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When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness., Comment: 6 pages, 4 figures (Supplemental Material: 11 pages, 8 figures)

We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous time-reversal allows us to derive a tighter version of the thermodynamic uncertainty relation (TUR) involving observables evaluated relative to their local mean value. Moreover, the family of dynamics realizing the continuous time-reversal contains an equilibrium dynamics halfway between the time-forward and time-reversed dynamics. We show that this equilibrium dynamics, together with an appropriate choice of the observable, turns the inequality in the TUR into an equality. We demonstrate our findings for the example of a particle diffusing in a tilted periodic potential., 18 pages, 2 figures

Two qualitatively different ways of driving a physical system out of equilibrium, time-dependent and non-conservative forcing, are reflected by the decomposition of the system's entropy production into excess and housekeeping parts. We show that the difference between these two types of driving gives rise to a geometric formulation in terms of two orthogonal contributions to the currents in the system. This geometric picture in a natural way leads to variational expressions for both the excess and housekeeping entropy, which allow calculating both contributions independently from the trajectory data of the system. We demonstrate this by calculating the excess and housekeeping entropy of a particle in a time-dependent, tilted periodic potential., 7 pages, 2 figures

We present an alternative form of intermittency, L\'evy on-off intermittency, which arises from multiplicative $\ensuremath{\alpha}$-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space $(\ensuremath{\alpha},\ensuremath{\beta})$ of the noise, with stability parameter $\ensuremath{\alpha}\ensuremath{\in}(0,2)$ and skewness parameter $\ensuremath{\beta}\ensuremath{\in}[\ensuremath{-}1,1]$. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case $\ensuremath{\alpha}=2$. Three regimes are located at $1l\ensuremath{\alpha}l2$, where the noise has finite mean but infinite variance. They are differentiated by $\ensuremath{\beta}$ and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at $0l\ensuremath{\alpha}\ensuremath{\le}1$. There, the mean of the noise diverges, and no critical transition occurs. In one case, the origin is always unstable, independently of the distance $\ensuremath{\mu}$ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of $\ensuremath{\mu}$. We thus demonstrate that an instability subject to nonequilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.

International audience; We develop a maximum likelihood method to infer relevant physical properties of elongated active particles. Using individual trajectories of advected swimmers as input, we are able to accurately determine their rotational diffusion coefficients and an effective measure of their aspect ratio, also providing reliable estimators for the uncertainties of such quantities. We validate our theoretical construction using numerically generated active trajectories upon no flow, simple shear, and Poiseuille flow, with excellent results. Being designed to rely on single-particle data, our method eases applications in experimental conditions where swimmers exhibit a strong morphological diversity. We briefly discuss some of such ongoing experimental applications, specifically, in the characterization of swimming E. coli in a flow.

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Levy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Levy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.

The kinetics of contact processes are determined by the interplay among local mass transfer mechanisms, spatial heterogeneity, and segregation. Determining the macroscopic behavior of a wide variety of phenomena across the disciplines requires linking reaction times to the statistical properties of spatially fluctuating quantities. We formulate the dynamics of advected agents interacting with segregated immobile components in terms of a chemical continuous-time random walk. The inter-reaction times result from the first-passage times of mobile species to and across reactive regions, and available immobile reactants undergo a restart procedure. Segregation leads to memory effects and enhances the role of concentration fluctuations in the large-scale dynamics., The authors acknowledge the support of the European Research Council (ERC) through the project MHetScale (617511).

We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of power-law temporally correlated noise. By means of extensive numerical simulations of models in the KPZ universality class we find that, as the noise correlator index increases above some threshold value, the surface exhibits anomalous kinetic roughening of the type described by the generic scaling theory of Ramasco [Phys. Rev. Lett. 84, 2199 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.2199]. Remarkably, as the driving noise temporal correlations increase, the surface develops a characteristic pattern of macroscopic facets that completely dominates the dynamics in the long time limit. We argue that standard scaling fails to capture the behavior of KPZ subject to long-range temporally correlated noise. These phenomena are not not described by the existing theoretical approaches, including renormalization group and self-consistent approaches., This work has been partially supported by the Program for Scientific Cooperation “I-COOP+” from Consejo Superior de Investigaciones Científicas (Spain) through Project No. COOPA20187. A.A. is grateful for the financial support from Programa de Pasantías de la Universidad de Cantabria in 2017 and 2018 (Projects No. 70-ZCE3-226.90 and No. 62-VCES-648), and CONICET (Argentina) for a Doctoral Fellowship. J.M.L is supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía, Industria y Competitividad (Spain), through Project No. FIS2016-74957-P.

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family; the energy dissipation of an AQFP gate can be arbitrarily reduced through adiabatic switching. In addition to high energy efficiency, AQFP logic has the advantage that it can easily introduce stochastic processes by exploiting naturally occurring thermal fluctuations. We propose using AQFP logic to implement an amoeba-inspired problem solver (APS), which is a stochastic local search method to explore solutions to combinatorial optimization problems such as the Boolean satisfiability problem (SAT). We designed a superconductor amoeba-inspired problem solver (SAPS) using AQFP logic, which finds solutions to a simple logical constraint satisfaction problem in the manner of APS, and fabricate it using a Nb integrated circuit fabrication process. Experimental results show that the probability distribution of the stochastic processes in AQFP logic can be controlled by the magnitude of bias current and that SAPS finds solutions using a small number of iterations when a moderate bias current is applied. The present results indicate the possibility of using AQFP logic to build hardware dedicated to the implementation of stochastic local search algorithms to solve combinatorial optimization problems such as SAT.

A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the endcaps. When the traveling velocities are large, the flow is turbulent and its azimuthal component displays random reversals. Power spectra of the velocity field exhibit a $1/f^\alpha$ power law on several decades and are related to power-law probability distributions $P(\tau)\sim\tau^{-\beta}$ of the waiting times between successive reversals. This $1/f$ type spectrum is observed only when the Reynolds number is large enough. In addition, the exponents $\alpha$ and $\beta$ are controlled by the symmetry of the system : a continuous transition between two different types of Flicker noise is observed as the equatorial symmetry of the flow is broken, in agreement with theoretical predictions., Comment: 5 pages, 7 figures

To characterize the statistics and indistinguishability of a source, it is common to measure the correlation functions of the emitted field using various interferometers. Here, we present a theoretical framework for the computation of the correlation functions of a two-level system that is resonantly driven by a realistic noisy cw excitation laser. Analytic expressions of the first and second-order auto-correlation functions are obtained where the various contributions of the noisy excitation source are correctly taken into account. We predict that, even in the low power regime, the noise source has a strong influence on the two-level system dynamics, which is not anticipated by simpler models. The characterization of photon indistinguishability in the pulsed excitation regime is usually done by measuring the value of the zero-delay intensity correlation obtained with a Hong-Ou-Mandel interferometer. We show that this figure is irrelevant in the cw excitation regime and we introduce the coalescence time window, a figure of merit based on a probabilistic interpretation of the notion of photon indistinguishability. We finally use the coalescence time window to quantify how noisy cw excitation influences photon indistinguishability., Comment: 15 pages, 9 figures, 2 tables

We present experimental and theoretical results of noise-induced attractor hopping between dynamical states found in a single transverse mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. These transitions involve dynamical states with different polarizations of the light emitted by the VCSEL. We report an experimental map identifying, in the injected power-frequency detuning plane, regions where attractor hopping between two, or even three, different states occur. The transition between these behaviors is characterized by using residence time distributions. We find multistability regions that are characterized by heavy-tailed residence time distributions. These distributions are characterized by a -1.83±0.17 power law. Between these regions we find coherence enhancement of noise-induced attractor hopping in which transitions between states occur regularly. Simulation results show that frequency detuning variations and spontaneous emission noise play a role in causing switching between attractors. We also find attractor hopping between chaotic states with different polarization properties. In this case, simulation results show that spontaneous emission noise inherent to the VCSEL is enough to induce this hopping., This work has been funded by the Ministerio de Economía y Competitividad (MINECO/FEDER, UE), Spain under project TEC2015-65212-C3-1-P. A.Q. acknowledges FWO for support from a Postdoc fellowship and K.P. is grateful to the Methusalem Foundation for financial support.

Conventional master equation approaches approximate the diffusion of molecules in continuum space by the process of particles hopping on a spatial lattice. The hopping probability from one voxel (spatial lattice point) to its neighbor is usually considered to be constant throughout space. Such an assumption is only consistent with pointlike molecules and thus neglects volume-exclusion effects due to finite particle size. A few studies have attempted to introduce volume-exclusion effects by choosing the hopping probability from one voxel to a neighboring one to be a linear function of the number density. Here, we formulate an alternative master equation in which the hopping probability is equal to the fraction of available space in the neighboring voxel as estimated using scaled particle theory. This leads to the hopping probability being a nonlinear function of the number density. A mean-field approximation (mfa) leads to a partial differential equation of the advection-diffusion type. We show that the time evolution of the particle number density sampled using the stochastic simulation algorithm associated with the new master equation and the number density obtained by numerical integration of the mfa are in good agreement with each other. They are also distinctly different than the time evolution predicted by the conventional master equation and those with hopping probabilities which are linear functions of the number density. The results from the new lattice description are also shown to be in very good agreement with the lattice-free method of Brownian dynamics, even for highly crowded scenarios.

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter ($i = 1,2$) consults a group of $q_i$ neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever $q_1 \neq q_2$ and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the non-equilibrium stationary state of the system in terms of its probability distribution, non-vanishing currents and unequal-time two-point correlation functions. We also study the switching times properties of the model by exploiting an approximate mapping onto the model of [Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and also outline some properties of the model near criticality., 17 pages, 12 figures

We provide the first quantitative comparison between Barkhausen-noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean-field. We study different classes of soft magnetic materials: polycrystals and amorphous samples, characterized by long-range and short-range elasticity, respectively; both for thick and thin samples, i.e. with and without eddy currents. The temporal avalanche shape at fixed size, and observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents., v1: 5 pages, 6 figures; Supplemental Materials, 5 pages, 6 figures. v2+v3: updated version as published in PRL. v3: 8 pages, 12 figures. v3 corrects errors induced by a bug in assembling the pdf-files

We investigate the 1/f noise properties of epitaxial graphene devices at low temperatures as a function of temperature, current, and magnetic flux density. At low currents, an exponential decay of the 1/f noise power spectral density with increasing temperature is observed that indicates mesoscopic conductance fluctuations as the origin of 1/f noise at temperatures below 50 K. At higher currents, deviations from the typical quadratic current dependence and the exponential temperature dependence occur as a result of nonequilibrium conditions due to current heating. By applying the Kubakaddi theory [S. S. Kubakaddi, Phys. Rev. B 79, 075417 (2009)10.1103/PhysRevB.79.075417], a model describing the 1/f noise power spectral density of nonequilibrium mesoscopic conductance fluctuations in epitaxial graphene is developed and used to determine the energy loss rate per carrier. In the regime of Shubnikov-de Haas oscillations, a strong increase of 1/f noise is observed, which we attribute to an additional conductance fluctuation mechanism due to localized states in quantizing magnetic fields. When the device enters the regime of quantized Hall resistance, the 1/f noise vanishes. It reappears if the current is increased and quantum Hall breakdown sets in. © 2016 American Physical Society.