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arXiv · 0712.3407

The Critical Exponent of the Fractional Langevin Equation is $α_c\approx 0.402$

S. Burov·E. Barkai
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Abstract

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 $α_c= 0.402\pm 0.002$ marks a transition to a non-monotonic under-damped phase. The critical exponent $α_{R}=0.441...$ 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 under-damped, the over-damped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal.

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S. Burov, E. Barkai. 2007-12-20. The Critical Exponent of the Fractional Langevin Equation is $α_c\approx 0.402$. https://doi.org/10.1103/physrevlett.100.070601

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