Smoluchowski dynamics and the ergodic-nonergodic transition

The classical operator formalism for Newtonian dynamics was introduced by J. von Neumann, Proc. Natl. Acad. Sci. U.S.A. 18

1932

Earlier work this paper cites.

There is an exact solution to the Percus-Yevick approximation for hard spheres. See the discussion in Chapter 4 in J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids

1966

Earlier work this paper cites.

The F 12 F_{12} model and stretching are discussed in detail by W. Goetze, in Liquids, Freezing and Glass Transition

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W. Goetze in Liquids, Freezing and Glass Transition

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The history of Smoluchowski dynamics is discussed in FTSPD

Cited in the paper.

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

Cited in the paper.

MSR actions are discussed in Appendix A in FTSPD

Cited in the paper.

See the discussion in FTSPD

Cited in the paper.

The static Ornstein-Zernike relation that connects the radial distribution function to the direct correlation function

Cited in the paper.

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

Cited in the paper.

Note that b 1 b_{1} depends on the n n t i t_{i} while the operator depends only on t 1 t_{1}

Cited in the paper.

P. N. Pusey, J. Phys. Condens. Matter 20

2008

Later among the works it cites.

B. Kim and K. Kawasaki, ”A FDR-Preserving Field Theory for Interacting Brownian Particles: One-Loop Theory and MCT,” AIP Conf. Proc. 982 (Complex Systems: 5th International Workshop on Complex Systems,” Sendai (Japan), Sept. 22-28, 2007.), 223 (2008)

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R. Velenich, C. Chamon, L. Cugliandolo, and D. Kreimer, J. Phys. A 41

2008

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G. F. Mazenko, Phys. Rev. E 81

2010

Closest in time.