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Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and entropy production. Here, we will link fluctuation theorems for the entropy production along trajectories with the action obtainable from the Freidlin--Wentzell theorem to elucidate the thermodynamics of switching between states in the large volume limit of multistable systems. We find that the entropy production at steady state plays no role, but the entropy production during switching is key. Steady-state entropy and diffusive noise strength can be neglected in this limit. The relevance to biology, ecological, and climate models is apparent., 8 pages, 3 figures

We investigate a modified spatial stochastic Lotka-Volterra formulation of the rock-paper-scissors model using off-lattice stochastic simulations. In this model one of the species moves preferentially in a specific direction -- the level of preference being controlled by a noise strength parameter $\eta \in [0, 1]$ ($\eta = 0$ and $\eta = 1$ corresponding to total preference and no preference, respectively) -- while the other two species have no referred direction of motion. We study the behaviour of the system starting from random initial conditions, showing that the species with asymmetric mobility has always an advantage over its predator. We also determine the optimal value of the noise strength parameter which gives the maximum advantage to that species. Finally, we find that the critical number of individuals, below which the probability of extinction becomes significant, decreases as the noise level increases, thus showing that the addition of a preferred mobility direction studied in the present paper does not favour coexistence., Comment: 5 pages, 7 figures

The dynamics of non-equilibrium spatially extended systems are often dominated by fluctuations, due to e.g.\ deterministic chaos or to intrinsic stochasticity. This reflects into generic scale invariant or kinetic roughening behavior that can be classified into universality classes defined by critical exponent values and by the probability distribution function (PDF) of field fluctuations. Suitable geometrical constraints are known to change secondary features of the PDF while keeping the values of the exponents unchanged, inducing universality subclasses. Working on the Kuramoto-Sivashinsky equation as a paradigm of spatiotemporal chaos, we show that the physical nature of the prevailing fluctuations (chaotic or stochastic) can also change the universality class while respecting the exponent values, as the PDF is substantially altered. This transition takes place at a non-zero value of the stochastic noise amplitude and may be suitable for experimental verification., Comment: 12 pages, 9 figures, submitted

In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow is symmetric with respect to a measure induced by Liouville Conformal Field Theory. Using the theory of Dirichlet forms, we construct a weak solution to the associated equation of the area measure on a flat torus, in the full "$L^1$ regime" $\sigma< \sigma_{L^1}=2\sqrt\pi$ where $\sigma$ is the noise strength. We also describe the main necessary modifications needed for the SRF on general compact surfaces, and list some open questions., Comment: 42 pages

Charge noise can be detrimental to the operation of quantum dot (QD) based semiconductor qubits. We study the low-frequency charge noise by charge offset drift measurements for Si-MOS devices with intentionally implanted donors near the QDs. We show that the MOS system exhibits non-equilibrium drift characteristics, in the form of transients and discrete jumps, that are not dependent on the properties of the donor implants. The equilibrium charge noise indicates a 1/f noise dependence, and a noise strength as low as $$1\,\mu {\rm{eV}}/\sqrt{{\rm{Hz}}}$$ 1 μ eV / Hz , comparable to that reported in more model GaAs and Si/SiGe systems (which have also not been implanted). We demonstrate that implanted qubits, therefore, can be fabricated without detrimental effects on long-term drift or 1/f noise for devices with less than 50 implanted donors near the qubit.

Implementation of logical entangling gates is an important step towards realizing a quantum computer. We use a gradient-based optimization approach to find single-qubit rotations which can be interleaved between applications of a noisy nonlocal gate to dramatically suppress arbitrary logical errors, while steering the evolution operator towards the perfectly entangling subset of SU(4) gates. The modularity of the approach allows for application to any two-qubit system, regardless of the Hamiltonian or details of the experimental implementation. This approach is effective for both quasi-static and time-dependent $1/f^{\alpha}$ noise. We also show how the fidelity of the final operation depends on both the fidelity of the local rotations and the noise strength., Comment: 8 pages, 5 figures, data available at https://gist.github.com/goerz/3e04cca5a5dc1e9bcabd247065c24ebe

We analyze \emph{RXTE} and \emph{Swift} observations of SWIFT J1729.9$-$3437 after its outburst from 2010 July 20 to 2010 August 12. We calculate a spin frequency and spin frequency derivative of $1.8734(8) \times 10^{-3}$ Hz and $6.42(6) \times 10^{-12}$ Hz/s respectively from the quadratic fit of pulse arrival times. The quadratic fit residuals fit well to a circular orbital model with a period of $15.3(2)$ days and a mass function of about $1.3M_{\odot}$, but they can also be explained by a torque noise strength of $6.8 \times 10^{-18}$ Hz sec$^{-2}$. Pulse profiles switches from double-peaked to single-peaked as the source flux continues to decrease. We find that the pulse shape generally shows no strong energy dependence. The hardness ratios reveal that the source becomes softer with decreasing flux. We construct a single spectrum from all the available RXTE and Swift observations. We find that adding an \emph{Fe} line complex feature around 6.51 keV slightly improves the spectral fit and that this feature is more likely to originate from the source rather than the Galactic ridge. From the pulse phase spectral analysis, it is shown that that photon index and folding energy of the high energy cut-off vary with varying pulse phase., 15 pages, 9 figures, accepted for publication in MNRAS

We show that a thermally isolated system driven across a quantum phase transition by a noisy control field exhibits anti-Kibble-Zurek behavior, whereby slower driving results in higher excitations. We characterize the density of excitations as a function of the ramping rate and the noise strength. The optimal driving time to minimize excitations is shown to scale as a universal power law of the noise strength. Our findings reveal the limitations of adiabatic protocols such as quantum annealing and demonstrate the universality of the optimal ramping rate., 5 pages, 3 figures, 2 pages of supplemental material

In this work we studied the diffusive behavior of active brownian particles under lateral parabolic confinement. The results showed that we go from subdiffusion to ballistic motion as we vary the angular noise strength and confinement intensity. We argued that the subdiffusion regimes appear as consequence of the restricted space available for diffusion (achieved either through large confinement and/or large noise); we saw that when there are large confinement and noise intensity, a similar configuration to single file diffusion appears; on the other hand, normal and superdiffusive regimes may occur due to low noise (longer persistent motion), either through exploring a wider region around the potential minimum in the transverse direction (low confinement), or by forming independent clusters (high confinement)., 6 pages, 6 figures, accepted for publication in Physica A

We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate., Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figures

Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the fractal repeller and the critical point of the map. Two methods give a precise meaning to the asymptotic expansion, Borel summation and Shafer approximants. These can then be compared with the escape rate as computed by alternative methods., Comment: 15 pages, 5 postscript figures incorporated into the text; v2: Quadratic Pade (Shafer) method added, also a few references

Phase turbulence is suppressed by applying common noise additively to the Kuramoto-Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is evaluated theoretically., 7 pages, 4 figures

We study the two time correlation for the noise driven dynamics of the double-well oscillator in the Suzuki regime. It is seen that for very small noise strength the correaltion function shows a lack of translational invariance for very long times characterised by the Suzuki scaling variable. We see that in this strongly out-of-equilibrium situation, the conventional mode-coupling approximation is not a convenient tool., Comment: 8 pages, no figure

We consider the effect of introducing a small number of non-aligning agents in a well-formed flock. To this end, we modify a minimal model of active Brownian particles with purely repulsive (excluded volume) forces to introduce an alignment interaction that will be experienced by all the particles except for a small minority of "dissenters". We find that even a very small fraction of dissenters disrupts the flocking state. Strikingly, these motile dissenters are much more effective than an equal number of static obstacles in breaking up the flock. For the studied system sizes we obtain clear evidence of scale invariance at the flocking-disorder transition point and the system can be effectively described with a finite-size scaling formalism. We develop a continuum model for the system which reveals that dissenters act like annealed noise on aligners, with a noise strength that grows with the persistence of the dissenters' dynamics., Comment: 22 pages, 8 figures. Version accepted for publication in New Journal of Physics

Repeated game theory has been one of the most prevailing tools for understanding the long-run relationships, which are footstones in building human society. Recent works have revealed a new set of "zero-determinant (ZD)" strategies, which is an important advance in repeated games. A ZD strategy player can exert a unilaterally control on two players' payoffs. In particular he can deterministically set the opponent's payoff, or enforce an unfair linear relationship between the players' payoffs, thereby always seizing an advantageous share of payoffs. One of the limitations of the original ZD strategy, however, is that it does not capture the notion of robustness when the game is subjected to stochastic errors. In this paper, we propose a general model of ZD strategies for noisy repeated games, and find that ZD strategies have high robustness against errors. We further derive the pinning strategy under noise, by which the ZD strategy player coercively set the opponent's expected payoff to his desired level, although his payoff control ability declines with the increase of noise strength. Due to the uncertainty caused by noise, the ZD strategy player cannot secure his payoff to be higher than the opponent's, which implies strong extortions do not exist even under low noise. While we show that the ZD strategy player can still establish a novel kind of extortions, named weak extortions, where any increase of his own payoff always exceeds that of the opponent's by a fixed percentage, and the conditions under which the weak extortions can be realized are more stringent as the noise becomes stronger., 8 pages, 4 figures

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong., Comment: 11 pages, 6 figures, other comments

Efficiency of generation of net unidirectional current in an adiabatically driven symmetric periodic potential system is studied. The efficiency shows a maximum, in the case of an inhomogeneous system with spatially varying periodic friction coefficient, as a function of temperature. The ratchet is not most efficient when it gives maximum current. The direction of current may also be reversed as a function of noise strength when, instead, an asymmetric periodic potential is considered., Comment: 14 pages, including 5 figures

In this paper we present a hydrodynamic approach to describe the motion of migrating bacteria as a special class of self-propelled systems. Analytical and numerical calculations has been performed to study the behavior of our model in the turbulent-like regime and to show that a phase transition occurs as a function of noise strength. Our results can explain previous experimental observations as well as results of numerical simulations., Comment: 8 pages, 10 figures

We investigate the effect of noise strength on the macroscopic ordering dynamics of systems with symmetric absorbing states. Using an explicit stochastic microscopic model, we present evidence for a phase transition in the coarsening dynamics, from an Ising-like to a voter-like behavior, as the noise strength is increased past a nontrivial critical value. By mapping to a thermal diffusion process, we argue that the transition arises due to locally-absorbing states being entered more readily in the high-noise regime, which in turn prevents surface tension from driving the ordering process., v2 with improved introduction and figures, to appear in PRL. 4 pages, 4 figures

The phenomenon of stochastic resonance (SR) is known to occur mostly in bistable systems. However, the question of the occurrence of SR in periodic potential systems has not been resolved conclusively. Our present numerical work shows that the periodic potential system indeed exhibits SR in the high-frequency regime, where the linear-response theory yields maximum frequency-dependent mobility as a function of noise strength. The existence of two (and only two) distinct dynamical states of trajectories in this moderately feebly damped periodically driven noisy periodic potential system plays an important role in the occurrence of SR.

The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In previous work the coefficients of such an expansion for a one-dimensional map were fitted to a general form containing a few parameters. These parameters were found to be related to the fractal structure of the repeller of the system. The parameter alpha, the "noise dimension", remains to be interpreted. This report presents new data for alpha showing that the relation to the dimensions is more complicated than predicted in earlier work and oscillates as a function of the map parameter, in contrast to other dimension-like quantities., Comment: 7 pages, 5 figures

We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes place most effectively, which is analogous to the stochastic resonance. Finally, we study the synchronization of coupled phase oscillators with nonvariational interaction on scale-free networks. We find a sharp transition and a weak hysteresis in the nonvariational systems. The sharp transition is found also in the mean-field approximation., 8 pages, 5 figures

A trapping mechanism is observed and proposed as the origin of the anomalous behavior recently discovered in transport properties of overdamped ratchets subject to external oscillatory drive in the presence of quenched noise. In particular, this mechanism is shown to appear whenever the quenched disorder strength is greater than a threshold value. The minimum disorder strength required for the existence of traps is determined by studying the trap structure in a disorder configuration space. An approximation to the trapping probability density function in a disordered region of finite length included in an otherwise perfect ratchet lattice is obtained. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength due to the presence of the traps., Comment: 21 pages, 6 figures, to appear in PRE

We propose and experimentally demonstrate detecting small single-cycle and few-cycle signals by using the symmetric double-well potential of a radio frequency superconducting quantum interference device (rf-SQUID). We show that the response of this bistable system to single- and few-cycle signals has a non-monotonic dependence on the noise strength. The response, measured by the probability of transition from initial potential well to the opposite one, becomes maximum when the noise-induced transition rate between the two stable states of the rf-SQUID is comparable to the signal frequency. Comparison to numerical simulations shows that the phenomenon is a manifestation of stochastic resonance., 5 pages 3 figures

The effect of a high-frequency signal on the FitzHugh-Nagumo excitable model is analyzed. We show that the firing rate is diminished as the ratio of the high-frequency amplitude to its frequency is increased. Moreover, it is demonstrated that the excitable character of the system, and consequently the firing activity, is suppressed for ratios above a given threshold value. In addition, we show that the vibrational resonance phenomenon turns up for sufficiently large noise strength values., Comment: 4 pages, 4 figures (to appear in Physical Review E)

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the timescales of noise-induced motion by changing the time delay., 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d) were amended. The reason is numerical error found, that affected the quantitative estimates of correlation time, but did not affect the main message

We challenge the misconception that Bloch-Redfield equations are a less powerful tool than phenomenological Lindblad equations for modeling exciton transport in photosynthetic complexes. This view predominantly originates from an indiscriminate use of the secular approximation. We provide a detailed description of how to model both coherent oscillations and several types of noise, giving explicit examples. All issues with non-positivity are overcome by a consistent straightforward physical noise model. Herein also lies the strength of the Bloch-Redfield approach because it facilitates the analysis of noise-effects by linking them back to physical parameters of the noise environment. This includes temporal and spatial correlations and the strength and type of interaction between the noise and the system of interest. Finally, we analyze a prototypical dimer system as well as a 7-site Fenna-Matthews-Olson complex in regards to spatial correlation length of the noise, noise strength, temperature, and their connection to the transfer time and transfer probability.

In assemblies of globally coupled dynamical units, weak noise perturbing independently the individual units can cause anomalous dispersion in the synchronized cloud of the units in the phase space. When the noise-free dynamics of the synchronized assembly is nonperiodic, various moments of the linear dimension of the cloud as a function of the noise strength exhibit multiscaling properties with parameter-dependent scaling exponents. Some numerical evidence of this peculiar behavior as well as its interpretation in terms of a multiplicative stochastic process with small additive noise is provided. Universality of the phenomenon is also discussed., 7pages,7figures,to appear in PRE

Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice-sites for whom values of dynamical variable follow certain predefined pattern). Number of structures is seen to follow a power-law decay with length of the structure for a given noise-strength. An interesting phenomenon, which we call stochastic coherence, is reported in which a rise of bell-shaped type in abundance and lifetimes of these structures is observed for a range of noise-strength values., 4 pages double column LaTeX file for text, 5 Postscript files for figures. Replaced version contains an analytic argument for stochastic coherence

We demonstrate the appearance of a purely entropic stochastic resonance (ESR) occurring in a geometrically confined system, where the irregular boundaries cause entropic barriers. The interplay between a periodic input signal, a constant bias and intrinsic thermal noise leads to a resonant ESR-phenomenon in which feeble signals become amplified. This new phenomenon is characterized by the presence of two peaks in the spectral amplification at corresponding optimal values of the noise strength. The main peak is associated with the manifest stochastic resonance synchronization mechanism involving the inter-well noise-activated dynamics while a second peak relates to a regime of optimal sensitivity for intra-well dynamics. The nature of ESR, occurring when the origin of the barrier is entropic rather than energetic, offers new perspectives for novel investigations and potential applications. ESR by itself presents yet another case where one constructively can harvest noise in driven nonequilibrium systems., 6 pages, 7 figures ; Europhys. Lett., in press (2009)

We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general synchronization transition becomes more difficult to meet when memory range increases, for intermediate ranges the synchronization tendency of systems can be enhanced. Generally the synchronization transition is found to depend on the memory range and the ratio of noise strength to memory amplitude, which indicates on a possibility of optimizing synchronization by memory. We also point out on a close link between dynamics with memory and noise, and recently discovered synchronizing properties of networks with delayed interactions.