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Approach to equilibrium in adiabatically evolving potentials.

H S Samanta1, J K Bhattacharjee, R Ramaswamy

  • 1Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India. tphss@mahendra.iacs.res.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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Time-dependent potentials accelerate diffusion over energy barriers. Adiabatic evolution of a harmonic potential to a double-well potential reduces Kramers time, enhancing barrier crossing efficiency.

Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Computational Physics

Background:

  • Studying the evolution of probability densities in overdamped dynamics is crucial for understanding systems transitioning between states.
  • Time-dependent potentials can introduce complex behaviors not observed in static systems.
  • The Kramers time quantifies the rate of barrier crossing in potential landscapes.

Purpose of the Study:

  • To investigate the impact of time-dependent potentials on the evolution of probability densities towards equilibrium.
  • To explore how specific potential variations, like from harmonic to double-well, affect diffusion dynamics.
  • To identify and analyze resonance phenomena arising from the interplay between potential evolution timescales and barrier crossing times.

Main Methods:

Related Experiment Videos

  • Simulating overdamped dynamics for a one-dimensional potential evolving over time.
  • Employing a specific time variation form: V(x,t) = V(f)(x) + (V(i) - V(f)) e^(-lambda t).
  • Analyzing the characteristic Kramers time for different initial and final potential configurations.

Main Results:

  • Adiabatic evolution from a simple harmonic to a double-well potential leads to a decreased Kramers time.
  • Time-dependent potentials can significantly enhance the efficiency of diffusion over energy barriers.
  • Resonance effects are observed when the potential variation timescale matches the Kramers time for displaced harmonic potentials.

Conclusions:

  • Time dependence in potentials can unexpectedly accelerate barrier crossing processes.
  • The observed reduction in Kramers time highlights a mechanism for more efficient diffusion.
  • Resonance phenomena offer new insights into controlling dynamic processes in complex potential landscapes.