# Time Correlation Functions And Transport Coefficients In Statistical Mechanics Pdf

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## Green–Kubo relations

A kinetic equation governing the time dependence of the correlation function of flux is established for dilute gases and is integrated to yield a relation between the correlation time and the transport cross section. The spectrum of the binary collision operator is determined for spherically symmetric forces between molecules, which, for the hard-core model, consists of two discrete values in the classical limit; hence it is shown that the question of validity of approximating the correlation function by an exponential decay depends upon the type of intermolecular force and the temperature of the system. Approximate eigenvalues of the master collision operator are obtained corresponding to the fluxes of viscosity and thermal conduction, and their relations to the macroscopic transport coefficients are derived. These relations lead to a new approach to the transport properties of dilute gases, which is different from Enskog-Chapman's method, but yields the same results in the classical limit. An expansion formula for the canonical transformation describing the motion of dilute gases is obtained and is employed to clarify the assumption of random a priori phases in the momentum representation for spatially uniform gases; this is done by formulating the quantum-mechanical equivalent of Brout's idea in the classical derivation of the master equation.

## 7.4: Time Correlation Functions

One of the most active research areas in statistical mechanics involves the evaluation of so-called equilibrium time correlation functions such as we encountered in Chapter 6. As shown above, an example of a time correlation function that relates to molecular spectroscopy is the dipole-dipole correlation function that we discussed in Chapter It turns out that many physical properties e. It is beyond the scope of this text to go much further in this direction, so I will limit my discussion to the optical spectroscopy case at hand, which requires that we now discuss how the time-evolution aspect of this problem is dealt with. The text Statistical Mechanics, D. McQuarrie, Harper and Row, New York has a nice treatment of such other correlation functions, so the reader is directed to that text for further details.

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Time correlation functions for the transport coefficients in the linear Landau-Khalatnikov equations are derived on the basis of a formal theory. These Green-Kubo expressions are then explicitly evaluated for a dilute superfluid and the resulting transport coefficients are shown to be identical to those obtained previously by using a distribution function method. This is a preview of subscription content, access via your institution.

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These metrics are regularly updated to reflect usage leading up to the last few days. Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts. The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online.

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