arXiv subjects

Takuma Akimoto

Publications and source records attributed to Takuma Akimoto.

At least 19 recordsLinked to original sources

arXiv2026

Breakdown of the Overdamped Approximation in Fluctuating Environments

The overdamped approximation is widely used to describe Brownian motion in complex environments, but its validity becomes nontrivial when the friction coefficient itself fluctuates in time. We investigate this problem by comparing underdamped and overdamped Langevin dynamics subject to the same fluctuating friction and satisfying the fluctuation--dissipation relation at a common temperature. We show that environmental averaging and inertial elimination generally lead to different long-time transport when environmental fluctuations are fast compared with velocity relaxation. For rapidly fluctuating friction, the underdamped dynamics is governed by the arithmetic mean friction and yields $D_{\rm eff}^{\rm under}=k_{\rm B}T/\langle\gamma\rangle$, whereas the overdamped dynamics gives $D_{\rm eff}^{\rm over}=k_{\rm B}T\langle\gamma^{-1}\rangle$. For a two-state Markov friction, we derive the finite-time effective diffusion coefficient exactly and identify the full crossover between these two regimes, controlled by the competition between velocity relaxation and environmental switching. We further establish the fast-fluctuation result for general stationary friction processes and verify it for a continuous log-Ornstein--Uhlenbeck environment, for which the characteristic crossover time can also be determined independently. Our results reveal a noncommutativity between environmental averaging and inertial elimination, establish a timescale-dependent criterion for the validity of overdamped dynamics in temporally heterogeneous environments, and show that rapid environmental fluctuations can enhance, rather than suppress, the consequences of inertia.

cond-mat.stat-mech↗

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↗

arXiv2026

Observation-Time-Induced Crossover in Driven Anomalous Transport

We investigate how a weak constant force becomes detectable through fluctuations in anomalous transport in strongly heterogeneous media. Rather than focusing on the mean drift, we show that the key signature of the force appears in the variance of the particle displacement. As representative models, we study a biased continuous-time random walk (CTRW) with nearest-neighbor jumps and a biased quenched trap model (QTM) with a power-law waiting-time tail. By analysing the force dependence of the displacement variance, we quantify how fluctuations respond to weak driving. We find that for $\alpha<2$, the response exhibits an observation-time-induced crossover: at fixed bias, the variance initially follows its unbiased scaling and only at later times crosses over to a force-dominated nonequilibrium regime. Equivalently, at fixed observation time $t$, there exists a threshold bias $\varepsilon_c(t)$ separating an apparently equilibrium-like regime from a detectable nonequilibrium response. This threshold decreases with increasing $t$, implying that weaker forces become observable over longer measurement windows. Quenched disorder further lowers the detection threshold compared with CTRW, and the crossover reflects a competition between the finite observation time and the intrinsic relaxation time of the driven heterogeneous system.

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arXiv2026

Breakdown of Linear Response Induced by Velocity-Dependent Stochastic Resetting

Linear response theory lies at the foundation of transport phenomena, predicting that physical systems respond proportionally to weak external forces. Here we show that this principle can break down in a minimal nonequilibrium setting due to state-dependent stochastic resetting. We consider a driven Langevin particle subject to a resetting mechanism whose rate grows as a power of the particle velocity, motivated by transport processes where faster carriers experience more frequent scattering events. We derive the exact steady-state velocity distribution and establish a moment balance relation that links external driving, viscous dissipation, and resetting-induced dissipation. This relation reveals that the response is controlled by a nonlinear coupling between the velocity and the resetting rate, leading to nonlinear transport. In particular, the mean velocity obeys the exact power law $\langle v\rangle \propto F^{1/(\alpha+1)}$, where $\alpha$ characterizes the velocity dependence of the resetting rate. Our results provide a solvable example in which linear response fails at the level of the leading-order behavior and identify velocity-dependent resetting as a minimal dynamical mechanism for generating nonlinear transport in nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2025

Observation-Time-Induced Crossover from Fluctuating Diffusivity

A sharp change in apparent mobility at a characteristic temperature that depends on the observation time has been reported in experiments and simulations of hydrated proteins. Such behavior is often discussed in the context of the protein dynamical transition, yet its general physical origin remains unclear. Here we show that fluctuating diffusivity within a Langevin framework naturally gives rise to an observation-time-induced crossover in translational diffusion: the effective diffusion coefficient exhibits a temperature-dependent change whose crossover point systematically shifts with the observation time. Through analytical and numerical analyses, we elucidate the mechanism of this crossover and identify the minimal conditions required for its emergence. Our results establish observation-time-induced crossover as a generic non-equilibrium phenomenon in systems with slowly relaxing mobility fluctuations. While distinct from internal dynamical transitions probed in neutron scattering, this framework provides a unified perspective that encompasses related finite-time crossover phenomena observed in hydrated proteins and other complex soft-matter systems.

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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.

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arXiv2025

Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking

Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates from classical Brownian behaviour, exhibiting striking phenomena such as Brownian yet non-Gaussian diffusion (BYNGD) and anomalous diffusion. BYNGD describes a frequently observed statistical feature characterised by the coexistence of linear mean-square displacement (MSD) and non-Gaussian displacement distributions. Anomalous diffusion, in contrast, involves a nonlinear time dependence of the MSD and often reflects mechanisms such as trapping, viscoelasticity, heterogeneity, or active processes. Both phenomena challenge the conventional framework based on constant diffusivity and Gaussian statistics. This review focuses the theoretical modelling of such behaviour via the Langevin equation with fluctuating diffusivity (LEFD) -- a flexible stochastic framework that captures essential features of diffusion in heterogeneous media. LEFD not only accounts for BYNGD but also naturally encompasses a wide range of anomalous transport phenomena, including subdiffusion, ageing, and weak ergodicity breaking. Ergodicity is discussed in terms of the correspondence between time and ensemble averages, as well as the trajectory-to-trajectory variability of time-averaged observables. The review further highlights the empirical relevance of LEFD and related models in explaining diverse experimental observations and underscores their value to uncovering the physical mechanisms governing transport in complex systems.

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↗

arXiv2025

Tunable Anomalous Diffusion in Subrecoil-Laser-Cooled Atoms

Laser cooling of atomic motion enables advances in quantum information and precision metrology. However, the spatial spreading of subrecoil-laser-cooled atoms---crucial for understanding cooling mechanisms and atomic confinement---remains largely unexplored. Here, we analyze anomalous diffusion in subrecoil-laser-cooled atoms, where a velocity-dependent fluorescence rate $R(v) \propto |v|^{\alpha}$ governs transport properties. By tuning $\alpha$, we uncover transitions between normal, subdiffusive, and superdiffusive regimes. Notably, at $\alpha = 3/2$, diffusion is minimized, leading to optimal atomic confinement. We further identify a conceptual link between subrecoil laser cooling and the Pomeau-Manneville map from nonlinear dynamics, revealing that anomalous diffusion can generically exhibit a nontrivial minimum in spatial spreading---even across seemingly unrelated physical systems.

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arXiv2025

Unveiling Optimal Diffusion for Infection Control in Brownian Particle Systems

Understanding the spread of infectious diseases requires integrating movement, physical constraints, and spatial configurations into epidemiological models. In this study, we investigate how particle diffusivity, hardcore interactions, and non-equilibrium initial conditions influence infection dynamics within a system of Brownian particles. Using numerical simulations and theoretical analysis, we reveal a nontrivial relationship between diffusivity and the speed of infection spread. Specifically, when particles are initially positioned at uniform distances greater than the infection radius -- a non-equilibrium configuration -- there exists an optimal diffusion coefficient that minimizes the infection propagation speed. This counterintuitive result arises from the competition between diffusive timescales and the rate of infection transmission. The presence of an optimal diffusivity is observed both in systems with and without hardcore interactions, provided that the infection radius exceeds the mean lattice spacing. Our findings provide a theoretical framework for understanding and controlling the spread of infections in confined and diffusive environments, with potential implications for designing movement-based strategies for infection control.

cond-mat.other↗

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↗

arXiv2024

Universality of giant diffusion in tilted periodic potentials

Giant diffusion, where the diffusion coefficient of a Brownian particle in a periodic potential with an external force is significantly enhanced by the external force, is a non-trivial non-equilibrium phenomenon. We propose a simple stochastic model of giant diffusion, which is based on a biased continuous-time random walk (CTRW) with flight time. By introducing a flight time representing traversal dynamics, we derive the diffusion coefficient using renewal theory and demonstrate its universal peak behavior under various periodic potentials, especially in low-temperature regimes. Giant diffusion is universally observed in the sense that there is a peak of the diffusion coefficient for any tilted periodic potentials and the degree of the diffusivity is greatly enhanced especially for low-temperature regimes. The biased CTRW models with flight times are applied to diffusion under three tilted periodic potentials. Furthermore, the temperature dependence of the maximum diffusion coefficient and the external force that attains the maximum are presented for diffusion under a tilted sawtooth potential.

cond-mat.stat-mech↗

arXiv2024

Diffusion of intrinsically disordered proteins within viscoelastic membraneless droplets

In living cells, intrinsically disordered proteins (IDPs), such as FUS and DDX4, undergo phase separation, forming biomolecular condensates. Using molecular dynamics simulations, we investigate their behavior in their respective homogenous droplets. We find that the proteins exhibit transient subdiffusion due to the viscoelastic nature and confinement effects in the droplets. The conformation and the instantaneous diffusivity of the proteins significantly vary between the interior and the interface of the droplet, resulting in non-Gaussianity in the displacement distributions. This study highlights key aspects of IDP behavior in biomolecular condensates.

cond-mat.soft↗

arXiv2023

Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity

Cell membranes phase separate into ordered ${\rm L_o}$ and disordered ${\rm L_d}$ domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in ${\rm L_o}$ and ${\rm L_d}$ domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into ${\rm L_o}$ and ${\rm L_d}$ domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the ${\rm L_o}$ domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

cond-mat.soft↗

arXiv2023

Statistics of the number of renewals, occupation times and correlation in ordinary, equilibrium and aging alternating renewal processes

Renewal process is a point process where an inter-event time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the renewal process, where the inter-event time distribution alternates between two distributions. We investigate statistical properties of the number of renewals and occupation times for one of the two states in alternating renewal processes. When both means of the inter-event times are finite, the alternating renewal process can reach an equilibrium. On the other hand, an alternating renewal process shows aging when one of the means diverges. We provide analytical calculations for the moments of the number of renewals, occupation time statistics, and the correlation function for several case studies in the inter-event-time distributions. We show anomalous fluctuations for the number of renewals and occupation times when the second moment of inter-event time diverges. When the mean inter-event time diverges, distributional limit theorems for the number of events and occupation times are shown analytically. These are known as the Mittag-Leffler distribution and the generalized arcsine law in probability theory.

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↗

arXiv2023

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↗

arXiv2023

Estimating relaxation times from a single trajectory

Complex systems such as protein conformational fluctuations and supercooled liquids exhibit a long relaxation time and are considered to posses multiple relaxation times. We analytically obtain the exact correlation function for stochastic processes with multiple relaxation times. We show that the time-averaged correlation function calculated by a trajectory whose length is shorter than the longest relaxation time exhibits an apparent aging behavior. We propose a method to extract relaxation times from a single trajectory. This method successfully extracts relaxation times of a stochastic process with multiple states when a state can be characterized by the values of the trajectory. As an application of this method, we estimate several relaxation times smaller than the longest relaxation time in conformational fluctuations of a small protein.

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