Mode coupling and generalized hydrodynamics

Schofield, Jeremy; Lim, Raymond; Oppenheim, Irwin

doi:10.1016/0378-4371(92)90198-y

Cited by 41 publications

(61 citation statements)

References 15 publications

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“…The N -ordering of various quantities has been discussed extensively elsewhere [44,46,47], so here we just state a few properties of the procedure that enable us to estimate N -orders of relevant quantities.…”

Section: N -Orderingmentioning

confidence: 99%

“…The N -ordering scheme was first introduced by Machta and Oppenheim [44] as an extension of Van Kampen's inverse system size expansion (Ω expansion) [50] and developed further in Ref. [46]. It is essential in obtaining the correct Stokes-Einstein law for a Brownian particle using mode coupling techniques [47].…”

Section: N -Orderingmentioning

confidence: 99%

“…The distinction between fast and slow behavior can be made more precise on the level of correlation functions, following the projection operator method as used by Oppenheim and others [44][45][46][47].…”

Section: B Generalized Langevin Equationmentioning

confidence: 99%

“…(4). Using only the linear projection P 1 will not give a proper mode coupling theory since the long-time dependence of dynamical variables due to multi-linear orders of the densities is not extracted by the projection operator [46][47][48][49]. It is therefore convenient to define an orthogonal, multi-linear basis as…”

Section: B Generalized Langevin Equationmentioning

confidence: 99%

“…It is based on the mode coupling theory obtained by a projection operator formalism [42,43] as developed by Oppenheim and coworkers [44][45][46][47]. By careful consideration of how to consistently identify fast and slow behavior in time correlation functions, we derive expressions for multi-point and multitime correlation functions in terms of simple time correlation functions.…”

Section: Introductionmentioning

confidence: 99%

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

Zon

Schofield

2001

Phys. Rev. E

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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 higherorder 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.

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Section: N -Orderingmentioning

confidence: 99%