Mode coupling theory for multi-point and multi-time correlation functions

Details Mode coupling theory for multi-point and multi-time correlation functions Mode coupling theory for multi-point and multi-time correlation functions

2001-08-02

arxiv.org/abs/cond-mat/0108029v1

Phys. Rev. E 65 (2002) 011106.

Physics

Condensed Matter

Statistical Mechanics

First one in a sequence of two. Subsequent one contains comparison with hard sphere simulations. 17 pages REVTeX double column

Scientific paper

10.1103/PhysRevE.65.011106

We present a theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system. Such higher-order correlation functions have attracted much interest recently in the context of various forms of multi-dimensional spectroscopy, and have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite, ``multi-linear'' basis composed of the products of slow variables of the system. Using the formalism, a formally exact mode coupling theory is derived for multi-point and multi-time correlation functions. The resulting expressions for higher-order correlation functions are made tractable by applying a rigorous perturbation scheme, called the N-ordering method, which is exact for systems with finite correlation lengths in the thermodynamic limit. The theory is contrasted with standard mode coupling theories in which the noise or fluctuating force appearing in the generalized Langevin equation is assumed to be Gaussian, and it is demonstrated that the non-Gaussian nature of the fluctuating forces leads to important contributions to higher-order correlation functions. Finally, the higher-order correlation functions are evaluated analytically for an ideal gas system for which it is shown that the mode coupling theory is exact.

Affiliated with

Also associated with

No associations

Rating

Mode coupling theory for multi-point and multi-time correlation functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mode coupling theory for multi-point and multi-time correlation functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mode coupling theory for multi-point and multi-time correlation functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-186409