Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

S. Burov, E. Barkai

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127 Scopus citations

Abstract

The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) αc =0.402±0.002 marks a transition to a nonmonotonic underdamped phase, (ii) αR =0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) α χ1 =0.527... and (iv) α χ2 =0.707... mark transitions to a double-peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal.

Original languageEnglish
Article number031112
JournalPhysical Review E
Volume78
Issue number3
DOIs
StatePublished - 10 Sep 2008

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