Smoluchowski dynamics and the ergodic-nonergodic transition

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 83, Issue 4, 2011, Pages

  Mazenko, Gene F ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL PARTICLE; CRITICAL VALUE; EFFECTIVE POTENTIALS; ERGODICITY; FLUCTUATION DISSIPATION THEOREM; HARD SPHERES; LIQUID-GLASS TRANSITION; PACKING FRACTIONS; PERCUS-YEVICK APPROXIMATIONS; PERTURBATION THEORY; SECOND ORDERS; STATIC STRUCTURE FACTORS; SYSTEMS-DRIVEN;

PERTURBATION TECHNIQUES;

GLASS TRANSITION;

EID: 79961069211     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.041125     Document Type: Article

References (25)

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10. 12 model and stretching are discussed in detail by W. Goetze, in Liquids, Freezing and Glass Transition, edited by, J. P. Hansen, D. Levesque, and, J. Zinn-Justin, (North-Holland, Amsterdam, 1991) Chap. 5.
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14. The history of Smoluchowski dynamics is discussed in FTSPD.
15. A brief discussion of the storied history of Brownian motion is given in Refs. [2] and [20] in FTSPD. We will refer to the noninteracting limit of Smoluchowski dynamics as the Brownian gas.
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21. See the discussion in FTSPD.
22. The static Ornstein-Zernike relation that connects the radial distribution function to the direct correlation function.
23. In different contexts the kinetic kernels have different names. In the field-theory context the kernels are typically called self-energies, in the kinetic theory case, where the analysis is in terms of retarded quantities, the kernel is called a memory function, and in the general case it can be called a dynamic direct correlation function.
24. G. F. Mazenko, D. D. McCowan, and P. Spyridis (unpublished).
25. An advantage of working in equilibrium is that we can take the initial time to minus infinity. We called this the field-theory protocol in FTSPD.