论文标题
当前的统计数据和在弱点限制中的一维langevin过程的过渡
Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit
论文作者
论文摘要
我们认为具有均匀的非保守力驱动的langevin动力学的粒子，具有周期性边界条件的一维电势。我们对系统的性质感兴趣，以实现广义粒子电流的时间综合值的非典型值。为了研究这些，我们通过在大泄漏形式主义内与电流结合的参数来偏向动力学。我们在弱噪声极限下研究了由物理驱动力和定义偏置过程的参数所跨的相图。我们特别关注此二维相图中的默认过渡。在没有轨迹偏差的情况下，默认过渡作为力的函数的特征是标准指数$ \ frac {1} {2} $。我们表明，对于任何非零偏差，默认过渡的特征是逆数行为作为偏见或力的函数，接近临界线。我们还报告了当前考虑偏置默认过渡时的缩放指数$ \ frac {1} {3} $，在没有偏见的情况下将非保守力固定在其临界值中。然后，关注时间集成的粒子电流，我们研究了倾斜电势表现出局部最小值时在零流相中的热圆形效应。在这种情况下，我们得出了粒子电流和缩放累积生成函数的小噪声限制的Arrhenius缩放。 Arrhenius缩放的这种推导依赖于偏见的Fokker-Planck运算符的左特征向量的确定，以低噪声限制指数级。综合电流的有效泊松统计在此限制中出现。
We consider a particle with a Langevin dynamics driven by a uniform non-conservative force, in a one-dimensional potential with periodic boundary conditions. We are interested in the properties of the system for atypical values of the time-integral of a generalized particle current. To study these, we bias the dynamics, at trajectory level, by a parameter conjugated to the current, within the large-deviation formalism. We investigate, in the weak-noise limit, the phase diagram spanned by the physical driving force and the parameter defining the biased process. We focus in particular on the depinning transition in this two-dimensional phase diagram. In the absence of trajectory bias, the depinning transition as a function of the force is characterized by the standard exponent $\frac{1}{2}$. We show that for any non-zero bias, the depinning transition is characterized by an inverse logarithmic behavior as a function of either the bias or the force, close to the critical lines. We also report a scaling exponent $\frac{1}{3}$ for the current when considering the depinning transition in terms of the bias, fixing the non-conservative force to its critical value in the absence of bias. Then, focusing on the time-integrated particle current, we study the thermal rounding effects in the zero-current phase when the tilted potential exhibits a local minimum. We derive in this case the Arrhenius scaling, in the small noise limit, of both the particle current and the scaled cumulant generating function. This derivation of the Arrhenius scaling relies on the determination of the left eigenvector of the biased Fokker-Planck operator, to exponential order in the low-noise limit. An effective Poissonian statistics of the integrated current emerges in this limit.
