Self-consistent approach to the description of relaxation processes in classical multiparticle systems

Abstract

The concept of time correlation functions is a very convenient theoretical tool in describing relaxation processes in multiparticle systems because, on one hand, correlation functions are directly related to experimentally measured quantities (for example, intensities in spectroscopic studies and kinetic coefficients via the Kubo-Green relation) and, on the other hand, the concept is also applicable beyond the equilibrium case. We show that the formalism of memory functions and the method of recurrence relations allow formulating a self-consistent approach for describing relaxation processes in classical multiparticle systems without needing a priori approximations of time correlation functions by model dependencies and with the satisfaction of sum rules and other physical conditions guaranteed. We also demonstrate that the approach can be used to treat the simplest relaxation scenarios and to develop microscopic theories of transport phenomena in liquids, the propagation of density fluctuations in equilibrium simple liquids, and structure relaxation in supercooled liquids. This approach generalizes the mode-coupling approximation in the Götze-Leutheusser realization and the Yulmetyev-Shurygin correlation approximations.

arXiv comment38 pages, 4 figures

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• Collective ion dynamics in Coulomb one-component plasmas within the self-consistent relaxation theory
• Three-Particle Correlations in Liquid and Amorphous Aluminium
• Is there a one-to-one correspondence between interparticle interactions and physical properties of liquid?
• Weak decaying collective-excitation approximation for Yukawa one-component plasmas
• Thermodynamics of Equilibrium Alkali Plasma. Simple and Accurate Analytical Model for Non-Trivial Case
• Recent advances in the calculation of dynamical correlation functions
• A model solution of the generalized Langevin equation: Emergence and Breaking of Time-Scale Invariance in Single-Particle Dynamics of Liquids