欠阻尼布朗粒子在倾斜搓板势中的输运态
Transport Regimes of Underdamped Brownian Particles in a Tilted Washboard Potential
摘要：
在本文中，一个全面的检查的温度和偏压依赖的扩散制度的欠阻尼布朗粒子。一个温度阈值之间的异常和正常的扩散行为的转变位于，产生一个新的相图系统。在低温制度，该系统表现出明显的负微分迁移率，由于持久的，长时间的亚扩散在低偏压;在高温（或临界偏压），该系统迅速接近正常扩散低于中间势垒高度，$U_o \sim k_B T$。考虑到数值结果，比较过阻尼的情况下，和相关的Kramers多稳态逃逸问题，它表明，低偏置非单调的温度依赖性的扩散，持续的亚扩散，和负微分迁移率可以追溯到惯性效应，这是明显的速度功率谱的振荡模式在低偏置。在巨扩散制度中，速度功率谱表现出耦合之间的“锁定”和“运行”状态，与阻尼，驱动平面摆的极限环的临界偏压附近的主频率相对应的特征频率。非线性二次谐波产生，对应于振荡瞬态异常扩散率，观察到随着偏压的增加和温度的降低，进一步强调低噪声扩散问题收敛到无噪声动力学，补充分析结果的平均速度[L. Cheng和N.K. Yip，Physica D，2015]。
英文摘要：
In this paper, a comprehensive examination of the temperature- and bias-dependent diffusion regimes of underdamped Brownian particles is presented. A temperature threshold for a transition between anomalous and normal diffusive behaviors is located, yielding a new phase diagram for the system. In the low-temperature regime, the system exhibits an apparent negative differential mobility due to persistent, long-time subdiffusion at low-bias; at high temperature (or critical bias,) the system rapidly approaches normal diffusion below an intermediate barrier height, $U_o \sim k_B T$. By consideration of numerical results, comparison to the overdamped case, and the related Kramers multistable escape problems, it is demonstrated that the low-bias non-monotonic temperature dependence of the diffusivity, persistent subdiffusion, and negative differential mobility can be traced to inertial effects, which are evident in the oscillatory modes of the velocity power spectra at low bias. In the giant diffusion regime, the velocity power spectra exhibit coupling between the ``locked" and ``running" states, with a characteristic frequency corresponding to the principal frequency of the limit cycles of a damped, driven plane pendulum near critical bias. Non-linear second harmonic generation, corresponding to oscillatory transient anomalous diffusivity, is observed with increasing bias and decreasing temperature, further emphasizing that the low-noise diffusion problem converges to noise-free dynamics, complementing analytic results for the average velocity [L. Cheng and N.K. Yip, Physica D, 2015].
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