Takuma Akimoto

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 Langevin particle driven by a constant external force F and subject to a velocity-dependent resetting rate r(v)=λ|v|^{α}, where α controls the velocity dependence of the resetting. 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 the deterministic limit without friction and diffusion, the mean velocity obeys the exact power law 〈v〉∝F^{1/(α+1)} at all force strengths. In the presence of friction or velocity diffusion with α>0, linear response is recovered at weak driving, followed by a crossover to the same nonlinear scaling at strong driving. 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. More broadly, they suggest a framework for understanding transport in stochastic systems with feedback or environment-dependent dynamics.

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.

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)∝|v|^{α} governs transport properties. By tuning α, we uncover transitions between normal, subdiffusive, and superdiffusive regimes. Notably, at α=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.

Diffusion can exhibit apparent transitions when observed over finite times. This work shows that such behavior arises from fluctuating mobility and slow relaxation.

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 solidlike 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 light on the connection between MIPS and nonequilibrium arrest.

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.

Many intrinsically disordered proteins (IDPs) may undergo a phase separation to form a biomolecular condensate. Understanding the behavior of individual molecules within condensates is crucial for characterizing their collective physical properties relevant to biological functions. Here, we investigate the diffusion dynamics of IDPs within protein condensates using molecular dynamics simulations. We find that the proteins exhibit transient subdiffusion due to the viscoelastic nature of the condensates. Under conditions when confinement arises from the finite size of the droplet, the conformation and instantaneous diffusivity of the proteins vary significantly between the droplet interior and the interface with the environment, resulting in non-Gaussian displacement distributions. Moreover, we demonstrate that the structural complexity and intermolecular interactions of proteins modulate the subdiffusive behavior and the relaxation of diffusivity fluctuations. This study highlights key aspects of the heterogeneous structural and dynamical behavior of IDPs within biomolecular condensates.

We investigate the relaxation dynamics of the generalized Langevin equation (GLE) with an exponential memory kernel. Our analysis reveals that the relaxation time to equilibrium scales inversely with the square of the memory decay rate λ, i.e., τrelax ∝ λ−2. To understand the origin of this scaling, we analyze the escape dynamics from a potential well and find that the mean escape time follows the same λ−2 dependence. This indicates that the slow relaxation arises from memory-suppressed fluctuations that delay escape events. To explain these findings, we reformulate the GLE using an auxiliary variable, embedding the non-Markovian dynamics in a higher-dimensional Markovian system. This approach provides a clear physical picture of how memory influences noise, diffusion, and relaxation in non-Markovian systems.

We introduce randomness to Pomeau–Manneville (PM) maps by incorporating dichotomous multiplicative noise that alternates between dynamics with an attracting and a repelling fixed point. We characterize the dynamical behavior by measuring the separation of two nearby orbits. Controlling the probability of selecting the repelling PM map, we find two noise-induced transitions. When the repelling map is selected with probability less than 1/2, orbits converge to the origin, which is an indifferent fixed point shared by both maps. When the selection probability exceeds 1/2, nearby orbits contract. When the noise-averaged PM map exhibits weak chaos, this leads to weak synchronization, where the distance between orbits asymptotically approaches zero at a subexponential rate. Further increases in the selection probability lead to the second transition to chaotic or weakly chaotic behavior, depending on whether the noise-averaged PM map exhibits chaos or weak chaos, respectively. Additionally, we show that a power-law exponent of 3/2 in the sojourn-time distribution near the indifferent fixed point is universally observed at the first transition point. These results provide insights into how introducing multiplicative noise to chaotic or weakly chaotic systems can lead to rich dynamical behaviors, shedding light on the effects of noise in intermittent dynamical systems.