, $<\delta x(t)>\sim v_{\alpha} t^{\alpha}/ \Gamma(1+\alpha)$, emerge asymptotically due to the breaking of the detailed balance symmetry by driving. The asymptotic exponent is $\alpha$, the same as for free subdiffusion, $<\delta x^2(t)>\propto t^\alpha$. However, a transient to this regime with some time-dependent $\alpha_{\rm eff}(t)$ gradually decaying in time, $\alpha\leq \alpha_{\rm eff}(t)\leq 1$, can be very slow depending on the barrier height and the driving field strength. In striking contrast to its normal diffusion counterpart, the anomalous rectification current is absent asymptotically in the limit of adiabatic driving with frequency $\Omega\to 0$, displaying a resonance like dependence on the driving frequency. However, an anomalous current inversion occurs for a sufficiently fast driving, like in the normal diffusion case. In the lowest order of the driving field, such a rectification current presents a quadratic response effect. Beyond perturbation regime it exhibits a broad maximum versus the driving field strength. Moreover, anomalous current exhibits a maximum versus the potential amplitude

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Non-linear Brownian motion: the problem of obtaining the thermal Langevin equation for a non-Gaussian bath

Cited by 24 publications

References 33 publications

Individual Tracer Atoms in an Ultracold Dilute Gas

Individual Tracer Atoms in an Ultracold Dilute Gas

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

Subdiffusive Brownian ratchets rocked by a periodic force

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