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

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

2007-12-20

arxiv.org/abs/0712.3407v1

Phys. Rev. Lett. 100, 070601 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.100.070601

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 $\alpha_c= 0.402\pm 0.002$ marks a transition to a non-monotonic under-damped phase. The critical exponent $\alpha_{R}=0.441...$ 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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