11,679 research outputs found
Microscopic dynamics underlying the anomalous diffusion
The time dependent Tsallis statistical distribution describing anomalous
diffusion is usually obtained in the literature as the solution of a non-linear
Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347
(1995)]. The scope of the present paper is twofold. Firstly we show that this
distribution can be obtained also as solution of the non-linear porous media
equation. Secondly we prove that the time dependent Tsallis distribution can be
obtained also as solution of a linear FP equation [G. Kaniadakis and P.
Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the
velocity, that describes a generalized Brownian motion. This linear FP equation
is shown to arise from a microscopic dynamics governed by a standard Langevin
equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200
Microscopic dynamics underlying the anomalous diffusion
The time dependent Tsallis statistical distribution describing anomalous
diffusion is usually obtained in the literature as the solution of a non-linear
Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347
(1995)]. The scope of the present paper is twofold. Firstly we show that this
distribution can be obtained also as solution of the non-linear porous media
equation. Secondly we prove that the time dependent Tsallis distribution can be
obtained also as solution of a linear FP equation [G. Kaniadakis and P.
Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the
velocity, that describes a generalized Brownian motion. This linear FP equation
is shown to arise from a microscopic dynamics governed by a standard Langevin
equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200
Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise
We study how thermal fluctuations affect the dynamics of vortices in the
two-dimensional classical, ferromagnetic, anisotropic Heisenberg model
depending on their additive or multiplicative character. Using a collective
coordinate theory, we analytically show that multiplicative noise, arising from
fluctuations in the local field term of the Landau-Lifshitz equations, and
Langevin-like additive noise both have the same effect on vortex dynamics
(within a very plausible assumption consistent with the collective coordinate
approach). This is a non-trivial result, as multiplicative and additive noises
usually modify the dynamics quite differently. We also carry out numerical
simulations of both versions of the model finding that they indeed give rise to
very similar vortex dynamics.Comment: 10 pages, 6 figure
Front propagation in stochastic neural fields
We analyse the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive–like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein–Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive
Energy representation for out-of-equilibrium Brownian-like systems: steady states and fluctuation relations
Stochastic dynamics in the energy representation is employed as a method to
study non-equilibrium Brownian-like systems. It is shown that the equation of
motion for the energy of such systems can be taken in the form of the Langevin
equation with multiplicative noise. Properties of the steady states are
examined by solving the Fokker-Planck equation for the energy distribution
functions. The generalized integral fluctuation theorem is deduced for the
systems characterized by the shifted probability flux operator. There are a
number of entropy and fluctuation relations such as the Hatano-Sasa identity
and the Jarzynski's equality that follow from this theorem.Comment: revtex4-1, 18 pages, extended discussion, references adde
Quantum state-dependent diffusion and multiplicative noise: a microscopic approach
The state-dependent diffusion, which concerns the Brownian motion of a
particle in inhomogeneous media has been described phenomenologically in a
number of ways. Based on a system-reservoir nonlinear coupling model we present
a microscopic approach to quantum state-dependent diffusion and multiplicative
noise in terms of a quantum Markovian Langevin description and an associated
Fokker-Planck equation in position space in the overdamped limit. We examine
the thermodynamic consistency and explore the possibility of observing a
quantum current, a generic quantum effect, as a consequence of this
state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B
{\bf 68}, 161 (1987)] in a classical context several years ago.Comment: To be published in Journal of Statistical Physics 28 pages, 3 figure
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