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- W2021004543 abstract "In the limit of weak noise, the conditional probabilities of a damped, noise-driven anharmonic oscillator can be expressed (at least formally) in terms of solutions to a nonlinear ordinary differential equation (“Onsager-Machlup” equation) of fourth order in the time derivative. In the case of a one-dimensional oscillator, this equation is recast in the form of a mapping; and in the limit of long time and weak time-independent friction, it is shown how to reduce the iteration of this map to quadratures. This procedure is checked by using it to reproduce a number of standard results usually derived in other ways. In connection with the statistical mechanics of electron-positron colliding-beam storage rings, an attempt is also made to apply this mapping formalism to the case of weak, periodically time-dependent friction. When no frequency in the Fourier decomposition of the friction coefficient is close to an (even, for symmetric potentials) integral multiple of the (amplitude-dependent) frequency of the oscillator, then results can be derived that parallel those obtained in the case of constant friction. Otherwise (“thermal resonance”) the situation is not clear." @default.
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- W2021004543 date "1985-03-01" @default.
- W2021004543 modified "2023-10-18" @default.
- W2021004543 title "A semiclassical theory of underdamped nonlinear Brownian processes" @default.
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- W2021004543 doi "https://doi.org/10.1016/0003-4916(85)90369-0" @default.
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