2008/02/26 by Stanislav Burov, S. Burov, Eli Barkai +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Critical exponent #Fractional Differential Equations Solutions #Langevin dynamics #Langevin equation #Mathematical physics #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Resonance (particle physics) #Statistical physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.78.031112
18 pages, 15 figures
arxiv created 2008/02/26 · openalex publication_date 2008/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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) alphac=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase, (ii) alphaR=0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) alpha_chi1=0.527... and (iv) alpha_chi2=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.