Gaussian density fluctuations and mode coupling theory for supercooled liquids

Europhysics Letters

Volumn 55, Issue 2, 2001, Pages 157-163

  Zaccarelli, E ^a   Foffi, G ^a   Sciortino, F ^b   Tartaglia, P ^b   Dawson, K A ^a  

^a UNIVERSITY COLLEGE DUBLIN   (Ireland)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035796146     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2001-00395-x     Document Type: Article

References (44)

1. BENGTZELIUS U., GÖTZE W. and SJÖLANDER A., J. Phys. C, 17 (1984) 5915; GÖTZE W., in Liquids, Freezing and Glass Transition, edited by HANSEN J. P., LEVESQUE D. and ZINN-JUSTIN J. (North-Holland, Amsterdam) 1991.
2. BENGTZELIUS U., GÖTZE W. and SJÖLANDER A., J. Phys. C, 17 (1984) 5915; GÖTZE W., in Liquids, Freezing and Glass Transition, edited by HANSEN J. P., LEVESQUE D. and ZINN-JUSTIN J. (North-Holland, Amsterdam) 1991.
3. DAS S. P. and MAZENKO G. F., Phys. Rev. A, 34 (1986) 2265.
4. DUFTY J. W. and SCHMITZ R., Transp. Theor. Stat. Phys., 24 (1995) 903.
5. KAWASAKI K., Transp. Theor. Stat. Phys., 24 (1995) 755; Physica A, 208 (1994) 35.
6. KAWASAKI K., Transp. Theor. Stat. Phys., 24 (1995) 755; Physica A, 208 (1994) 35.
7. KIRKPATRICK T. R. and THIRUMALAI D., Phys. Rev. Lett., 58 (1987) 2091.
8. CONIGLIO A., DE CANDIA A., FIERRO A. and NICODEMI M., J. Phys. Condens. Matter, 11 (1999) A167.
9. MÉZARD M. and PARISI G., J. Phys. Condens. Matter, 11 (1999) A157; CARDENAS M., FRANZ S. and PARISI G., J. Chem. Phys., 110 (1999) 1726.
10. MÉZARD M. and PARISI G., J. Phys. Condens. Matter, 11 (1999) A157; CARDENAS M., FRANZ S. and PARISI G., J. Chem. Phys., 110 (1999) 1726.
11. SJÖGREN L., Phys. Rev. A, 22 (1980) 2866; GÖTZE W. and SJÖGREN L., Z. Phys. B, 65 (1987) 415.
12. SJÖGREN L., Phys. Rev. A, 22 (1980) 2866; GÖTZE W. and SJÖGREN L., Z. Phys. B, 65 (1987) 415.
13. VAN MEGEN W., UNDERWOOD S. M. and PUSEY P. N., Phys. Rev. Lett., 67 (1991) 1586; VAN MEGEN W. and UNDERWOOD S. M., Phys. Rev. Lett., 70 (1993) 2766; 72 (1994) 1773.
14. VAN MEGEN W., UNDERWOOD S. M. and PUSEY P. N., Phys. Rev. Lett., 67 (1991) 1586; VAN MEGEN W. and UNDERWOOD S. M., Phys. Rev. Lett., 70 (1993) 2766; 72 (1994) 1773.
15. VAN MEGEN W., UNDERWOOD S. M. and PUSEY P. N., Phys. Rev. Lett., 67 (1991) 1586; VAN MEGEN W. and UNDERWOOD S. M., Phys. Rev. Lett., 70 (1993) 2766; 72 (1994) 1773.
16. GÖTZE W., J. Phys. Condens. Matter, 11 (1999) A1.
17. GLEIM T., KOB W. and BINDER K., Phys. Rev. Lett., 81 (1998) 4404.
18. SCIORTINO F. and KOB W., Phys. Rev. Lett., 86 (2001) 648.
19. FABBIAN L., LATZ A., SCHILLING R., SCIORTINO F., TARTAGLIA P. and THEIS C., Phys. Rev. E., 60 (1999) 5768.
20. See, e.g., CHANDLER D., Phys. Rev. E., 48 (1993) 2898; HUMMER G., GARDE S., GARCIA A. E., POHORILLE A. and PRATT L. R., Proc. Natl. Acad. Sci., 93 (1996) 8951; CROOKS G. E. and CHANDLER D., Phys. Rev. E, 56 (1997) 4217. Note that static density fluctuations do not necessarily imply Gaussian dynamics.
21. See, e.g., CHANDLER D., Phys. Rev. E., 48 (1993) 2898; HUMMER G., GARDE S., GARCIA A. E., POHORILLE A. and PRATT L. R., Proc. Natl. Acad. Sci., 93 (1996) 8951; CROOKS G. E. and CHANDLER D., Phys. Rev. E, 56 (1997) 4217. Note that static density fluctuations do not necessarily imply Gaussian dynamics.
22. See, e.g., CHANDLER D., Phys. Rev. E., 48 (1993) 2898; HUMMER G., GARDE S., GARCIA A. E., POHORILLE A. and PRATT L. R., Proc. Natl. Acad. Sci., 93 (1996) 8951; CROOKS G. E. and CHANDLER D., Phys. Rev. E, 56 (1997) 4217. Note that static density fluctuations do not necessarily imply Gaussian dynamics.
23. PERCUS J. K., in Studies in Statistical Mechanics, edited by MONTROLL E. W. and LEBOWITZ J. L., Vol. VIII (North-Holland, Amsterdam) 1982.
24. ZWANZIG R., Phys. Rev., 156 (1967) 190.
25. HANSEN J. P. and MCDONALD I. R., Theory of Simple Liquids, 2nd edition (Academic Press, London) 1986.
26. MARCH A. N. H. and TOSI M. P., Atomic Dynamics in Liquids (Dover, New York) 1991.
27. ZWANZIG R., in Lectures of Theoretical Physics, Vol. III (Wiley Interscience, New York) 1961; MORI H., Prog. Theor. Phys., 33 (1965) 423; 34 (1965) 399.
28. ZWANZIG R., in Lectures of Theoretical Physics, Vol. III (Wiley Interscience, New York) 1961; MORI H., Prog. Theor. Phys., 33 (1965) 423; 34 (1965) 399.
29. ZWANZIG R., in Lectures of Theoretical Physics, Vol. III (Wiley Interscience, New York) 1961; MORI H., Prog. Theor. Phys., 33 (1965) 423; 34 (1965) 399.
30. KUBO R., TODA M. and HASHITSUME N., Statistical Physics II, 2nd edition (Springer-Verlag, Berlin) 1991.
31. t′ρk(t′)dt′〉.
32. Instead of using the explicit force implied by eqs. (3), (7), it is possible to use the force implied by eq. (10). The result requires time correlations of ρ̈k, which cannot be carried out explicitly. Previously ρ̈k have been projected onto density pairs and Gaussian statistics is used to factorize the 4-point correlations [1], thus getting rid of the bare potential.
33. The Gaussian approximation for noise (and density) implies that, in eq. (6), all terms in the sum are neglected, except for k = k′. Evidently this step could have equally well been represented as RPA, but in essence all what follows stems logically and exactly from the choice of Gaussian noise.
34. PINES D. and NOZIÉRES P., The Theory of Quantum Liquids (W. A. Benjamin, New York) 1966.
35. By multiplying both sides of eq. (2) by ρk(0) and averaging, an exact equation for 〈ρk(t)ρ-k(0)〉 is found. Assuming ρk(t) to be a Gaussian process, 〈Fk(t)ρ-k(0)〉 = 0.
36. CRISANTI A. and SOMMERS H.-J., Z. Phys. B, 87 (1992) 341.
37. SINGWI K. S., TOSI M. P., LAND R. H. and SJÖLANDER A., Phys. Rev., 176 (1968) 589.
38. E. ZACCARELLI et al., work in preparation.
39. SCHILLING R. and SCHEIDSTEGER T., Phys. Rev. E, 56 (1997) 2932.
40. CHONG S.-H. and HIRATA F., Phys. Rev. E, 57 (1998) 1691; 58 (1998) 6188; 7296.
41. CHONG S.-H. and HIRATA F., Phys. Rev. E, 57 (1998) 1691; 58 (1998) 6188; 7296.
42. CHONG S.-H. and HIRATA F., Phys. Rev. E, 57 (1998) 1691; 58 (1998) 6188; 7296.
43. FRANOSCH T., FUCHS M., GÖTZE W., MAYR M. R. and SINGH A. P., Phys. Rev. E, 56 (1997) 5659.
44. FUCHS M. and SCHWEIZER K. S., Macromolecules, 30 (1997) 5133.