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Chemical Dynamics in Condensed PhasesRelaxation, Transfer and Reactions in Condensed Molecular Systems$
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Abraham Nitzan

Print publication date: 2006

Print ISBN-13: 9780198529798

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198529798.001.0001

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Time Correlation Functions

Time Correlation Functions

6 Time Correlation Functions
Chemical Dynamics in Condensed Phases

Abraham Nitzan

Oxford University Press

In the previous chapter we have seen how spatial correlation functions express useful structural information about our system. This chapter focuses on time correlation functions that, as will be seen, convey important dynamical information. Time correlation functions will repeatedly appear in our future discussions of reduced descriptions of physical systems. A typical task is to derive dynamical equations for the time evolution of an interesting subsystem, in which only relevant information about the surrounding thermal environment (bath) is included. We will see that dynamic aspects of this relevant information usually enter via time correlation functions involving bath variables. Another type of reduction aims to derive equations for the evolution of macroscopic variables by averaging out microscopic information. This leads to kinetic equations that involve rates and transport coefficients, which are also expressed as time correlation functions of microscopic variables. Such functions are therefore instrumental in all discussions that relate macroscopic dynamics to microscopic equations of motion. It is important to keep in mind that dynamical properties are not exclusively relevant only to nonequilibrium system. One may naively think that dynamics is unimportant at equilibrium because in this state there is no evolution on the average. Indeed in such systems all times are equivalent, in analogy to the fact that in spatially homogeneous systems all positions are equivalent. On the other hand, just as in the previous chapter we analyzed equilibrium structures by examining correlations between particles located at different spatial points, also here we can gain dynamical information by looking at the correlations between events that occur at different temporal points. Time correlation functions are our main tools for conveying this information in stationary systems. These are systems at thermodynamic equilibrium or at steady state with steady fluxes present.

Keywords:   Drude spectral density, Einstein frequency of fluids, Ohmic spectral density, Wiener–Khintchine theorem, autocorrelation function, detailed balance, golden rule rates, instantaneous normal modes, optical absorption, stationary systems

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