时间周期外力驱动下欠阻尼空间周期系统的温度反常扩散系数
Temperature-abnormal diffusivity in underdamped space-periodic systems driven by external time-periodic force
摘要：
本文研究了在一维对称空间周期势场中，由于具有零平均值的对称时间周期强迫，欠阻尼布朗粒子的扩散增强。我们发现，扩散率可以提高了许多数量级，在适当的选择强迫振幅和频率。扩散率表现出反常的温度依赖性，在强迫振幅超过一定值。在任何固定的强迫频率$Ω$正常的温度依赖性的扩散率恢复在足够低的温度，$T<T_\textrm{TAD}(Ω)$ -与恒定的外部强迫的问题。在固定的温度下，在小的强迫频率的扩散缓慢下降与$Ω$，或（在较强的强迫）经过一个最大值附近的$Ω_2$，倒数超扩散阶段的持续时间。在高频率下，在$Ω_2$和在潜在的最小值的振荡频率的一部分之间，扩散率示出与$Ω$根据幂律减少，与指数相关的瞬态超扩散指数。这种行为被发现类似的正弦的情况下，在时间和分段恒定的周期性（“平方”）强迫。
英文摘要：
We present a study of diffusion enhancement of underdamped Brownian particles in 1D symmetric space-periodic potential due to external symmetric time-periodic forcing with zero mean. We show that the diffusivity can be enhanced by many orders of magnitude at appropriate choice of the forcing amplitude and frequency. The diffusivity demonstrates TAD, abnormal (decreasing) temperature dependence at forcing amplitudes exceeding certain value. At any fixed forcing frequency $Ω$ normal temperature dependence of the diffusivity is restored at low enough temperatures, $T<T_\textrm{TAD}(Ω)$ --- in contrast with the problem with constant external forcing. At fixed temperature at small forcing frequency the diffusivity either slowly decreases with $Ω$, or (at stronger forcing) goes through a maximum near $Ω_2$, reciprocal superdiffusion stage duration. At high frequencies, between $Ω_2$ and a fraction of the oscillation frequency at the potential minimum, the diffusivity is shown to decrease with $Ω$ according to a power law, with exponent related to the transient superdiffusion exponent. This behavior is found similar for the cases of sinusoidal in time and piecewise constant periodic ("square") forcing.
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