Critical dynamics and fluctuations for a mean-field model of cooperative behavior

The main objective of this paper is to examine in some detail the dynamics and fluctuations in the critical situation for a simple model exhibiting bistable macroscopic behavior. The model under consideration is a dynamic model of a collection of anharmonic oscillators in a two-well potential together with an attractive mean-field interaction. The system is studied in the limit as the number of oscillators goes to infinity. The limit is described by a nonlinear partial differential equation and the existence of a phase transition for this limiting system is established. The main result deals with the fluctuations at the critical point in the limit as the number of oscillators goes to infinity. It is established that these fluctuations are non-Gaussian and occur at a time scale slower than the noncritical fluctuations. The method used is based on the perturbation theory for Markov processes developed by Papanicolaou, Stroock, and Varadhan adapted to the context of probability-measure-valued processes.     

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.     

Glass transition of the monodisperse Gaussian core model

We numerically investigate the dynamical properties of the one-component Gaussian core model in supercooled states. We find that nucleation is increasingly suppressed with increasing density. The system concomitantly exhibits glassy, slow dynamics characterized by the two-step stretched exponential relaxation of the density correlation and a drastic increase of the relaxation time. We also find a weaker violation of the Stokes-Einstein relation and a smaller non-Gaussian parameter than in typical model glass formers, implying weaker dynamic heterogeneities. Additionally, the agreement of the simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of the slow dynamics of this ultrasoft particle fluid is mean-field-like. This fact may be understood as a consequence of the long-range nature of the interaction.     

Reprint of : Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.     

Rare events and scale-invariant dynamics of perturbations in delayed chaotic systems

We study the dynamics of perturbations in time-delay dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be described by the linear Zhang surface growth model [J. Phys. (France) 51, 2129 (1990)]], which is known to describe surface roughening driven by power-law distributed noise. As a consequence, Lyapunov vector dynamics is dominated by rare random events that lead to non-Gaussian fluctuations and multiscaling properties.     

Multiscale model of gradient evolution in turbulent flows

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples "restricted Euler" (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.     

Experimental test of the fluctuation theorem for a driven two-level system with time-dependent rates

A single defect center in diamond periodically excited by a laser is shown to provide a simple realization for a system obeying a fluctuation theorem for nonthermal noise. The distribution of these fluctuations is distinctly non-Gaussian, which has also been verified by numerical calculation. For driving protocols symmetric under time reversal a more restricted form of the theorem holds, which is also known from entropy fluctuations caused by thermal noise.     

Large fluctuations in driven dissipative media

We analyze the fluctuations of the dissipated energy in a simple and general model where dissipation, diffusion, and driving are the key ingredients. The full dissipation distribution, which follows from hydrodynamic fluctuation theory, shows non-Gaussian tails and no negative branch, thus violating the fluctuation theorem as expected from the irreversibility of the dynamics. It exhibits simple scaling forms in the weak- and strong-dissipation limits, with large fluctuations favored in the former case but strongly suppressed in the latter. The typical path associated with a given dissipation fluctuation is also analyzed in detail. Our results, confirmed in extensive simulations, strongly support the validity of hydrodynamic fluctuation theory to describe fluctuating behavior in driven dissipative media.     

Fluctuations of spacetime and holographic noise in atomic interferometry

On small scales spacetime can be understood as some kind of spacetime foam of fluctuating bubbles or loops which are expected to be an outcome of a theory of quantum gravity. One recently discussed model for this kind of spacetime fluctuations is the holographic principle which allows to deduce the structure of these fluctuations. We review and discuss two scenarios which rely on the holographic principle leading to holographic noise. One scenario leads to fluctuations of the spacetime metric affecting the dynamics of quantum systems: (i) an apparent violation of the equivalence principle, (ii) a modification of the spreading of wave packets, and (iii) a loss of quantum coherence. All these effects can be tested with cold atoms.     

Non-Gaussian noise in quantum wells infrared photodetectors

Non-Gaussian dark current noise has been observed in quantum wells infrared photo detectors. The non-Gaussian component of the noise was ascribed to fluctuations of spatial distribution of electric field in the device. Non-Gaussian noise was found in both n- and p-type QWIPs, however, it was significantly less pronounce. In n-type devices non-Gaussian noise manifests itself only as randomly distributed excess current bursts. In p-type QWIPs the non-Gaussian noise takes form of bias dependent random telegraph-like fluctuations with a finite time of transition between the levels. The lifetime at both levels is Poisson distributed and the average lifetime, together with the level spacing, strongly depend on bias voltage. At low voltages the system stays predominantly in the low current level while at higher voltages the average lifetime of the high current level is longer. The transient time of passing between the states has been related to the charging time constant of the system determined by QWIP capacitance and contacts resistance.     

Hydrodynamics and the fluctuation theorem

The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume, and time. We study the fluctuation theorem in computer simulations of planar shear flow. The simulations are performed by employing the method of multiparticle collision dynamics, which captures both thermal fluctuations and hydrodynamic interactions. The main outcome of our analysis is that the fluctuation theorem is verified at any averaging time provided that the measurement volume exhibits a specific dependence on a hydrodynamic time scale.     

Manifestly non-Gaussian fluctuations in superconductor-normal metal tunnel nanostructures

We propose a mesoscopic setup which exhibits strong and manifestly non-Gaussian fluctuations of energy and temperature when suitably driven out of equilibrium. The setup consists of a normal metal island (N) coupled by tunnel junctions (I) to two superconducting leads (S), forming a SINIS structure, and is biased near the threshold voltage for quasiparticle tunneling, eV≈2Δ. The fluctuations can be measured by monitoring the time-dependent electric current through the system. This makes the setup suitable for the realization of feedback schemes which can be used to stabilize the temperature to the desired value.     

Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Influence of non-Gaussian noise on a tumor growth system under immune surveillance

In this paper, the stationary probability distribution (SPD) function and the mean first passage time (MFPT) are investigated in a tumor growth model driven by non-Gaussian noise which is introduced to mimic random fluctuations in the levels of the immune system. Results demonstrate the different transitions induced by the strength of non-Gaussian noise under different immune coefficients and the dual roles of non-Gaussian noise in promoting host protection against cancer and in facilitating tumor escape from immune destruction. Additionally, it can be discovered that increases in noise strength, the degree of departure from Gaussian noise, and the immune coefficient can accelerate the extinction of tumor cells. Numerical simulations are performed, and their results present good agreement with the theoretical results.     

Power fluctuations in a closed turbulent shear flow

We study experimentally the power consumption P of a confined turbulent flow at constant Reynolds number Re. We analyze in details its temporal dynamics and statistical properties, in a setup that covers two decades in Reynolds numbers. We show that nontrivial power fluctuations occur over a wide range of amplitudes and that they involve coherent fluid motions over the entire system size. As a result, the power fluctuations do not result from averaging of independent subsystems and its probability density function Pi(P) is strongly non-Gaussian. The shape of Pi(P) is Reynolds number independant and we show that the relative intensity of fluctuations decreases very slowly as Re increases. These results are discussed in terms of an analogy with critical phenomena.     

Current fluctuations in nonequilibrium diffusive systems: an additivity principle

We formulate a simple additivity principle allowing one to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two cumulants. This distribution (which in general is non-Gaussian) satisfies the Gallavotti-Cohen symmetry and generalizes the one predicted recently for the symmetric simple exclusion process. The additivity principle can be used to study more complex diffusive networks including loops.     

Non-Gaussian noise in quantum spin glasses and interacting two-level systems

We study a general model for non-Gaussian 1/f noise based on an infinite range quantum Ising spin system in the paramagnetic state, or, equivalently, interacting two-level classical fluctuators. We identify a dilatation interaction term in the dynamics which survives the thermodynamic limit and circumvents the central limit theorem to produce non-Gaussian noise even when the equilibrium distribution is that of noninteracting spins. The resulting second spectrum ("noise of the noise") itself has a universal 1/f form which we analyze within a dynamical mean-field approximation.     

Fluctuations and rheology in active bacterial suspensions

We probe nonequilibrium properties of an active bacterial bath through measurements of correlations of passive tracer particles and the response function of a driven, optically trapped tracer. These measurements demonstrate violation of the fluctuation-dissipation theorem and enable us to extract the power spectrum of the active stress fluctuations. In some cases, we observe 1/sqrt[omega] scaling in the noise spectrum which we show can be derived from a theoretical model incorporating coupled stress, orientation, and concentration fluctuations of the bacteria.     

Radiation-induced robust oscillation [2mm]and non-Gaussian fluctuation

There have been many recent studies devoted to the consequences of stochasticity in protein circuitry. Stress conditions, including DNA damage, hypoxia, heat shock, nutrient deprivation, and oncogene activation, can result in the activation and accumulation of p53. Several experimental studies show that oscillations can be induced by DNA damage following nuclear irradiation. To explore the underlying dynamical features and the role of stochasticity, we discuss the oscillatory dynamics in the well-studied regulatory network motif. The fluctuations around the fixed point of a delayed system are Gaussian in the limit of sufficiently weak delayed feedback, and remain Gaussian along a limit cycle when viewed tangential to the trajectory. The experimental results are recapitulated in this study. We illustrate several features of the p53 activities, which are robust when the parameters change. Furthermore, the distribution in protein abundance can be characterized by its non-Gaussian nature.     

Cooperative motions in a finite size model of liquid silica: an anomalous behavior

Finite size effects on dynamical heterogeneity are studied in liquid silica with Molecular Dynamics simulations using the BKS potential model. When the system size decreases relaxation times are found to increase in accordance with previous results in finite-size simulations and confined liquids. It has been suggested that this increase may be related to a modification of the spatially heterogeneous dynamics in confined liquids. In agreement with this hypothesis we observe a decrease of the spatially heterogeneous dynamics when the size decreases. The spatially heterogeneous dynamics is usually characterized by the dynamical aggregation of the most or the least mobile atoms. However we find that the decrease of the dynamical aggregation associated to the least mobile atoms is much more important than the decrease associated to the most mobile atoms when the size decreases. This result associated with a slowing down of the liquid is surprising as it is expected that the dynamical aggregation of the least mobile atoms should increase the slowing down of the liquid dynamics. The decrease of the heterogeneous behaviour is also in contradiction with the increase of the spatially heterogeneous dynamics observed in liquids confined inside nanopores. However, an increase of the non-Gaussian parameter appears both for the confinement inside nanopores and for the finite size simulations. As the non-Gaussian parameter is usually associated with the heterogeneous dynamics, the increase of the non-Gaussian parameter together with a decrease of the spatially heterogeneous dynamics is also surprising.