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Relation between the dynamic friction kernel and the random force

  • Page ID
    5309
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    From the definitions of \(R(t)\) and \(\zeta(t)\), it is straightforward to show that there is a relation between them of the form

    \[\langle R(0)R(t)\rangle = kT\zeta(t)\]

    This relation is known as the second fluctuation dissipation theorem. The fact that it involves a simple autocorrelation function of the random force is particular to the harmonic bath model. We will see later that a more general form of this relation exists, valid for a general bath. This relation must be kept in mind when introducing models for \(R(t)\) and \zeta(t). In effect, it acts as a constraint on the possible ways in which one can model the random force and friction kernel.

    Contributors and Attributions

    Mark Tuckerman (New York University)


    Relation between the dynamic friction kernel and the random force is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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