Fluctuation-driven directed transport in the presence of Levy flights

Abstract

Numerical evidence of directed transport driven by symmetric Levy noise in time-independent ratchet potentials in the absence of an external tilting force is presented. The results are based on the numerical solution of the fractional Fokker-Planck equation in a periodic potential and the corresponding Langevin equation with Levy noise. The Levy noise drives the system out of thermodynamic equilibrium and an up-hill net current is generated. For small values of the noise intensity there is an optimal value of the Levy noise index yielding the maximum current. The direction and magnitude of the current can be manipulated by changing the Levy noise asymmetry and the potential asymmetry.

References in corpus (14)

• Brownian motors: noisy transport far from equilibrium
• The scaling laws of human travel
• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Non-diffusive transport in plasma turbulence: a fractional diffusion approach
• Optimal target search on a fast folding polymer chain with volume exchange
• Anomalous jumping in a double-well potential
• Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries
• Lévy flights in a steep potential well
• Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field
• Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
• Levy Flights in External Force Fields: From Models to Equations
• Levy Flights in Inhomogeneous Media
• Escape driven by $\alpha$-stable white noises
• Transport in a Levy ratchet: Group velocity and distribution spread

Cited by in corpus (17)

• Matrix approach to discrete fractional calculus II: partial fractional differential equations
• Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis
• Lévy Ratchet in a Weak Noise Limit: Theory and Simulation
• Stationary states in single-well potentials under symmetric Levy noises
• Transport in periodic potentials induced by fractional Gaussian noise
• Heat and work distributions for mixed Gauss-Cauchy process
• Lévy flights on a comb and the plasma staircase
• Levy ratchets with dichotomic random flashing
• Escape from the potential well: competition between long jumps and long waiting times
• Analytic solution to space-fractional Fokker-Planck equations for tempered-stable Lévy distributions with spatially linear, time-dependent drift
• Noise driven current reversal and stabilisation in the tilted ratchet potential subject to tempered stable Lévy noise
• Competition between ac driving-forces and Lévy flights in a nonthermal ratchet
• Finite Domain Anomalous Spreading Consistent with First and Second Law
• Large Deviations for SDE driven by Heavy-tailed Lévy Processes
• Strong Existence and Uniqueness for Singular SDEs Driven by Stable Processes
• How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme
• Rotation-translation coupling of a double-headed brownian motor in a traveling-wave potential