Showing 1–3 of 3 results for author: Touya, C
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Dipole diffusion in a random electrical potential
Authors:
Clement Touya,
David S. Dean,
Clement Sire
Abstract:
We study the Langevin dynamics of a dipole diffusing in a random electrical field E derived from a quenched Gaussian potential. We show that in a suitable adiabatic limit (where the dynamics of the dipole moment is much faster than the dynamics of its position), one can reduce the coupled stochastic equations to an effective Langevin equation for a particle diffusing in an effective potential wi…
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We study the Langevin dynamics of a dipole diffusing in a random electrical field E derived from a quenched Gaussian potential. We show that in a suitable adiabatic limit (where the dynamics of the dipole moment is much faster than the dynamics of its position), one can reduce the coupled stochastic equations to an effective Langevin equation for a particle diffusing in an effective potential with a spatially varying and anisotropic local diffusivity $κ_{ij}$. Analytic results, close to the adiabatic limit, for the diffusion constant $κ_e$ are found in one dimension and a finite temperature dynamical transition is found. The system is also studied numerically. In particular, we study the anomalous diffusion exponent in the low temperature regime. Our findings strongly support the conclusion that the location of the dynamical transition and the anomalous diffusion exponents are determined by purely static considerations, i.e. they are independent of the relative values of the diffusion constants of the particle position and its dipole moment.
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Submitted 12 June, 2009;
originally announced June 2009.
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Self Similar Renormalization Group Applied to Diffusion in non-Gaussian Potentials
Authors:
David S. Dean,
Clement Touya
Abstract:
We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(φ)$ of a Gaussian field $φ$. A self similar renormalization group analysis is applied to a mathematically related problem of the effective permeability of a random porous medium from which the diffusion constant of the random potential…
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We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(φ)$ of a Gaussian field $φ$. A self similar renormalization group analysis is applied to a mathematically related problem of the effective permeability of a random porous medium from which the diffusion constant of the random potential problem can be extracted. This renormalization group approach reproduces practically all known exact results in one and two dimensions. The results are confronted with numerical simulations and we find that their accuracy is good up to points well beyond the expected perturbative regime. The results obtained are also tentatively applied to interacting particle systems without disorder and we obtain expressions for the self-diffusion constant in terms of the excess thermodynamic entropy. This result is of a form that has commonly been used to fit the self diffusion constant in molecular dynamics simulations.
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Submitted 3 April, 2008;
originally announced April 2008.
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Dynamical transition for a particle in a squared Gaussian potential
Authors:
C. Touya,
D. S. Dean
Abstract:
We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $ψ= φ^2/2$ where $φ$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations w…
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We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $ψ= φ^2/2$ where $φ$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.
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Submitted 17 October, 2006;
originally announced October 2006.