Fractional Langevin equation: overdamped, underdamped, and critical behaviors.
Fractional Langevin equation: overdamped, underdamped, and critical behaviors.
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DOI：
10.1103/physreve.78.031112
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发表时间：
2008-02
期刊：
影响因子：
--
通讯作者：
S. Burov;E. Barkai
中科院分区：
文献类型：
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作者：
S. Burov;E. Barkai
研究了调和束缚粒子的分数式 Langevin 方程的动态相图。结果表明，临界指数标志着系统行为的动态转变。发现了四种不同的临界指数。 (i) alpha_{c}=0.402+/-0.002 标志着向非单调欠阻尼阶段的转变，(ii) alpha_{R}=0.441... 标志着当外部振荡场驱动系统时向谐振阶段的转变，以及 (iii) alpha_{chi_{1}}=0.527... 和 (iv) alpha_{chi_{2}}=0.707...当存在这样的振荡场时，标记过渡到“损失”的双峰阶段。作为物理解释，我们提出笼效应，其中介质引起弹性类型的摩擦。描述过阻尼和欠阻尼状态的相图，无论是否有共振，都显示出与正常情况不同的行为。
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) alpha_{c}=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase, (ii) alpha_{R}=0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) alpha_{chi_{1}}=0.527... and (iv) alpha_{chi_{2}}=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.