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Rate processes with dynamical disorder: a direct variational approach.

Ananya Debnath1, Rajarshi Chakrabarti, K L Sebastian

  • 1Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.

The Journal of Chemical Physics
|June 16, 2006
PubMed
Summary
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We developed a new method using path integral approximations to calculate survival probability for complex rate processes with dynamical disorder. This approach provides accurate bounds for survival probability and process rates, even when numerical solutions are infeasible.

Area of Science:

  • Theoretical Physics
  • Chemical Physics
  • Statistical Mechanics

Background:

  • Dynamical disorder significantly complicates the calculation of survival probabilities in rate processes.
  • Existing methods often struggle with complex systems where analytical or numerical solutions are intractable.

Purpose of the Study:

  • To develop a novel variational approximation for calculating survival probabilities in rate processes with dynamical disorder.
  • To establish rigorous upper and lower bounds for survival probability and the rate of the process.

Main Methods:

  • Utilizing the path integral approach to derive variational approximations.
  • Applying Jensen's inequality to establish bounds for survival probability.
  • Employing a trial action for exact path integral evaluation and parameter optimization.

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Main Results:

  • Derived both upper and lower bounds for survival probability using Jensen's inequality.
  • Developed a lower bound for the rate of the process.
  • Validated the method by applying it to Brownian motion in a harmonic potential with a sink, confirming the derived inequalities.

Conclusions:

  • The developed variational path integral method provides accurate bounds for survival probability and rates in systems with dynamical disorder.
  • This approach is particularly valuable for complex problems where exact numerical solutions are not feasible.
  • The method offers a powerful tool for theoretical and computational studies in various fields of physics and chemistry.