Critical exponent of the fractional Langevin equation

S. Burov, E. Barkai

Research output: Contribution to journalArticlepeer-review

105 Scopus citations


We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent αc=0.402±0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent αR=0.441... marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal.

Original languageEnglish
Article number070601
JournalPhysical Review Letters
Issue number7
StatePublished - 22 Feb 2008


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