Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations

Abstract

We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions explicitely. The CTRW curve exhibits aging, i.e. it is not translationally invariant in the time-domain. This is different from what happens under fractional Fokker-Planck conditions.

References in corpus (1)

• Thermodynamics and Fractional Fokker-Planck Equations

Cited by in corpus (24)

• Lévy walks
• Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
• Continuous time random walk and parametric subordination in fractional diffusion
• Aging Continuous Time Random Walks
• CTRW Pathways to the Fractional Diffusion Equation
• The inspection paradox in stochastic resetting
• Levy Flights in External Force Fields: From Models to Equations
• Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
• Transmission of Information between Complex Networks: 1/f-Resonance
• Beyond the Death of Linear Response: 1/f optimal information transport
• Brain, Music and non-Poisson Renewal Processes
• Linear response to perturbation of non-exponential renewal processes
• Non-Markovian non-stationary completely positive open quantum system dynamics
• The Unequal Twins - Probability Distributions Aren't Everything
• Quantum response theory for open systems and its application to Hall conductance
• Subdiffusion in an external force field
• Fractional Fokker-Planck subdiffusion in alternating fields
• Lévy flights in inhomogeneous environments
• Aging two-state process with Lévy walk and Brownian motion
• Anomalous diffusion. A competition between the very large jumps in physical and operational times
• Non-Ergodic Complexity Management
• Kerr effect as a tool for the investigation of dynamic heterogeneities
• Aging Feynman-Kac Equation
• Spectral properties of stochastic processes possessing finite propagation velocity