闭路格林函数和非线性响应理论(Ⅱ)

本文是关于非线性响应理论的文章的后半部分。我们利用文献[1]的结果将线性情形的涨落耗散定理形式地推广到含有n点关联和响应函数的非线性情形。 关键词：     

Spectral Theorem of Many-Body Green＇s Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.     

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.     

Thermal and non-thermal fluctuations in active polar gels

We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.     

Fluctuation-dissipation ratio in three-dimensional spin glasses

We present an analysis of the data on aging in the three-dimensional Edwards-Anderson spin-glass model with nearest-neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean-field theory. We measure the parameterx(q) describing the violation of the relation among correlation and response functions implied by the fluctuation-dissipation theorem.     

Renormalized perturbation theory for a multiplicative noise system

We study an anharmonic overdamped oscillator driven by both additive and multiplicative Gaussian white noise. Within the Martin-Siggia-Rose formalism we employ renormalized perturbation theory to calculate the stationary correlation function and the response function of the oscillator variable. Due to the absence of a simple fluctuation-dissipation theorem renormalization cannot make use of exact stationary moments, but is perormed with the help of renormalization conditions.     

Surface polariton response function approach to dispersion forces between macroscopic bodies

A new method for the calculation of dispersion forces between macroscopic bodies is developed. The basis idea here is to use the surface polariton response function and the fluctuation-dissipation theorem.     

Extension of the fluctuation-dissipation theorem to non-equilibrium systems

The fluctuation-dissipation theorem is generalized to the case of nonequilibrium (albeit in a stable steady state) systems. The relationship between the correlation function of the current fluctuations and the average energy absorbed by the system as a consequence of dissipation is used. For a nonequilibrium classical system, the responce function is connected with the correlation function in which the averaging is over the derivative of the energy distribution function. Using the spectrum of the electromagnetic fluctuations, inverting the fluctuation-dissipation relation one can find the permittivity of the medium.     

Fluctuations in nonequilibrium systems and broken supersymmetry

The fluctuation-dissipation theorem is not expected to hold for systems that either violate detailed balance or have time-dependent or nonpotential forces. Therefore the relation between response and correlation functions should have contributions due to the nonequilibrium nature. An explicit formula for such a contribution is calculated, which in the present derivation appears as a historydependent term. These relations are the Ward-Takahashi identities of a supersymmetric formulation of the Langevin models, and the new term results from a broken supersymmetry.     

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.     

Calculation of the fluctuation-dissipation ratio for the nonequilibrium critical behavior of disordered systems

The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.     

Activated aging dynamics and negative fluctuation-dissipation ratios

In glassy materials, aging proceeds at large times via thermal activation. We show that this can lead to negative dynamical response functions and novel and well-defined violations of the fluctuation-dissipation theorem, in particular, negative fluctuation-dissipation ratios. Our analysis is based on detailed theoretical and numerical results for the activated aging regime of simple kinetically constrained models. The results are relevant to a variety of physical situations, such as aging in glass formers, thermally activated domain growth, and granular compaction.     

On linewidth of phonons associated to a disorder mechanism

An expression for the linewidth of phonons associated to a disorder mechanism in crystals is deduced. The linewidth of these ‘noise’ phonons is a function of the correlation time describing the statistical behavior of the disorder mechanism. A new view point to the application of the fluctuation-dissipation theorem for order-disorder crystals is presented. The relationship between the behavior of the linewidth of these phonons and phase-transitions mechanisms is discussed.     

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.     

Leading Order Response of Statistical Averages of a Dynamical System to Small Stochastic Perturbations

The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes.     

On the fluctuation-dissipation theorem in a disordered nonequilibrium system

We present a modified perturbational calculation for a model with quenched disorder in nonequilibrium. A systematic way is proposed to obtain corrections to the usual fluctuation-dissipation theorem.     

涨落耗散定理概述

本文从一个最早的例子——Einstein关系,到Callen和Welton及Kubo公式,简述了涨落耗散定理形成和发展的历史,阐明了这个在统计物理学中占有重要地位的定理的物理实质,并列举了它在各个领域一些应用实例,通过这些具体例子,记述了涨落耗散定理与线性响应理论、广义Langevin方程、非平衡统计力学等的关系。     

Effective temperature and fluctuation-dissipation theorem in athermal granular systems:A review

The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.