Kinetic theories of dynamics and persistent caging in a one-dimensional lattice gas

Proceedings of the National Academy of Sciences of the United States of America

Volumn 106, Issue 36, 2009, Pages 15142-15147

  Abel, Steven M ^a   Tse, Ying Lung Steve ^b   Andersen, Hans C ^b  

^a Stanford University   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Liquids; Mode coupling

Indexed keywords

ARTICLE; COMPUTER SIMULATION; DIFFUSION; GAS; KINETICS; MOLECULAR DYNAMICS; PRIORITY JOURNAL; THEORETICAL MODEL;

COMPUTER SIMULATION; DIFFUSION; KINETICS; MODELS, CHEMICAL; PHASE TRANSITION;

EID: 70349339277     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.0901693106     Document Type: Article

References (35)

1. Boon JP, Yip S (1980) Molecular Hydrodynamics (McGraw-Hill, New York).
2. Richards P (1977) Theory of one-dimensional hopping conductivity and diffusion. Phys Rev B 16:1393-1409.
3. Fedders PA (1978) Two-point correlation functions for a distinguishable particle hopping on a uniform one-dimensional chain. Phys Rev B 17:40-46.
4. Alexander S, Pincus P (1978) Diffusion of labeled particles on one-dimensional chains. Phys Rev B 18:2011-2012.
5. Arratia R (1983) The motion of a tagged particle in the simple symmetric exclusion system on Z. Ann Prob 11:362-373.
6. van Beijeren H, Kehr KW, Kutner R (1983) Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice. Phys Rev B 28:5711-5723.
7. Kärger J (1992) Straightforward derivation of the long-time limit of the mean-square displacement in one-dimensional diffusion. Phys Rev A 45:4173-4174.
8. Kärger J (1993) Long-time limit of the self-correlation-function of one-dimensional diffusion. Phys Rev E 47:1427-1428.
9. Andersen HC (2002) A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. I. The fluctuation basis and the cluster properties of associated functions. J Phys Chem B 106:8326-8337.
10. Andersen HC (2003) A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. II. Equations of motion of the fluctuation fields and their diagrammatic solution. J Phys Chem B 107:10226-10233.
11. Andersen HC (2003) A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. III. Cluster analysis of the renormalized interactions and a second diagrammatic representation of the correlation functions. J Phys Chem B 107:10234-10242.
12. Feng EH, Andersen HC (2004) A diagrammatic kinetic theory for a lattice model of a liquid. I. Theory. J Chem Phys 121:3582-3597.
13. Feng EH, Andersen HC (2004) A diagrammatic kinetic theory for a lattice model of a liquid. II. Comparison of theory and simulation results. J Chem Phys 121:3598-3604.
14. Götze W (1991) Liquids, Freezing, and the Glass Transition, eds Hansen JP, Levesque D, Zinn-Justin D (North-Holland, Amsterdam).
15. Götze W, Sjögren L (1995) The mode coupling theory of structural relaxations. Transp Theory Stat Phys 24:801-853.
16. Das SP (2004) Mode-coupling theory and the glass transition in supercooled liquids. Rev Mod Phys 76:785-851. (Pubitemid 40180192)
17. Harris TE (1965) Diffusion with "collisions" between particles. J Appl Prob 2:323-338.
18. Spitzer FL (1970) Interaction of Markov processes. Adv Math 5:246-290.
19. Levitt DG (1973) Dynamics of a single-file pore: non-Fickian behavior. Phys Rev A 8:3050-3054.
20. Kollmann M (2003) Single-file diffusion of atomic and colloidal systems: Asymptotic laws. Phys Rev Lett 90:180602.
21. Ambjörnsson T, Lizana L, Lomholt MA, Silbey RJ (2008) Single-file dynamics with different diffusion constants. J Chem Phys 129:185106.
22. Mon KK, Percus JK (2002) Self-diffusion of fluids in narrow cylindrical pores. J Chem Phys 117:2289-2292.
23. Mon KK, Percus JK (2005) Soluble stochastic dynamics of quasi-one-dimensional single-file fluid self-diffusion. J Chem Phys 122:21453.
24. Lin B, Meron M, Cui B, Rice SA, Diamant H (2005) From random walk to single-file diffusion. Phys Rev Lett 94:216001.
25. Fedders PA, Sankey OF (1977) The generalized atomic hopping problem - Occupancy correlation functions. Phys Rev B 15:3580-3585.
26. Sankey OF, Fedders PA (1977) The generalized atomic hopping problem-Particle correlation functions. Phys Rev B 15:3586-3591.
27. Kehr KW, Kutner R, Binder K (1981) Diffusion in concentrated lattice gases. Self-diffusion of noninteracting particles in three-dimensional lattices. Phys Rev B 23:4931-4945.
28. Tahir-Kheli RA, Elliott RJ (1983) Correlated random walk in lattices: tracer diffusion at general concentration. Phys Rev B 27:844-857.
29. Mayer P, Miyazaki K, Reichman DR (2006) Cooperativity beyond caging: generalized mode-coupling theory. Phys Rev Lett 97:095702. (Pubitemid 44329377)
30. Biroli G, Bouchaud J-P, Miyazaki K, Reichman DR (2006) Inhomogeneous mode-coupling theory and growing dynamic length in supercooled liquids. Phys Rev Lett 97:195701. (Pubitemid 44707961)
31. Szamel G (2008) Divergent four-point dynamic density correlation function of a glassy suspension. Phys Rev Lett 101:205701.
32. Abel SM (2009) Kinetic theories for stochastic models of liquids with highly cooperative dynamics. PhD Thesis (Stanford University, Stanford, CA).
33. Pitts SJ, Andersen HC (2000) The meaning of the irreducible memory function in stochastic theories of dynamics with detailed balance. J Chem Phys 113:3945-3950.
34. Mazenko GF (1974) Fully renormalized kinetic theory. III. Density fluctuations. Phys Rev A 9:360-387.
35. Mazenko GF, Yip S (1977) Statistical Mechanics. Part B. Time-Dependent Processes, ed Berne BJ (Plenum, New York).