The Valididy of the Langevin Equation
J Frenkel, J C Taylor
TL;DR
This paper investigates the conditions under which the classical and quantum Langevin equations are valid, especially when the system's equations of motion are nonlinear or involve bilinear interactions with the environment.
Contribution
It provides a detailed analysis of the validity limits of the Langevin equation in nonlinear and bilinear interaction scenarios.
Findings
Valid near the system's natural frequency
Invalid for nonlinear system equations
No general validity condition for nonlinear cases
Abstract
The validity of the Langevin equation (both classical and quantum) is studied in cases when not all the equations of motion are linear. In particular, a model is studied in which the interaction is bilinear in the environment variables. We conclude that the equation is valid only for frequencies close to the frequency of the system alone. If the equation of motion of the system alone is nonlinear, we are unable to find a condition for the validity of the Langevin equation.
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Taxonomy
TopicsComplex Network Analysis Techniques · Gene Regulatory Network Analysis · Machine Learning in Materials Science