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• W4313366931 abstract "Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the Jacobian matrix of the mapping. In this work, a detailed analysis of the transformation rules for Langevin equations under general nonlinear mappings is presented. We show how to identify systems with exact potentials by understanding their differential-geometric properties. To demonstrate the power of our method, we use it to derive exact potentials for broadly studied models of nonlinear deterministic and stochastic oscillations. In selected examples, we visualize the identified potentials. Our results imply a broad class of exactly solvable stochastic models, which can be self-consistently defined from given deterministic gradient systems." @default.
• W4313366931 created "2023-01-06" @default.
• W4313366931 creator A5005160866 @default.
• W4313366931 creator A5057539913 @default.
• W4313366931 date "2022-12-01" @default.
• W4313366931 modified "2023-09-30" @default.
• W4313366931 title "Exact potentials in multivariate Langevin equations" @default.
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• W4313366931 doi "https://doi.org/10.1063/5.0124031" @default.
• W4313366931 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/36587313" @default.
• W4313366931 hasPublicationYear "2022" @default.
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