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Volumn 41, Issue 4, 2000, Pages 1979-2020

Functional and graphical methods for classical statistical dynamics. I. A formulation of the Martin-Siggia-Rose method

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EID: 0034347149     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533223     Document Type: Article
Times cited : (21)

References (44)
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • Deem, M.W.1    Chandler, D.2
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • Sun, T.1    Plischke, M.2
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • Mou, C.Y.1    Weichman, P.B.2
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    • See, for example: S. P. Das, and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); S. P. Das, Phys. Rev. 36, 211-221 (1987); J.-P. Bouchaud, and A. Georges, Phys. Rep. 195, 127 (1990); G. H. Fredrickson and E. Helfand, J. Chem. Phys. 93, 2048 (1990); P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990); B. Kim and G. F. Mazenko, Adv. Chem. Phys. 78, 129 (1990); G. F. Mazenko, Phys. Rev. B 42, 4487 (1990); B. Kim, Phys. Rev. 46, 1992 (1992); O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993); M. W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994); G. L. Eyink, Phys. Fluids 6, 3063 (1994); E. Frey and U. C. Tauber, Phys. Rev. E 50, 1024 (1994); G. F. Mazenko and J. Yeo, J Stat. Phys. 74, 1017 (1994); T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994); M. W. Deem, Phys. Rev. E 51, 4319 (1995); C. Y. Mou and P. B. Weichman, Phys. Rev. E 52, 3738 (1995); S. Scheidl, Phys. Rev. Lett. 75, 4760 (1995); S. P. Das, J. Chem. Phys. 105, 8822 (1996).
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    • note
    • 2, is symmetric under interchange of its two indices. In this case, as noted in the text, all points on a vertex are equivalent and both points on a bond are equivalent. Then this definition of topological equivalence of labeled diagrams is appropriate. In subsequent developments, we shall be concerned with functions that are not symmetric. Thus, the various points attached to a vertex might not be equivalent but might be of two or more types, and the points on the ends of a bond might be of different types. In this case, topological equivalence of two labeled diagrams requires not only the conditions given in the text but also the condition that corresponding points in the diagrams be of the same type.


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