arXiv subjects

Issei Sakai

Publications and source records attributed to Issei Sakai.

6 recordsLinked to original sources

arXiv2026

Sample-specific rectification-like response in a boundary-driven exclusion process

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 $\rho$, in contrast to the homogeneous case. Through the linear-response relation, this dependence leads to an equilibrium current-fluctuation coefficient that is asymmetric under $\rho\rightarrow 1-\rho$. 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.

cond-mat.stat-mech↗

arXiv2025

Symmetry Breaking of Current Response in Disordered Exclusion Processes

The bias-reversal symmetry -- where reversing an external bias inverts the current without changing its magnitude -- is a hallmark of nonequilibrium transport. While this property holds in homogeneous systems such as the asymmetric simple exclusion process, how disorder and its interplay with particle interactions affect this symmetry has remained unclear. Here, we identify a general criterion in disordered exclusion processes showing that the bias-reversal symmetry holds if and only if the local left-right bond-bias ratio is spatially uniform. This criterion provides a practical diagnostic that separates heterogeneous environments into symmetry-preserving and symmetry-breaking classes. Mean-field and numerical analyses reveal that bond disorder preserves the symmetry beyond linear response, whereas site disorder breaks it through an interplay between heterogeneity and particle interactions. Our results demonstrate how environmental disorder and interparticle interactions cooperate to generate asymmetric transport, thereby providing insight that is potentially relevant to transport through biological and artificial nanochannels.

cond-mat.stat-mech↗

arXiv2025

Density-Independent transient caging in the high-density phase of motility-induced phase separation

We investigate the nonequilibrium dynamics of active matter using a two-dimensional active Brownian particles model. In these systems, self-propelled particles undergo motility-induced phase separation (MIPS), spontaneously segregating into dense and dilute phases. We find that in the high-density phase, local particle mobility exhibits transient caging, with diffusivity remaining unchanged despite variations in the global system density. As global density increases further, the system undergoes a transition to a solid-like state through an intermediate regime with pronounced dynamical arrest. Our findings identify a distinct high-density regime characterized by transient caging and dynamical slowing down in a monodisperse active system, shedding new light on the connection between MIPS and nonequilibrium arrest.

cond-mat.soft↗

arXiv2024

Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process

We explore how the disorder impacts the current fluctuations in the symmetric simple exclusion process (SSEP) within a heterogeneous environment. First, we analyze the SSEP with a defect site under the periodic boundary conditions. We derive the exact expression for the second moment of the current and observe deviations from that of the homogeneous system. Notably, the second moment of the current shows asymmetric density dependence around a density of 1/2 and surpassing that of the homogeneous system in the low-density region. Furthermore, based on the finding from the SSEP with a defect site, we present an approximate derivation of the second moment of the current in the SSEP on a quenched random energy landscape using a partial-mean-field approach. The second moment of the current is heavily influenced by the energy landscape, revealing unique effects arising from the interplay between the heterogeneous environment and the many-body system. Our findings provide valuable insights that can be applied to control current fluctuations in systems involving the interactions of many particles, such as biological transport.

cond-mat.stat-mech↗

arXiv2023

Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder

We consider the totally asymmetric simple exclusion processes on quenched random energy landscapes. We show that the current and the diffusion coefficient differ from those for homogeneous environments. Using the mean-field approximation, we analytically obtain the site density when the particle density is low or high. As a result, the current and the diffusion coefficient are described by the dilute limit of particles or holes, respectively. However, in the intermediate regime, due to the many-body effect, the current and the diffusion coefficient differ from those for single-particle dynamics. The current is almost constant and becomes the maximal value in the intermediate regime. Moreover, the diffusion coefficient decreases with the particle density in the intermediate regime. We obtain analytical expressions for the maximal current and the diffusion coefficient based on the renewal theory. The deepest energy depth plays a central role in determining the maximal current and the diffusion coefficient. As a result, the maximal current and the diffusion coefficient depend crucially on the disorder, i.e., non-self-averaging. Based on the extreme value theory, we find that sample-to-sample fluctuations of the maximal current and diffusion coefficient are characterized by the Weibull distribution. We show that the disorder averages of the maximal current and the diffusion coefficient converge to zero as the system size is increased and quantify the degree of the non-self-averaging effect for the maximal current and the diffusion coefficient.

cond-mat.stat-mech↗

arXiv2022

Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder

We investigate the current properties in the totally asymmetric simple exclusion process (TASEP) on a quenched random energy landscape. In low- and high-density regimes, the properties are characterized by single-particle dynamics. In the intermediate one, the current becomes constant and is maximized. Based on the renewal theory, we derive accurate results for the maximum current. The maximum current significantly depends on a disorder realization, i.e., non-self-averaging (SA). We demonstrate that the disorder average of the maximum current decreases with the system size, and the sample-to-sample fluctuations of the maximum current exceed those of current in the low- and high-density regimes. We find a significant difference between single-particle dynamics and the TASEP. In particular, the non-SA behavior of the maximum current is always observed, whereas the transition from non-SA to SA for current in single-particle dynamics exists.

cond-mat.stat-mech↗