Observable dependence of fluctuation-dissipation relations and effective temperatures

We study the nonequilibrium fluctuation-dissipation theorem (FDT) in the glass phase of Bouchaud's trap model. We incorporate an arbitrary observable m and obtain its correlation and response functions in closed form. A limiting nonequilibrium FDT plot is approached at long times for most choices of m. In contrast to standard mean field models, however, the shape of the plot depends nontrivially on the observable, and its slope varies continuously even though there is a single scaling of relaxation times with age. Nonequilibrium FDT plots can therefore not be used to define a meaningful effective temperature T(eff) in this model. Consequences for the wider applicability of an FDT-derived T(eff) are discussed.     

A test model for fluctuation-dissipation theorems with time-periodic statistics

The recently developed time-periodic fluctuation-dissipation theorem (FDT) provides a very convenient way of addressing the climate change of atmospheric systems with seasonal cycle by utilizing statistics of the present climate. A triad nonlinear stochastic model with exactly solvable first and second order statistics is introduced here as an unambiguous test model for FDT in a time-periodic setting. This model mimics the nonlinear interaction of two Rossby waves forced by baroclinic processes with a zonal jet forced by a polar temperature gradient. Periodic forcing naturally introduces the seasonal cycle into the model. The exactly solvable first and second order statistics are utilized to compute both the ideal mean and variance response to the perturbations in forcing or dissipation and the quasi-Gaussian approximation of FDT (qG-FDT) that uses the mean and the covariance in the equilibrium state. The time-averaged mean and variance qG-FDT response to perturbations of forcing or dissipation is compared with the corresponding ideal response utilizing the triad test model in a number of regimes with various dynamical and statistical properties such as weak or strong non-Gaussianity and resonant or non-resonant forcing. It is shown that even in a strongly non-Gaussian regime, qG-FDT has surprisingly high skill for the mean response to the changes in forcing. On the other hand, the performance of qG-FDT for the variance response to the perturbations of dissipation is good in the near-Gaussian regime and deteriorates in the strongly non-Gaussian regime. The results here on the test model should provide useful guidelines for applying the time-periodic FDT to more complex realistic systems such as atmospheric general circulation models.     

Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales. A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.     

Kirchhoff-Planck law for freely radiating bodies and fluctuation-dissipation theorem

The interrelation between the Kirchhoff-Planck law (KPL) and the fluctuation-dissipation theorem (FDT) is discussed. It is known that the KPL is valid for freely radiating atoms if (i) the occupation probability of the atomic levels is the Boltzmann equilibrium probability and if (ii) the induced emission is treated as negative absorption. It is shown that the assumption (ii) is also inherent in the definition of the generalized susceptability. The susceptability is directly connected with the corresponding correlation function (FDT). It is proofed that the attached dipole fluctuation spectrum in its normally ordered form and the classical Maxwell equations reproduce the KPL. This result serves as the guideline for the extension of this procedure to macroscopic systems (susceptability ε (ω)). The theory can be used to describe radiative heat transfer in inhomogeneous systems. The validity of this macroscopic theory implies the same assumptions as the validity of the KPL for freely radiating atoms. The freely radiating dielectric half-space is treated as a simple example.     

Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.     

Strong dynamical heterogeneities in the violation of the fluctuation-dissipation theorem in spin glasses

We analyze numerically the violation of the fluctuation-dissipation theorem (FDT) in the +/-J Edwards-Anderson (EA) spin-glass model. Using single spin probability densities we reveal the presence of strong dynamical heterogeneities, which correlate with ground-state information. The physical interpretation of the results shows that the spins can be divided into two sets. In 3D, one set forms a compact structure which presents a coarseninglike behavior with its characteristic violation of the FDT, while the other asymptotically follows the FDT. Finally, we compare the dynamical behavior observed in 3D with 2D.     

Probing the fluctuation-dissipation theorem in a Perrin-like experiment

In this Letter, we present a new experimental approach to investigate the effective temperature concept as a generalization of the fluctuation-dissipation theorem (FDT) for nonequilibrium systems. Simultaneous measurements of diffusion coefficient and sedimentation velocity of heavy colloids, embedded in a Laponite clay suspension, are performed with a fluorescence-recovery-based setup. This nonperturbative dual measurement, performed at a single time in a single sample, allows for a direct application of the FDT to the tracer velocity observable. It thus provides a well-defined derivation of the effective temperature in this ageing colloidal gel. For a wide range of concentrations and ageing times, we report no violation of the FDT, with effective temperature agreeing with bath temperature. This result is consistent with recent theoretical predictions on the coupling between the velocity observable and nonequilibrium gels dynamics.     

Statistical analysis and model determination for thermal desorption spectra: Nitrogen on tungsten

Thermal desorption spectra of nitrogen chemisorbed on tungsten have been examined in order to discriminate between two simple alternative kinetic models for the desorption process. Both these models consider the β₂ desorption as a second order process, while for the β₁ peak they assume first order and second order kinetics, respectively. The maximum likelihood method has been used for fitting the spectra and the resulting kinetic parameters have been discussed through the analysis of the correlation matrix. The strict correlation which exists between activation energies and frequency factors prevents effective discrimination and should diminish confidence in too simple and rigid models.     

Multi-fractal formulation of compressible fully developed turbulence: Parabolic-profile approximation for the singularity spectrum

A parabolic-profile approximation (PPA) for the singularity spectrum D (h) in the multi-fractal model for compressible fully developed turbulence (FDT) is considered and is then extrapolated to the Kolmogorov microscale regime. The generalization of Kolmogorov’s “4/5th law” relating the third-order velocity structure function to the mean energy dissipation rate ε to compressible FDT is considered. The PPA is also shown to afford, unlike the generic multi-fractal model, an analytical calculation of probability distribution function (PDF) of velocity gradients and to describe intermittency corrections for this PDF that complement those provided by homogeneous-fractal model.     

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation. Received: 9 January 1998 / Revised: 24 April 1998 / Accepted: 2 July 1998     

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging.     

在近平衡态QGP中费米子的分布函数

从QGP动力论出发,得到QGP在色场涨落扰动下偏离平衡态而处于近平衡时的分布函数, 进而分析了决定偏离因子的物理因素.并分别讨论了在高温低密和低温高密区偏离因子特征.     

Model for the analytical signal in atomic absorption spectrometry with electrothermal atomization

A method for verification of analytical measurements in electrothermal atomic absorption spectrometry using a phenomenological model for physicochemical atomization processes is discussed. The influence of the sample matrix on basic kinetic parameters of atomization such as the analyte free-atom formation energy and the atomization rate constant has been shown. The similarity of atomization kinetic parameters obtained by calibrating the spectrometer to those for samples under study can be used as a verification criterion for analysis. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 295–298, May–June, 2008.     

Fluorescence diffuse tomography of small animals with DsRed2 fluorescent protein

Fluorescent compounds are used as markers to diagnose oncological diseases, to study molecular processes typical for carcinogenesis, and to investigate metastasis formation and tumor regress under the influence of therapeutics. Different types of tomography, such as continuous wave (CW), frequency-domain (FD), and time-domain (TD) tomography, allow fluorescence imaging of tumors located deep in human or animal tissue. In this work, preliminary results of the frequency domain fluorescent diffuse tomography (FDT) method in application to DsRed2 protein as a fluorescent agent are presented. For the first step of our experiments, we utilized low-frequency amplitude modulation (1 kHz) of second harmonic of Nd: YAG (532 nm). The transilluminative configuration was used in the setup. The results of post mortem experiments with capsules containing DsRed2 inserted inside the esophagus of a 3-day-old hairless rat to simulate tumor are shown. An algorithm of processing fluorescent images based on calculating the zero of maximum curvature has been applied to detect fluorescent inclusion boundaries in the image. This work demonstrates the potential capability of the FDT method for imaging deep fluorescent tumors in human tissue or animal models of human cancer. Improvement of the setup can be accomplished by using high-frequency modulation (using a 110-MHz acoustooptical modulator).     

Investigation of the erosion drop fraction for liquid-metalexplosive-emission cathodes

The velocity spectrum of drops emitted by a liquid-metal explosive-emission cathode has been investigated. A relation between the sizes of the drops and their maximum velocities has been found for the velocity range 10³-8×10⁴ cm/s. The relation obtained supports the earlier established mechanism for the emission of drops under the action of high pressures developing in explosive emission centers. The possibilities of an additional acceleration of drops due to the explosion of necks formed on breaking the drops off the cathode surface and at the expense of the kinetic energy of the ions of the expanding cathode plasma have been discussed     

Out-of-equilibrium dynamics of the vortex glass in superconductors

We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures the system does not equilibrate with its thermal bath: a simple multiplicative aging is found, the FDT is violated, and we find that an effective temperature characterizes the slow modes of the system. The generic features of the evolution--scaling laws--are dictated by those of the single elastic line in a random environment.     

Kinetic Models for Granular Flow

The generalization of the Boltzmann and Enskog kinetic equations to allow inelastic collisions provides a basis for studies of granular media at a fundamental level. For elastic collisions the significant technical challenges presented in solving these equations have been circumvented by the use of corresponding model kinetic equations. The objective here is to discuss the formulation of model kinetic equations for the case of inelastic collisions. To illustrate the qualitative changes resulting from inelastic collisions the dynamics of a heavy particle in a gas of much lighter particles is considered first. The Boltzmann–Lorentz equation is reduced to a Fokker–Planck equation and its exact solution is obtained. Qualitative differences from the elastic case arise primarily from the cooling of the surrounding gas. The excitations, or physical spectrum, are no longer determined simply from the Fokker–Planck operator, but rather from a related operator incorporating the cooling effects. Nevertheless, it is shown that a diffusion mode dominates for long times just as in the elastic case. From the spectral analysis of the Fokker–Planck equation an associated kinetic model is obtained. In appropriate dimensionless variables it has the same form as the BGK kinetic model for elastic collisions, known to be an accurate representation of the Fokker–Planck equation. On the basis of these considerations, a kinetic model for the Boltzmann equation is derived. The exact solution for states near the homogeneous cooling state is obtained and the transport properties are discussed, including the relaxation toward hydrodynamics. As a second application of this model, it is shown that the exact solution for uniform shear flow arbitrarily far from equilibrium can be obtained from the corresponding known solution for elastic collisions. Finally, the kinetic model for the dense fluid Enskog equation is described.     

KDP晶体台阶生长动力学的激光干涉实验研究

采用迈克尔逊干涉技术 ,通过测量KDP晶体生长的法向速率和台阶斜率来研究其台阶生长的动力学系数、台阶自由能、溶质在边界层内的扩散特征以及激发晶体生长台阶的位错活性 .实验表明 ,KDP中不同活性位错的台阶动力学系数差异较大 ,例如高活性和低活性台阶动力学系数分别为 10 .3× 10 -2 和 5 .2 1× 10 -2 cm/s,位错源在晶体表面的形状、面积的变化 ,以及Burgers矢量的变化是造成晶体生长动力学测量数据重复性差的主要原因     

催化动力学光度法测定痕量铜的研究进展

本文探讨和论述了近年来催化动力学光度法测定痕量铜的研究进展，比较了催化光度法与原子吸收法、萃取光度法的优缺点；介绍了催化动力学光度法的原理；评述了催化褪色光度法、催化显色光度法、催化荧光光度法等的研究进展，探讨和展望了催化动力学光度法未来的研究方向和发展前景，包括：1．对传统显色剂改性或合成新的高灵敏度、高选择性显色剂；2．活性剂增敏研究；3．加强相关催化机理的研究和探讨。全文参考文献29篇。     

Dislocation structure of plastic relaxation waves in polycrystals and alloys under intense shock wave loading

The influence of the structure factors (sizes of grains and precipitates) on the dislocation structure formed in polycrystals and alloys behind the shock wave front (elastic precursor) has been theoretically discussed in terms of the dislocation kinetic relationships and kinetic equation for the dislocation density. The critical conditions of the transition from the cellular dislocation structure to a uniform dislocation distribution have been formulated. These conditions are used to determine the dependences of the critical pressure, above which the dislocation distribution becomes uniform, on the grain size and precipitate volume density.