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Complex Dynamics of Glass-Forming LiquidsA Mode-Coupling Theory$
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Wolfgang Götze

Print publication date: 2008

Print ISBN-13: 9780199235346

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199235346.001.0001

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Correlation Functions

Correlation Functions

(p.51) 2 Correlation Functions
Complex Dynamics of Glass-Forming Liquids

Wolfgang Götze

Oxford University Press

This chapter reviews the theory of correlation functions for classical Hamiltonian systems as a method for a statistical description of the dynamics. Mathematical tools are introduced, which provide a connection of the description in the time domain with that in the frequency domain. The results of linear response theory are summarized; they relate the mathematical description to quantities relevant for the discussion of experiments. The concept of arrested parts of correlations is explained. The Zwanzig–Mori equations of motion are derived as a reformulation of the correlation functions in terms of relaxation kernels. The latter are fluctuating-force-correlation functions defined for a reduced dynamics. The chapter discusses how the structure of these equations can be used as a framework for the construction of correlation-function models.

Keywords:   linear-response theory, arrested parts, Zwanzig–Mori equations, relaxation kernels, fluctuating-force correlations, reduced dynamics

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