Abstract
The long-time behavior of the velocity correlation functions characteristic for transport coefficients has been calculated for a gas of hard disks or hard spheres on the basis of an appropriate generalized Boltzmann equation. In d-dimensions one finds that, after several mean free times t0, these correlation functions exhibit a decay proportional to (t/t0)−d/2. This decay can be understood as the result of the same sequences of binary collisions that are responsible for the divergences encountered in the virial expansion of the transport coefficients. This long-time behavior in two dimensions is consistent with the results of computer studies of velocity correlation functions for hard disk gases. The possible implications for hydrodynamics of the t−d/2 behavior of the correlation functions is discussed.
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References
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Although we consider here only the relations between the time correlation functions and the transport coefficients, similar time correlation function expressions appear for example in the theory of neutron scattering, of light scattering, and of spectral line shapes.
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Dorfman, J.R. (1973). Velocity Correlation Functions for Moderately Dense Gases. In: Cohen, E.G.D., Thirring, W. (eds) The Boltzmann Equation. Acta Physica Austriaca, vol 10/1973. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8336-6_11
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