Symmetry Breaking of Current Response in Disordered Exclusion Processes

Abstract

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 establish a general criterion showing that the bias-reversal symmetry holds if and only if the local left-right bond-bias ratio is spatially uniform. Analytical 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 a unified theoretical framework relevant to transport through biological and artificial nanochannels.

Figures (3)

• Figure 1: Schematic illustration of the disordered ASEP. (a) Particles hop on a one-dimensional lattice with site-dependent left/right rates. (b) Quenched barrier model, in which each bond has a symmetric barrier. (c) Quenched trap model, in which each site has a symmetric trap.
• Figure 2: Current-density relation in the ASEP with the quenched barrier model ($L=100$, $T/T_g=1.5$, $\tau_c=1$). The vertical axis shows the scaled current $J(\rho,\varepsilon)/\varepsilon$. Symbols represent numerical results obtained for a single realization of the quenched random energy landscape (circles: $\varepsilon=0.005$; triangles: $\varepsilon=0.02$). Dashed lines correspond to the first-order term of Eq. \ref{['eq: current in QBM']}, and solid lines include the third-order correction for $\varepsilon=0.02$.
• Figure 3: (a)--(c): Symmetry indicators versus the bias magnitude $|\varepsilon|$ ($L=100$, $T/T_g=2.5$, $\tau_c=1$). Panels (a) and (b) show results for a single quenched energy landscape, whereas panel (c) shows results for multiple independent landscapes. (a) Current-density symmetry ratio $J(\rho,\varepsilon)/J(1-\rho,\varepsilon)$ at $\rho=1/4$. Squares and triangles represent numerical results for $\varepsilon>0$ and for $\varepsilon<0$, respectively. Deviations from unity indicate current-density symmetry breaking. (b) Bias-reversal ratio $-J(\rho,\varepsilon)/J(\rho,-\varepsilon)$ at $\rho=1/2$. Symbols denote numerical results. Deviations from unity indicate bias-reversal asymmetry. (c) Bias-reversal ratio $-J(\rho,\varepsilon)/J(\rho,-\varepsilon)$ at $\rho=1/2$ in the QTM for various quenched energy landscapes. Cross symbols correspond to individual landscapes. Squares show the disorder-averaged result $-\Braket{J(\rho,\varepsilon)}_{\mathrm{dis}}/\Braket{J(\rho,-\varepsilon)}_{\mathrm{dis}}$, where $\Braket{\cdot}_{\mathrm{dis}}$ is the disorder average.