DOI: 10.1063/1.2759487. Dynamics of interacting Brownian particles: A diagrammatic formulation

Dynamics of interacting Brownian particles: A diagrammatic formulation

10.1063/1.2759487

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion, we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three- and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.

Bibliography

Szamel, G. (2007). Dynamics of interacting Brownian particles: A diagrammatic formulation. The Journal of Chemical Physics, 127(8).

Authors 1

Grzegorz Szamel (first)

References 41 Referenced 25

10.1063/1.1578632 / J. Chem. Phys. (2003)
10.1103/PhysRevLett.92.148302 / Phys. Rev. Lett. (2004)
10.1103/PhysRevLett.95.078301 / Phys. Rev. Lett. (2005)
10.1063/1.2137701 / J. Chem. Phys. (2005)
10.1103/PhysRevLett.98.058301 / Phys. Rev. Lett. (2007)
{'volume-title': 'An Introduction to Dynamics of Colloids', 'year': '1996', 'key': '2023073122123593900_c2'} / An Introduction to Dynamics of Colloids (1996)
10.1103/PhysRevLett.99.028301 / Phys. Rev. Lett. (2007)
10.1103/PhysRevLett.99.025702 / Phys. Rev. Lett. (2007)
10.1088/0953-8984/17/6/R01 / J. Phys.: Condens. Matter (2005)
10.1021/jp0258661 / J. Phys. Chem. B (2002)
10.1021/jp034753u / J. Phys. Chem. B (2003)
10.1021/jp034754m / J. Phys. Chem. B (2003)
10.1103/PhysRevA.11.328 / Phys. Rev. A (1975)
10.1016/0378-4371(92)90198-Y / Physica A (1992)
10.1016/S0378-4371(97)00409-3 / Physica A (1997)
10.1088/0305-4470/38/20/L03 / J. Phys. A (2005)
{'volume': '2006', 'journal-title': 'J. Stat. Mech.: Theory Exp.', 'first-page': 'P07008', 'key': '2023073122123593900_c10'} / J. Stat. Mech.: Theory Exp.
10.1088/1751-8113/40/1/F04 / J. Phys. A (2007)
10.1103/PhysRevE.74.030101 / Phys. Rev. E (2006)
{'volume-title': 'Liquids, Freezing and Glass Transition', 'year': '1991', 'author': 'Hansen', 'key': '2023073122123593900_c13'} / Liquids, Freezing and Glass Transition by Hansen (1991)
10.1103/PhysRevA.44.8215 / Phys. Rev. A (1991)
10.1007/s002570050396 / Z. Phys. B: Condens. Matter (1997)
10.1103/PhysRevLett.81.2514 / Phys. Rev. Lett. (1998)
10.1103/PhysRevLett.97.036402 / Phys. Rev. Lett. (2006)
10.1103/PhysRevB.74.245101 / Phys. Rev. B (2006)
10.1103/PhysRevA.46.5012 / Phys. Rev. A (1992)
10.1209/epl/i2003-10115-2 / Europhys. Lett. (2004)
{'volume-title': 'Statistical Mechanics', 'year': '1977', 'author': 'Berne', 'key': '2023073122123593900_c20a'} / Statistical Mechanics by Berne (1977)
{'volume-title': 'Theory of Simple Liquids', 'year': '1986', 'key': '2023073122123593900_c20b'} / Theory of Simple Liquids (1986)
10.1080/00018738300101551 / Adv. Phys. (1983)
10.1016/0378-4371(87)90176-2 / Physica A (1987)
10.1103/PhysRevLett.89.248304 / Phys. Rev. Lett. (2002)
10.1016/0378-4371(94)90533-9 / Physica A (1994)
10.1103/PhysRevLett.90.228301 / Phys. Rev. Lett. (2003)
10.1103/PhysRevLett.97.095702 / Phys. Rev. Lett. (2006)
10.1063/1.480541 / J. Chem. Phys. (2000)
10.1063/1.1605094 / J. Chem. Phys. (2003)
10.1209/epl/i2004-10044-6 / Europhys. Lett. (2004)
10.1063/1.2721554 / J. Chem. Phys. (2007)
10.1063/1.2721555 / J. Chem. Phys. (2007)
{'volume': '2005', 'journal-title': 'J. Stat. Mech.: Theory Exp.', 'first-page': 'P05013', 'key': '2023073122123593900_c27'} / J. Stat. Mech.: Theory Exp.

Dates

Type	When
Created	17 years, 11 months ago (Aug. 31, 2007, 7:12 p.m.)
Deposited	2 years ago (July 31, 2023, 6:13 p.m.)
Indexed	3 weeks, 1 day ago (July 30, 2025, 6:49 a.m.)
Issued	17 years, 11 months ago (Aug. 28, 2007)
Published	17 years, 11 months ago (Aug. 28, 2007)
Published Online	17 years, 11 months ago (Aug. 31, 2007)
Published Print	17 years, 11 months ago (Aug. 28, 2007)

Funders 0

None

BibTeX

@article{Szamel_2007, title={Dynamics of interacting Brownian particles: A diagrammatic formulation}, volume={127}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2759487}, DOI={10.1063/1.2759487}, number={8}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Szamel, Grzegorz}, year={2007}, month=aug }

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