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Current inversion in a periodically driven two-dimensional Brownian ratchet.

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Brownian ratchets show current reversals with driving frequency. This study uses discrete-space models to show low-frequency currents come from typical events, while high-frequency currents arise from rare events.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Brownian ratchets are known to exhibit current reversals.
  • The sign of the current depends on the driving frequency.

Purpose of the Study:

  • To introduce spatial discretization for efficient computation of currents in 2D Brownian ratchets.
  • To study Markovian dynamics conditioned on specific current values.

Main Methods:

  • Spatial discretization of a 2D Brownian ratchet.
  • Application of spectral methods for current computation.
  • Analysis of conditioned Markovian dynamics.

Main Results:

  • Low-frequency negative currents originate from typical events.
  • High-frequency positive currents originate from rare events.
  • Demonstration of frequency response sculpting for potential landscapes.

Conclusions:

  • Discrete-space models facilitate the study of conditioned dynamics in Brownian ratchets.
  • Understanding the origin of typical vs. rare events informs control strategies.
  • Potential landscapes can be engineered for specific frequency responses.