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Area of Science:

  • Statistical Physics
  • Non-equilibrium Thermodynamics
  • Stochastic Processes

Background:

  • Generalized Langevin equations describe non-Markovian processes under thermal equilibrium.
  • Superdiffusion can emerge from vanishing memory kernel integrals, characteristic of super-Ohmic thermal baths.
  • Biexponential memory kernels offer a simple model for ballistic superdiffusion.

Purpose of the Study:

  • Investigate Markovian embeddings of non-Markovian processes.
  • Analyze the impact of potentials and forces on superdiffusion.
  • Characterize transient behaviors and their relation to asymptotic dynamics.

Main Methods:

  • Considered Markovian embedding schemes for generalized Langevin equations.
  • Numerically implemented the simplest four-dimensional Markovian embedding of a biexponential memory kernel model.
  • Studied the effects of periodic potentials and biasing forces on the dynamics.

Main Results:

  • Identified infinitely many Markovian embeddings for a specific non-Markovian model.
  • Demonstrated that periodic potentials change ballistic superdiffusion to normal diffusion.
  • Showed that biasing forces restore superdiffusion, with transients mimicking asymptotics.
  • Observed giant transient superdiffusion and superballistic currents in tilted washboard potentials.

Conclusions:

  • Non-Markovian dynamics exhibit complex transient behaviors that can differ from long-time asymptotics.
  • Periodic potentials can suppress superdiffusion, while external forces can re-establish it.
  • Intermediate asymptotics in tilted potentials can show giant superdiffusion, potentially misleading.