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Stationary energy probability density of oscillators driven by a random external force
Vicenç Méndez1, Daniel Campos, Werner Horsthemke
1Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
Summary
This study provides analytical solutions for the energy distribution of oscillators under Gaussian noise. We analyze both linear and nonlinear systems, offering insights into energy dynamics.
Area of Science:
- Statistical physics
- Nonlinear dynamics
- Stochastic processes
Background:
- Oscillators are fundamental systems in physics.
- Understanding their behavior under noise is crucial.
- Previous studies often simplified noise models.
Purpose of the Study:
- To derive rigorous analytical results for the stationary energy probability density function.
- To analyze linear and nonlinear oscillators driven by Gaussian noise.
- To investigate energy distribution and partition in these systems.
Main Methods:
- Derivation of analytical expressions for energy probability density.
- Analysis of harmonic oscillators with colored Gaussian noise.
- Analysis of nonlinear oscillators with white Gaussian noise.
- Use of Langevin simulations for validation.
Main Results:
- Obtained exact analytical results for stationary energy distributions.
- Derived expressions for stationary energy moments.
- Investigated the kinetic and potential energy partition.
- Illustrated results with specific noise and potential models.
Conclusions:
- The analytical framework provides a robust tool for studying noisy oscillators.
- Results offer a deeper understanding of energy dynamics in complex systems.
- The findings are validated by numerical simulations.
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