Theoretical derivation of 1/f noise in quantum chaos

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the 1/f (1/f(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.     

海洋湍流中光波特征参量和短期光束扩展的研究

Nikishov等建立的海洋湍流功率谱模型中,假设了海水有着稳定的分层.但是,实际海水通常不是稳定分层的,温度与盐度的涡流扩散率是不相等的.2017年,Elamassie等建立了考虑这些因素的更合理的海洋湍流功率谱模型.湍流介质中光波空间相干长度等基本特征参量在表征湍流强度和光传输相位校正技术等方面起着重要作用.本文基于Elamassie海洋湍流功率谱模型,重新推导出了海洋湍流中光波结构函数、光波空间相干长度和Fried参数的解析公式,并校验了所得公式的正确性.研究发现：当温度变化引起的光学湍流占主导地位时,Nikishov海洋湍流功率谱模型把湍流强度低估了;当盐度变化引起的光学湍流占主导地位时,Nikishov海洋湍流功率谱模型把湍流强度高估了.基于Elamassie海洋湍流功率谱模型,本文推导出了高斯光束短期光束扩展的半解析公式,并验证了其正确性.研究还表明：海水稳定分层与否,短期光束扩展差异很大.本文研究结果对水下湍流环境中的光通信、成像和传感等应用具有重要意义.     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

Thermal noise influences fluid flow in thin films during spinodal dewetting

Experiments on dewetting thin polymer films confirm the theoretical prediction that thermal noise can strongly influence characteristic time scales of fluid flow and cause coarsening of typical length scales. Comparing the experiments with deterministic simulations, we show that the Navier-Stokes equation has to be extended by a conserved bulk noise term to accomplish the observed spectrum of capillary waves. Because of thermal fluctuations the spectrum changes from an exponential to a power law decay for large wave vectors. Also the time evolution of the typical wave vector of unstable perturbations exhibits noise-induced coarsening that is absent in deterministic hydrodynamic flow.     

Power spectrum analysis to identify exotic events in ultra-relativistic heavy-ion collisions

The usefulness of the power spectrum method has been studied for identifying non-statistical fluctuations artificially injected in a small subset of normal simulated events in S + Au and Pb + Pb collisions at CERN SPS energy. Number of peaks in the power spectrum above a threshold is used as the selection criterion. In most cases the efficiency of selection is high and the impurity in the filtered sample due to the statistical fluctuation of normal events is quite low. Special treatment is suggested for weak non-statistical component at a level of admixture comparable to the statistical fluctuation.     

Scaling of 1/<Emphasis Type="Italic">f</Emphasis> noise in nonequilibrium phase transitions

Investigation of the dynamics of fluctuations of heat and mass transfer reveals that its crisis and transient modes exhibit high-energy pulsations with a power spectrum that is inversely proportional to frequency (flicker or 1/f fluctuations). Such a spectrum suggests energy transfer from high-to low-frequency modes and the possibility of large-scale catastrophic outbursts in the system being considered. The theory shows that such fluctuations arise in the system owing to the simultaneous occurrence of interacting phase transitions in the presence of white noise having a sufficiently high intensity. The distribution of fluctuations for scale transformations of the set of stochastic equations that describe the generation of 1/f noise is investigated. It is shown that, under a scale transformation, the Gaussian distribution of a random process having a 1/f spectrum passes to an exponential distribution, which is characteristic of the statistics of extreme outbursts. The probability of such outbursts must be taken into account in predicting the stability of various heat-transfer modes.     

Next‐to‐next‐to‐leading order post‐Newtonian spin(1)‐spin(2) Hamiltonian for self‐gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin(1)‐spin(2) Hamiltonian for two self‐gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.     

Noise measurements in bilayer lipid membranes during electroporation

A study of voltage fluctuations in bilayer lipid membranes during electroporation and under current-clamp conditions is presented. Qualitative considerations based on the electroporation theory are used in order to explain the phenomenon on long time scale. Indeed, the current-clamp condition induces a feedback mechanism on the pore formation and therefore on the macroscopic conductance. Voltage fluctuations can thus be recorded. These fluctuations are nonstationary long-living and have a flicker power spectrum over nearly four decades of frequency between about 10^-2 and 10²Hz. The study of the fluctuations in the time domain has been performed by introducing an electrical model of the system formed by the membrane and the circuit under current-clamp configuration. The analysis of the time series gives a characteristic time of 100ms for the circuitry response to the fragments of electroporation signals with characteristic times faster than 100ms. During electroporation, the response to an external periodic stimulus in the frequency range 10^-1-10Hz shows that the system behaves linearly, even if voltage fluctuations are present. Received 1 June 1999 and Received in final form 1 October 1999     

Statistical estimation of the spatial spectrum of secondary sources

A statistical problem of estimating the shape and maximum possible width of the spatial energy spectrum of secondary sources is formulated and solved. The secondary sources under consideration are characteristic of the class of scatterers with preset statistical mean parameters. This estimation is important for analyzing the possibility of solving inverse scattering problems, including the question of the uniqueness and stability of the solution and also the correct organization of a tomographic experiment. Results of a computer simulation are presented, and the expected statistical mean spectrum is compared with a particular realization of the spectrum. In the case of a strongly pronounced rescattering, the statistical mean width of the spectrum is mainly determined by the effective velocity contrast in the ensemble of scatterers and depends only weakly on the scale of spatial fluctuations of the scatterers’ characteristics.     

Current noise in ac-driven nanoscale conductors

The theory for current fluctuations in ac-driven transport through nanoscale systems is put forward. By use of a generalized, non-Hermitian Floquet theory we derive novel explicit expressions for the time-averaged current and the zero-frequency component of the power spectrum of current fluctuations. A distinct suppression of both the zero-frequency noise and the dc current occurs for suitably tailored ac fields. The relative level of transport noise, being characterized by a Fano factor, can selectively be manipulated by ac sources; in particular, it exhibits both characteristic maxima and minima near current suppression.     

Statistics of low-frequency pulsations in critical regimes of heat mass exchange with phase transitions

Experimental investigation of fluctuation dynamics in critical and transitional modes of heat mass exchange shows existence of irregular high-energy pulsations with power spectrum inversely proportional to the frequency—so called 1/f spectrum. Such regimes are characterized by the fact that an essential part of the pulsations energy is connected with very slow processes and mean that large high-energy bursts are possible in the system. Another characteristic feature of such regimes is scale invariance of the fluctuations distribution function. According to the theory, the 1/f fluctuations can emerge in physical systems due to simultaneous phase transitions in presence of sufficiently intensive white noise. This paper is devoted to detailed investigation of relaxation processes at steadying of stationary stochastic process in non-equilibrium phase transitions in system of two nonlinear stochastic differential equation. Such an information reveals statistical patterns of particular large-scale low-frequency bursts. Discontinuous “forgetting” of the initial conditions takes place. It is shown by numerical methods that distributions of duration and maximal values of the low-frequency extreme bursts have the power-like form. Experimental investigation results of statistical characteristics of fluctuation processes at ultrasonic cavitation and flash boiling of overheated water jets are presented. Results of the experiments carried out fit conclusions of the theoretical model for interacting heterogeneous phase transitions.     

Next‐to‐next‐to‐leading order post‐Newtonian spin‐orbit Hamiltonian for self‐gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin‐orbit Hamiltonian for two self‐gravitating spinning compact objects. If at least one of the objects is rapidly rotating, then the corresponding interaction is comparable in strength to a 3.5PN effect. The result in the present paper in fact completes the knowledge of the post‐Newtonian Hamiltonian for binary spinning black holes up to and including 3.5PN. The Hamiltonian is checked via known results for the test‐spin case and via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.     

1/f alpha noise in spectral fluctuations of quantum systems

The power law 1/f(alpha) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1/f(alpha) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.     

Characterization of the noise in continuously operating mode-locked lasers

An experimental and theoretical investigation of the fluctuations of the pulses from continuous-wave mode-locked lasers is presented. It is shown that these fluctuations can be detected and quantitatively characterized from measurements of the power spectrum of the light intensity. Such power spectra can be measured with great accuracy by shining the laser output on a suitable photodetector and by processing the detector signal with the use of an electronic spectrum analyzer. Different types of noise such as fluctuations of the pulse energy, pulse repetition time, and pulse duration, can be readily recognized from their characteristic spectral signature. Experimental results of noise measurements are presented for a synchronously mode-locked dye laser pumped by an acousto-optically mode-locked argon ion laser, and also for a colliding pulse passively mode-locked dye laser.     

Realization of SOC behavior in a dc glow discharge plasma

Experimental observations consistent with Self Organized Criticality (SOC) have been obtained in the electrostatic floating potential fluctuations of a dc glow discharge plasma. Power spectrum exhibits a power law which is compatible with the requirement for SOC systems. Also the estimated value of the Hurst exponent (self similarity parameter), H being greater than 0.5, along with an algebraic decay of the autocorrelation function, indicate the presence of temporal long-range correlations, as may be expected from SOC dynamics. This type of observations in our opinion has been reported for the first time in a glow discharge system.     

Power spectrum crossover in sediments of a paleolake disturbed by volcanism

We study density fluctuations from sediments of a paleolake in central Mexico that was subjected to volcanic perturbations by means of computed tomography (CT) measurements on blocks chiselled out of mines at the lake's bed. The mine walls show laminations corresponding to the alternation of low density diatom sediments and high density volcanic ash depositions. We have previously shown that there is a range of scales where these fluctuations present a self-similar behavior [1]. Here we relate density correlation calculations to the power spectrum of the fluctuations. We show that a scaling region in the power spectrum coincides with the scaling region in the correlations produced by relaxation from intense volcanic perturbations to steady state fluctuations. There appears to be a kink-like crossover in the power spectrum from mid range scaling to a shorter range scale invariance. This, together with the density probability distribution of the fluctuations, draws attention to the dominant role of rare events. We believe that our analysis may be useful for the understanding of other phenomena with similar power spectrum properties, in which a scale invariance in the unperturbed system is altered by external perturbations that induce an additional scaling behavior.     

Conductance noise spectrum of mesoscopic systems

We investigate the shape as well as the size- and temperature-dependence of the conductance noise spectrum of a small system containing electrons and both fixed and mobile scatterers. If the number of mobile scatterers within a phase-coherent region is sufficiently large, the temporal variation of the conductance can be viewed as a random walk process limited by the universal conductance fluctuations, resulting in a practically Lorentzian power spectrum. We discuss the conditions under which the noise spectrum of a system consisting of many phase-coherent regions is either Lorentzian or 1/f-like. The temperature-dependence of the power spectrum is determined by the hopping mechanism and the variation of the phase breaking length. As a function of temperature the spectrum satisfies power law scaling relations with exponents depending on the dimension and the temperature range; the spectral intensity can both increase and decrease with decreasing temperature.     

Relativity,thermodynamics and entropic forces

A recent assertion that inertial and gravitational forces are entropic forces is discussed. A more conventional approach is stressed herein, whereby entropy is treated as a result of relative motion between observers in different frames of reference. It is demonstrated that the entropy associated with inertial and gravitational forces is dependent upon the well known lapse function of general relativity. An interpretation of the temperature and entropy of an accelerating body is then developed, and used to relate the entropic force to Newton's second law of motion. The entropic force is also derived in general coordinates. An expression of the gravitational entropy of in‐falling matter is then derived by way of Schwarzschild coordinates. As a final consideration, the entropy of a weakly gravitating matter distribution is shown to be proportional to the self‐energy and the stress‐energy‐momentum content of the matter distribution.     

Annular beam scintillations in non-Kolmogorov weak turbulence

In a weakly turbulent atmosphere governed by the non-Kolmogorov spectrum, the on-axis scintillation index is formulated and evaluated when the incidence is an annular Gaussian type. When the power law of the non-Kolmogorov spectrum is varied, the scintillation index first increases, and reaches a peak value, then starts to decrease, and eventually approaches zero. The general trend is that when turbulence has a non-Kolmogorov spectrum with power law larger than the Kolmogorov power law, the scintillation index values become smaller. For all power laws, collimated annular Gaussian beams exhibit smaller scintillations when compared to pure Gaussian beams of the same size. Intensity fluctuations at a fixed propagation distance diminish for the non-Kolmogorov spectrum with a very large power law, irrespective of the focal length and the thickness of optical annular Gaussian sources.