发表机构
Tokyo University of Science（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在具有淬火位点无序的边界驱动对称排斥过程中，揭示样本特异性空间异质性可产生类整流输运，平衡密度分布的空间反射对称性破缺是其必要条件，系综层面无序平均电流仍保持反对称。
AI 中文摘要
我们研究具有淬火位点无序的边界驱动对称排斥过程的电流响应。硬核粒子在具有位点依赖速率的一维晶格上对称跳跃，由两个密度不同的储库在边界处注入和移除。我们用线性阶的Galerkin投影和高阶的平均场闭合近似稳态密度分布，从而得到电流作为储库密度差的非线性函数。在储库密度差的线性阶下，电流响应系数依赖于平均储库密度ρ，这与均匀情况形成对比。通过线性响应关系，这种依赖导致平衡电流涨落系数在ρ→1−ρ下不对称。超出线性响应，非零偶次电流贡献会打破电流在储库密度差反转下的反对称性，在单个无序实现中产生类整流行为。我们进一步表明，平衡密度分布的空间反射对称性排除了这种行为，因此分布的空间反射对称性破缺是类整流行为的必要条件。在当前近似内，我们还发现，对于连续分布的位点无序，几乎每个无序实现在任意接近平衡时都会发生类整流行为。然而在系综层面，由于无序系综在空间反射下不变，无序平均电流仍保持反对称。这些结果提供了一种类整流输运的机制，源于样本特异性的空间异质性，而非显式施加的方向不对称性。
英文摘要
We investigate the current response of a boundary-driven symmetric exclusion process with quenched site disorder. Hard-core particles hop symmetrically on a one-dimensional lattice with site-dependent rates and are injected and removed at the boundaries by two reservoirs of different densities. We approximate the steady-state density profile using a Galerkin projection at linear order and a mean-field closure at higher orders, and thereby obtain the current as a nonlinear function of the reservoir density difference. At linear order in the reservoir density difference, the current-response coefficient depends on the mean reservoir density $ρ$, in contrast to the homogeneous case. Through the linear-response relation, this dependence leads to an equilibrium current-fluctuation coefficient that is asymmetric under $ρ\rightarrow 1-ρ$. Beyond linear response, nonzero even-order current contributions break the antisymmetry of the current under reversal of the reservoir density difference, producing rectification-like behavior in individual disorder realizations. We further show that spatial-reflection symmetry of the equilibrium density profile rules out such behavior, so broken spatial-reflection symmetry of the profile is a necessary condition for rectification-like behavior. Within the present approximation, we further find that, for continuously distributed site disorder, rectification-like behavior occurs arbitrarily close to equilibrium for almost every disorder realization. At the ensemble level, however, the disorder-averaged current remains antisymmetric because the disorder ensemble is invariant under spatial reflection. These results provide a mechanism for rectification-like transport arising from sample-specific spatial heterogeneity rather than from an explicitly imposed directional asymmetry.
Comments15 pages, 6 figures
