Non-Normalizable Quasi-Equilibrium Solution of the Fokker–Planck Equation for Nonconfining Fields

  title={Non-Normalizable Quasi-Equilibrium Solution of the Fokker–Planck Equation for Nonconfining Fields},
  author={Celia Anteneodo and Lucianno Defaveri and Eli Barkai and David A. Kessler},
We investigate the overdamped Langevin motion for particles in a potential well that is asymptotically flat. When the potential well is deep as compared to the temperature, physical observables, like the mean square displacement, are essentially time-independent over a long time interval, the stagnation epoch. However, the standard Boltzmann-Gibbs (BG) distribution is non-normalizable, given that the usual partition function is divergent. For this regime, we have previously shown that a… Expand

Figures from this paper


From Non-Normalizable Boltzmann-Gibbs Statistics to Infinite-Ergodic Theory.
This work merges infinite-ergodic theory with Boltzmann-Gibbs statistics, thus extending the scope of the latter while shedding new light on the concept of ergodicity. Expand
Solution of the Fokker-Planck Equation with a Logarithmic Potential
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large |x| using the Fokker-Planck equation. An eigenfunction expansion shows thatExpand
Regularized Boltzmann-Gibbs statistics for a Brownian particle in a nonconfining field
We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depthExpand
Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem.
This work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multifractal anomalous diffusion, as it is complementary to the central limit theorem. Expand
The Fokker-Planck Equation
In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for oneExpand
Shift in the velocity of a front due to a cutoff
We consider the effect of a small cutoff $\ensuremath{\varepsilon}$ on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simpleExpand
Freezing Transition in the Barrier Crossing Rate of a Diffusing Particle.
It is shown that the freezing transition occurs when in the associated quantum problem, the gap between the ground state (bound) and the continuum of scattering states vanishes. Expand
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Abstract Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type are presented as a useful approach for the description of transport dynamics in complex systemsExpand
Reaction-rate theory: fifty years after Kramers
The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermallyExpand
Aging generates regular motions in weakly chaotic systems
Using intermittent maps with infinite invariant measures, we investigate the universality of time-averaged observables under aging conditions. According to Aaronson's Darling-Kac theorem, in non-agedExpand