Fluctuation-dissipation Theory Research Articles

Markovian fluctuation-dissipation theory of open radiophysical systems

Markovian fluctuation-dissipation theory of open radiophysical systems

Spatial correlations in nonequilibrium systems: The effect of diffusion

We show how the ideas of the fluctuation-dissipation theory can be used to calculate spatial correlations in interacting systems away from equilibrium. The only spatially dependent dissipative process considered is diffusion, and spatial correlations are generated by the nonlocal spatial dependence of the chemical potential. The results are the lowest order in a hierarchy of generalized hydrodynamic type calculations applicable to nonequilibrium systems. We derive equations for the density correlation functions at stationary state supported by diffusive fluxes and show that they have the local equilibrium form. The static correlation function is obtained from the fluctuation-dissipation theorem, which we show to be equivalent to the Ornstein-Zernike integral equation. At equilibrium we demonstrate that the dynamical structure factor obtained by these methods includes the expected wave-vector dependent diffusion constant. Finally we derive a necessary and sufficient condition for local equilibrium to obtain at a stationary state and show by explicit calculation that chemical processes can give rise to significant nonequilibrium correlations.

The effects of electron‐neutral collisions on the intensity of plasma lines

In the earth's ionosphere the presence of nonthermal electrons causes enhancement of the electron plasma line resonance observed by incoherent backscatter radar. This paper extends previous calculations of the plasma intensity by including resonance broadening due to electron‐neutral collisions. A BGK collision term is included in the derivation of the electron spectral density function obtained from fluctuation dissipation theory. Assuming the nonthermal electron distribution is a small perturbation on a Maxwellian distribution of background electrons, the expression describing the signal intensity for a plasma line reduces to the form obtained previously when only electron‐ion collisions were included. Results of this extended model are compared to recent measurements made with the Chatanika radar.

Calculation of voltage fluctuations at the Gunn instability

Recent measurements of voltage fluctuations near the threshold of the Gunn instability in GaAs by Kabashima, Yamazaki, and Kawakubo yield a Gaussian distribution of fluctuations and an anomalous increase in the variance. These results confirm the qualitative predictions of the fluctuation–dissipation theory of molecular fluctuations. In this note, a quantitative calculation of the fluctuations below threshold is given. Only experimentally determined parameters are involved, and the results are in good agreement with experiment.

Thermodynamics at nonequilibrium steady states

This work continues a discussion of how to extend equilibrium thermodynamics to nonequilibrium steady states. The extension is based on molecular fluctuations of the extensive variables and gives rise to a state function, called the σ function. The σ function reduces to the entropy at equilibrium and can be constructed from a knowledge of the local equilibrium entropy and the molecular fluctuations. The σ function depends on all the variables characterizing a steady state, including fluxes of the extensive variables and reservoir parameters. The theoretical analysis of nonequilibrium fluctuations predicts that the σ function is related to stability and the kinetics around a steady state just like the entropy is at equilibrium. Calculations of the σ function are outlined for several multicomponent systems of experimental interest. Using the fluctuation–dissipation theory, a generalization of the Clausius inequality is obtained. This leads to a class of extremum principles at steady state for Legendre transformations of the σ function.

Anti-Stokes stimulated Raman scattering of light by polaritons

A theoretical analysis is made of anti-Stokes stimulated Raman scattering (STRS) of light by polaritons in noncentrosymmetric crystals. This is due to the superposition of parametric four-photon and two-stage three-photon processes, in addition to three-photon processes associated with the possible existence of thermal polariton excitations. These processes are mutually coherent and their contributions interfere. The fluctuation-dissipation theory of polariton STRS is applied to derive and analyze general formulas for the frequency-angular distribution of the Stokes and anti-Stokes radiation intensity at the exit face of a plane-parallel crystal layer pumped by a given plane monochromatic wave. Unlike the phonon process, frequency-tunable polariton anti-Stokes STRS is found in scattering at any angles within the polariton range of scattering angles. The anti-Stokes processes also affect the Stokes scattering. In particular, a doublet fine is observed near the center of the gain line with a dip on one side and a on the other. If the is sufficiently large, it may determine the line observed in strong STRS. The anti-Stokes lines are generally considerably narrower than the Stokes lines but their peak intensities are of the same order of magnitude. They also have a doublet structure with a dip and whose width, in this case, is of the order of the total line width. Spontaneous anti-Stokes scatterng is attributable only to thermal polariton excitations in the medium.

On the macroscopic equivalence of descriptions of fluctuations for chemical reactions

Three descriptions of spontaneous fluctuations in macroscopic systems have been proposed: One uses generalized Fokker–Planck equations and treats fluctuations as a stochastic diffusion process; another uses a connection between fluctuations and dissipation and generalizes the Langevin method; the third is the master equation theory which treats fluctuations as arising from a birth and death process. For a variety of systems it is known that the master equation theory is identical to the fluctuation–dissipation theory in the macroscopic limit. For chemical reactions it is shown here that the appropriate diffusion process also becomes identical with the fluctuation–dissipation theory in the macroscopic limit.

The theory of Raman scattering by surface polaritons

AbstractThe fluctuation–dissipation theory of spontaneous Raman scattering (RS) by surface polaritons (SP) is carried out. The appearance of scattering emission is treated as the result of mixing of the pump emission and the fluctuating surface electromagnetic field. A calculation is made of the surface electromagnetic fluctuations near the interface between the two dissipative media and in the absorbing layer surrounded by transparent dielectrics. Expressions are found and analysed describing the frequency–angular distribution of the scattering emission intensity in the layer, taking into account the interference of SP localized near different surfaces (and near the interface of two absorbing media). The RS intensities are expressed by the phenomenological parameters of the media. It is also shown that the RS intensity decreases essentially with increasing scattering angle θ (when the scattering frequency approaches the frequency of the surface phonon) due to the increasing localization of SP. Various essential physical features of the phenomenon are analysed in detail: scattering line shape and its angular dependence; the Fermi resonance of SP and its display in the RS; mixing of SP of different media and RS by appearing mixed modes; RS by SP connected genetically with the linear medium which borders with the transparent nonlinear medium; evolution of RS in a layer by decreasing its thickness, and others.