Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

S. Burov, E. Barkai

Research output: Contribution to journalArticlepeer-review

127 Scopus citations


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
Issue number3
StatePublished - 10 Sep 2008


Dive into the research topics of 'Fractional Langevin equation: Overdamped, underdamped, and critical behaviors'. Together they form a unique fingerprint.

Cite this