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Numerical path integral calculation of the probability function and exit time: an application to non-gradient drift
Fernando Mora1,2, Pierre Coullet2, Sergio Rica1
1Facultad de Ingeniería y Ciencias and UAI Physics Center, Universidad Adolfo Ibáñez, Santiago, Chile.
Summary
This study presents numerical solutions for stochastic processes with non-gradient drift Langevin forces and noise. The method accurately tracks probability density functions and calculates exit times, showing excellent agreement with theory in the weak noise limit.
Area of Science:
- Physics
- Chemistry
- Biology
- Non-equilibrium thermodynamics
Background:
- Stochastic processes are fundamental to understanding systems with inherent randomness.
- Non-gradient drift Langevin forces and noise are common in physical and chemical systems.
- Accurate computation of probability density functions and exit times is crucial for system analysis.
Purpose of the Study:
- To develop numerical solutions for stochastic processes involving non-gradient drift Langevin forces and noise.
- To accurately follow the temporal evolution of probability density functions.
- To compute exit times for systems with arbitrary noise characteristics.
Main Methods:
- Utilizing the path integral representation of stochastic processes.
- Implementing numerical solutions for non-gradient drift Langevin dynamics.
- Comparing numerical results with theoretical calculations.
Main Results:
- The developed numerical method successfully tracks the temporal evolution of probability density functions.
- Exit times were computed accurately for systems with arbitrary noise.
- Excellent agreement was observed between numerical solutions and theoretical calculations in the weak noise limit.
Conclusions:
- The path integral approach provides a robust framework for solving complex stochastic processes.
- The numerical solutions are reliable for analyzing systems with non-gradient drift and noise.
- This method offers a valuable tool for studying dissipative structures in non-equilibrium systems.
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