周期力作用下的亚扩散布朗棘轮
Subdiffusive Brownian ratchets rocked by a periodic force
摘要：
这项工作提出了一个推广的著名的摇摆马尔可夫布朗棘轮领域的反持续非马尔可夫亚扩散粘弹性介质。在具有幂律记忆核$η(t)\propto t^{-α}$（$0<α<1$）的非马尔可夫广义朗之万方程（GLE）描述下，研究了宇称破缺棘轮势中周期性受迫子扩散.结果表明，亚扩散整流电流，定义通过平均位移和亚速度$v_α$，$<δx(t)>\sim v_α t^α/ Γ(1+α)$，出现渐近由于打破的细致平衡对称性的驱动。渐近指数为$α$，与自由子扩散的指数$<δx^2(t)>\propto t^α$相同。然而，根据势垒高度和驱动场强度，到具有一些随时间逐渐衰减的时间依赖性$α_{\rm eff}(t)$的该状态的瞬态$α\leq α_{\rm eff}(t)\leq 1$可能非常慢。与其正常扩散对应物形成鲜明对比的是，在具有频率$Ω\to 0$的绝热驱动的极限中，不存在渐进的异常整流电流，显示出对驱动频率的共振依赖性。然而，异常电流反转发生足够快的驱动，像在正常扩散的情况下。在驱动场的最低阶，这样的整流电流呈现二次响应效应。在微扰区之外，它表现出一个很宽的最大值与驱动场强的关系。此外，异常电流表现出最大值与电位振幅。
英文摘要：
This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to the realm of antipersistent non-Markovian subdiffusion in viscoelastic media. A periodically forced subdiffusion in a parity-broken ratchet potential is considered within the non-Markovian generalized Langevin equation (GLE) description with a power-law memory kernel $η(t)\propto t^{-α}$ ($0<α<1$). It is shown that subdiffusive rectification currents, defined through the mean displacement and subvelocity $v_α$, $<δx(t)>\sim v_α t^α/ Γ(1+α)$, emerge asymptotically due to the breaking of the detailed balance symmetry by driving. The asymptotic exponent is $α$, the same as for free subdiffusion, $<δx^2(t)>\propto t^α$. However, a transient to this regime with some time-dependent $α_{\rm eff}(t)$ gradually decaying in time, $α\leq α_{\rm eff}(t)\leq 1$, can be very slow depending on the barrier height and the driving field strength. In striking contrast to its normal diffusion counterpart, the anomalous rectification current is absent asymptotically in the limit of adiabatic driving with frequency $Ω\to 0$, displaying a resonance like dependence on the driving frequency. However, an anomalous current inversion occurs for a sufficiently fast driving, like in the normal diffusion case. In the lowest order of the driving field, such a rectification current presents a quadratic response effect. Beyond perturbation regime it exhibits a broad maximum versus the driving field strength. Moreover, anomalous current exhibits a maximum versus the potential amplitude.
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