Negative power spectra in quantum field theory

We consider the spatial power spectra associated with fluctuations of quadratic operators in field theory, such as quantum stress tensor components. We show that the power spectrum can be negative, in contrast to most fluctuation phenomena where the Wiener-Khinchin theorem requires a positive power spectrum. We show why the usual argument for positivity fails in this case, and discuss the physical interpretation of negative power spectra. Possible applications to cosmology are discussed.     

Nonequilibrium fluctuation relation for sheared micellar gel in a jammed state

We show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress, and in all cases show similar symmetry properties as predicted by the Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear-rate fluctuations increase with the decrease of the system size.     

Heat fluctuations in a nonequilibrium bath

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.     

介观电容耦合LC电路在有限温度下的能量及热效应

由正则量子化方法导出了介观电容耦合LC电路体系的哈密顿算符, 利用幺正变换使哈密顿算符对角化. 用系综理论给出了体系的平均能量及其涨落, 在此基础上, 借助于广义Hellmann-Feynman定理, 讨论了有限温度下电路体系中电荷与自感磁通的量子涨落. 结果表明, 体系中电荷与自感磁通的量子涨落不仅与电路元件参数有关, 而且还与温度有关. 关键词： 介观电路 量子涨落 广义Hellmann-Feynman定理 有限温度     

Fluctuations of internal energy flow in a vibrated granular gas

The nonequilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301 (2004)], which was announced to be a verification of the fluctuation relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such nonequilibrium systems. We explain these results in terms of a two-temperature Poisson process. Within this model, supported by independent molecular dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective temperature is clarified. In the pursuit of a hypothetical global quantity fulfilling the FR, this points to the need of considering candidates other than the power flux.     

Hydrodynamic modes,soft modes and fluctuation spectra near the threshold of a current instability

We give a full threedimensional treatment of the stability and the fluctuations of the uniform stationary current state in a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The model consists of Langevin equations for the mean momentum and the mean energy of the charged carriers, coupled to Maxwell's equations. We investigate the normal modes and the fluctuation spectra of this system, in particular the occurrence of soft modes and of critical fluctuations at the stability limit of the uniform current state. It is shown that the nature of the normal modes is strongly determined by the electromagnetic interactions between the carriers, giving rise to hydrodynamic flux modes and to dielectric relaxation modes. As the threshold field is approached, the dielectric relaxation modes soften and couple strongly to the flux modes. It is shown that as a consequence of this coupling the exponential decay of the correlation functions due to ordinary dielectric relaxation is followed at very long times by a power law decay due to the hydrodynamic modes.Work supported by the Swiss National Science Foundation     

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.     

Stochastic resonance and heat fluctuations in a driven double-well system

We study a periodically driven (symmetric as well as asymmetric) double-well potential system at finite temperature. We show that mean heat loss by the system to the environment (bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat loss over a large number of periods satisfies the conventional steady-state fluctuation theorem.     

Extension of the fluctuation theorem

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.     

Characterizing plastic depinning dynamics with the fluctuation theorem

We demonstrate that the fluctuation theorem can be used to characterize plastic flow phases in collectively interacting particle assemblies driven over quenched disorder when strong fluctuations and crackling noise with 1/f ^α character occur. By measuring the frequency of entropy-destroying trajectories and the diffusivity near the threshold for motion, we map out the different dynamic phases and demonstrate that the fluctuation theorem holds in the strongly fluctuating plastic flow regime which was previously shown to be chaotic. For different driving rates and disorder strength, we find that it is possible to define an effective temperature which decreases with increasing drive, as expected for this type of system. When the size of the pinning sites is large, we identify specific regimes where the fluctuation theorem holds only at long times due to an excess of negative entropy events that occur when particles undergo circular motions within the traps. We discuss how the fluctuation theorem could be applied to plastic flow in other driven nonthermal systems with quenched disorder such as superconducting vortices, magnetic domain walls, Coulomb glasses, and earthquake models.     

Toy model of hydrodynamic fluctuations

We study hydrodynamic fluctuations in an ideal gas. Because one is interested in thermodynamic properties of small volume elements, Einstein's theory of equilibrium fluctuations in large systems is insufficient. A toy model of correlated fluctuations in neighboring small cells leads us to the distinction of biased and unbiased momentum densities. Hydrodynamic equations that satisfy the fluctuation-dissipation theorem can then be formulated in terms of these two different momentum densities or velocities.     

HT-7超导托卡马克边缘涨落谱特征及湍流输运研究

用郎缪尔三探针对HT-7超导托卡马克边缘等离子体涨落进行了高时空分辩测量.给出了欧姆放电下涨落幅度的径向分布、谱特征及传播特性.实验观察表明,在由E_r×B确定的极向旋转速度剪切层附近,等离子体电位、电子温度和电子密度的相对涨落水平和两两间的相干系数均有明显下降,其极向互相关函数亦减小,这说明剪切层对涨落具有去相关作用.由涨落驱动的径向局域粒子输运通量Γ_tur测量显示出湍动输运具有时间上的阵发特性。将悬浮电位涨落φ_f2的自动率谱P_{( 关键词： 托卡马克 边界涨落 湍流输运}     

Evaporating Black Holes and Long Range Scaling

For an effective treatment of the evaporation process of a large black hole the problem concerning the role played by the fluctuations of the (vacuum) stress tensor close to the horizon is addressed. We present arguments which establish a principal relationship between the outwards fluctuations of the stress tensor close to the horizon and quantities describing the onset of the evaporation process. This suggest that the evaporation process may be described by a fluctuation-dissipation theorem relating the noise of the horizon to the black hole evaporation rate.     

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.     

Brownian Motion of a Charged Particle in Electromagnetic Fluctuations at Finite Temperature

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.     

Power injected in dissipative systems and the fluctuation theorem

We consider three examples of dissipative dynamical systems involving many degrees of freedom, driven far from equilibrium by a constant or time dependent forcing. We study the statistical properties of the injected and dissipated power as well as the fluctuations of the total energy of these systems. The three systems under consideration are: a shell model of turbulence, a gas of hard spheres colliding inelastically and excited by a vibrating piston, and a Burridge-Knopoff spring-block model. Although they involve different types of forcing and dissipation, we show that the statistics of the injected power obey the “fluctuation theorem" demonstrated in the case of time reversible dissipative systems maintained at constant total energy, or in the case of some stochastic processes. Although this may be only a consequence of the theory of large deviations, this allows a possible definition of “temperature" for a dissipative system out of equilibrium. We consider how this “temperature" scales with the energy and the number of degrees of freedom in the different systems under consideration. Received 26 June 2000 and Received in final form 24 October 2000     

Flux line lattice melting and the formation of a coherent quasiparticle Bloch state in the ultraclean URu2Si2 superconductor

We find that in the ultraclean heavy-fermion superconductor URu(2)Si(2) (T_{c0}=1.45 K) a distinct flux line lattice melting transition with outstanding characters occurs well below the mean-field upper critical fields. We show that a very small number of carriers with heavy mass in this system results in exceptionally large thermal fluctuations even at sub-Kelvin temperatures, which are witnessed by a sizable region of the flux line liquid phase. The uniqueness is further highlighted by an enhancement of the quasiparticle mean free path below the melting transition, implying a possible formation of a quasiparticle Bloch state in the periodic flux line lattice.     

Vortices in the Two-Dimensional Simple Exclusion Process

We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partial flux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed in an Appendix.     

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional I. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.     

Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Lévy regime α < 2, the power law decay with large exponent ( α > 2), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement. Received 29 July 2000 and Received in final form 25 September 2000