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• W2068936727 abstract "The statistical dynamics of a Lorentz system produced by freezing in a dynamical bath in thermal equilibrium with a tagged particle which continues to move in the static environment after the quench is described in terms of canonical ensemble averages over the phase-space variables of the system: scatterer positions and coordinates of the particle. A generalized hydrodynamics theory for the fluctuation spectra of the densities of particle number and energy, of their currents, and of their velocities is developed in terms of dispersion-relation representations for the above correlation functions. The coupling between number and energy-density fluctuations showing up via off-diagonal elements of the generalized diffusivity matrix is elucidated. The transition to the localized state and the accompanying slowing down of the zero-frequency relaxation rate of velocity fluctuations is investigated. Simple approximations based upon Lorentzian or Gaussian relaxation kernels are presented and the dependence of spectra and diffusivities on the ratio of mean potential fluctuations and mean kinetic energy is discussed. In the second part a kinetic equation is derived for the 2 ifmmodetimeselsetexttimesfi{} 2 correlation-function matrix of the two phase-space densities of the two constants of the motion, particle number, and energy. For its collision kernel a novel, systematic operator expansion is presented which is manifestly preserving both particle number and energy for arbitrary scatterer densities and interaction potentials. The correlation functions of the currents resulting from the leading order in the expansion are given explicitly in terms of incomplete gamma functions. They yield, in the long-wavelength limit, the proper dispersion-relation representation of the velocity-correlation matrix." @default.
• W2068936727 created "2016-06-24" @default.
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• W2068936727 date "1981-10-01" @default.
• W2068936727 modified "2023-09-27" @default.
• W2068936727 title "Statistical dynamics of a classical particle in the continuous potential of randomly fixed scatterers" @default.
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• W2068936727 doi "https://doi.org/10.1103/physrevb.24.3967" @default.
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