# Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory

Evstigneev M, Reimann P (2005) *PHYSICAL REVIEW E* 72(4).

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Abstract

We consider periodically driven noisy systems in the limit of long times. To deduce their asymptotic time-periodic probability distributions, two approaches are commonly used: adiabatic theory, valid if driving is very slow, and linear-response theory, applicable when driving is weak. We introduce an approximation scheme that combines these two approaches to yield the driven probability distribution even when driving is strong and moderately fast, so that both linear-response and adiabatic approximations break down. The high accuracy of this scheme is demonstrated on a driven overdamped noisy oscillator in a bistable quartic potential.

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Evstigneev M, Reimann P. Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory.

*PHYSICAL REVIEW E*. 2005;72(4).Evstigneev, M., & Reimann, P. (2005). Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory.

*PHYSICAL REVIEW E*,*72*(4). doi:10.1103/PhysRevE.72.045101Evstigneev, M., and Reimann, P. (2005). Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory.

*PHYSICAL REVIEW E*72.Evstigneev, M., & Reimann, P., 2005. Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory.

*PHYSICAL REVIEW E*, 72(4). M. Evstigneev and P. Reimann, “Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory”,

*PHYSICAL REVIEW E*, vol. 72, 2005. Evstigneev, M., Reimann, P.: Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory. PHYSICAL REVIEW E. 72, (2005).

Evstigneev, Mykhaylo, and Reimann, Peter. “Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory”.

*PHYSICAL REVIEW E*72.4 (2005).
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