Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

[en] We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established in [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an iterative algorithm and a straightforward discretization of time. We also discuss the case of hard spheres, for which we first derive analytically the dynamical mean field theory as a non-trivial limit of the soft sphere one. We present numerical results for the memory function and the mean square displacement. Our results reproduce and extend kinetic theory in the dilute or short-time limit, while they also describe dynamical arrest towards the glass phase in the dense strongly-interacting regime.

Disciplines :

Physics

Author, co-author :

MANACORDA, Alessandro ; Laboratoire de Physique de l'École Normale Supérieure - LPENS

Schehr, Grégory

Zamponi, Francesco

External co-authors :

yes

Language :

English

Title :

Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

Publication date :

24 April 2020

Journal title :

Journal of Chemical Physics

ISSN :

0021-9606

eISSN :

1089-7690

Publisher :

American Institute of Physics, New York, United States - New York

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://arxiv.org/abs/2002.09216

European Projects :

H2020 - 723955 - GlassUniversality - Universal explanation of low-temperature glass anomalies

Funders :

CE - Commission Européenne
European Union

Available on ORBilu :

since 07 January 2022

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Bibliography

J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. ( Academic Press, 1986).
U. Bengtzelius, W. Gotze, and A. Sjolander, J. Phys. C: Solid State Phys. 17, 5915 ( 1984). 10.1088/0022-3719/17/33/005
W. Götze, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory ( Oxford University Press, 2008).
S. P. Das and G. F. Mazenko, Phys. Rev. A 34, 2265 ( 1986). 10.1103/physreva.34.2265
A. Andreanov, G. Biroli, and A. Lefèvre, J. Stat. Mech.: Theory Exp. 2006, P07008. 10.1088/1742-5468/2006/07/p07008
B. Kim and K. Kawasaki, J. Phys. A: Math. Theor. 40, F33 ( 2007). 10.1088/1751-8113/40/1/f04
H. Jacquin and F. Van Wijland, Phys. Rev. Lett. 106, 210602 ( 2011). 10.1103/physrevlett.106.210602
W. Götze, J. Phys.: Condens. Matter 11, A1 ( 1999). 10.1088/0953-8984/11/10a/002
H. L. Frisch, N. Rivier, and D. Wyler, Phys. Rev. Lett. 54, 2061 ( 1985). 10.1103/physrevlett.54.2061
H. L. Frisch and J. K. Percus, Phys. Rev. A 35, 4696 ( 1987). 10.1103/physreva.35.4696
D. Wyler, N. Rivier, and H. L. Frisch, Phys. Rev. A 36, 2422 ( 1987). 10.1103/physreva.36.2422
H. L. Frisch and J. K. Percus, Phys. Rev. E 60, 2942 ( 1999). 10.1103/physreve.60.2942
T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35, 3072 ( 1987). 10.1103/physreva.35.3072
Y. Elskens and H. L. Frisch, Phys. Rev. A 37, 4351 ( 1988). 10.1103/physreva.37.4351
T. Maimbourg, J. Kurchan, and F. Zamponi, Phys. Rev. Lett. 116, 015902 ( 2016). 10.1103/physrevlett.116.015902
G. Szamel, Phys. Rev. Lett. 119, 155502 ( 2017). 10.1103/physrevlett.119.155502
E. Agoritsas, G. Biroli, P. Urbani, and F. Zamponi, J. Phys. A: Math. Theor. 51, 085002 ( 2018). 10.1088/1751-8121/aaa68d
E. Agoritsas, T. Maimbourg, and F. Zamponi, J. Phys. A: Math. Theor. 52, 144002 ( 2019). 10.1088/1751-8121/ab099d
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 ( 1996). 10.1103/revmodphys.68.13
P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Annu. Rev. Condens. Matter Phys. 8, 265 ( 2017). 10.1146/annurev-conmatphys-031016-025334
E. Agoritsas, T. Maimbourg, and F. Zamponi, J. Phys. A: Math. Theor. 52, 334001 ( 2019). 10.1088/1751-8121/ab2b68
G. Parisi, P. Urbani, and F. Zamponi, Theory of Simple Glasses: Exact Solutions in Infinite Dimensions ( Cambridge University Press, 2020).
T. A. de Pirey, G. Lozano, and F. van Wijland, Phys. Rev. Lett. 123, 260602 ( 2019). 10.1103/physrevlett.123.260602
L. F. Cugliandolo, in Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, edited by J. Barrat, M. Feigelman, J. Kurchan, and J. Dalibard ( Springer-Verlag, 2003); arXiv.org:cond-mat/0210312.
A. J. Bray, S. N. Majumdar, and G. Schehr, Adv. Phys. 62, 225 ( 2013). 10.1080/00018732.2013.803819
R. A. Lionberger and W. B. Russel, J. Rheol. 38, 1885 ( 1994). 10.1122/1.550530
R. Verberg, I. M. De Schepper, M. J. Feigenbaum, and E. G. D. Cohen, J. Stat. Phys. 87, 1037 ( 1997). 10.1007/bf02181269
E. Lange, J. B. Caballero, A. M. Puertas, and M. Fuchs, J. Chem. Phys. 130, 174903 ( 2009). 10.1063/1.3124182
S. Hanna, W. Hess, and R. Klein, Physica A 111, 181 ( 1982). 10.1016/0378-4371(82)90088-7
B. J. Ackerson and L. Fleishman, J. Chem. Phys. 76, 2675 ( 1982). 10.1063/1.443251
H. N. W. Lekkerkerker and J. K. G. Dhont, J. Chem. Phys. 80, 5790 ( 1984). 10.1063/1.446602
B. J. Alder and T. E. Wainwright, Phys. Rev. A 1, 18 ( 1970). 10.1103/physreva.1.18
A. N. Borodin and P. Salminen, Handbook of Brownian Motion - Facts and Formulae ( Birkhäuser, 2012).
J. W. Dufty, Mol. Phys. 100, 2331 ( 2002). 10.1080/00268970110109934
A. C. Brańka and D. M. Heyes, Phys. Rev. E 69, 021202 ( 2004). 10.1103/physreve.69.021202
I. M. de Schepper, M. H. Ernst, and E. G. D. Cohen, J. Stat. Phys. 25, 321 ( 1981). 10.1007/bf01022190
M. Bishop, J. P. J. Michels, and I. M. De Schepper, Phys. Lett. A 111, 169 ( 1985). 10.1016/0375-9601(85)90568-7
K. Miyazaki, G. Srinivas, and B. Bagchi, J. Chem. Phys. 114, 6276 ( 2001). 10.1063/1.1355978
B. Charbonneau, P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, J. Chem. Phys. 139, 164502 ( 2013). 10.1063/1.4825177
A. Singer and Z. Schuss, Phys. Rev. Lett. 95, 110601 ( 2005). 10.1103/physrevlett.95.110601
T. W. Burkhardt, J. Stat. Mech.: Theory Exp. 2007, P07004. 10.1088/1742-5468/2007/07/p07004
F. Roy, G. Biroli, G. Bunin, and C. Cammarota, J. Phys. A: Math. Theor. 52, 484001 ( 2019). 10.1088/1751-8121/ab1f32
B. Kim and A. Latz, EPL (Europhys. Lett.) 53, 660 ( 2001). 10.1209/epl/i2001-00202-4
C. Scalliet, L. Berthier, and F. Zamponi, Phys. Rev. E 99, 012107 ( 2019). 10.1103/physreve.99.012107
J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, J. Phys. Chem. B 117, 12979 ( 2013). 10.1021/jp402235d
B. Charbonneau, P. Charbonneau, and G. Szamel, J. Chem. Phys. 148, 224503 ( 2018). 10.1063/1.5029464
P. Charbonneau, E. I. Corwin, G. Parisi, and F. Zamponi, Phys. Rev. Lett. 109, 205501 ( 2012). 10.1103/physrevlett.109.205501
G. Biroli and J.-P. Bouchaud, J. Phys.: Condens. Matter 19, 205101 ( 2007). 10.1088/0953-8984/19/20/205101
L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, and W. van Saarloos, Dynamical Heterogeneities and Glasses ( Oxford University Press, 2011).
L. F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. 71, 173 ( 1993). 10.1103/physrevlett.71.173
G. Folena, S. Franz, and F. Ricci-Tersenghi, arXiv:1903.01421 ( 2019).
M. Fuchs, W. Gotze, I. Hofacker, and A. Latz, J. Phys.: Condens. Matter 3, 5047 ( 1991). 10.1088/0953-8984/3/26/022
A. Liluashvili, J. Ónody, and T. Voigtmann, Phys. Rev. E 96, 062608 ( 2017). 10.1103/physreve.96.062608
M. Gruber, A. M. Puertas, and M. Fuchs, Phys. Rev. E 101, 012612 ( 2020). 10.1103/physreve.101.012612
L. Berthier and J. Kurchan, Nat. Phys. 9, 310 ( 2013). 10.1038/nphys2592
G. Szamel, E. Flenner, and L. Berthier, Phys. Rev. E 91, 062304 ( 2015). 10.1103/physreve.91.062304
L. Berthier, J.-L. Barrat, and J. Kurchan, Phys. Rev. E 61, 5464 ( 2000). 10.1103/physreve.61.5464
M. Fuchs and M. E. Cates, Phys. Rev. Lett. 89, 248304 ( 2002). 10.1103/physrevlett.89.248304
J. M. Brader, T. Voigtmann, M. Fuchs, R. G. Larson, and M. E. Cates, Proc. Natl. Acad. Sci. U. S. A. 106, 15186 ( 2009). 10.1073/pnas.0905330106
J. M. Brader, M. E. Cates, and M. Fuchs, Phys. Rev. E 86, 021403 ( 2012). 10.1103/physreve.86.021403
A. Nicolas, E. E. Ferrero, K. Martens, and J.-L. Barrat, Rev. Mod. Phys. 90, 045006 ( 2018). 10.1103/revmodphys.90.045006
M. Baity-Jesi and D. R. Reichman, J. Chem. Phys. 151, 084503 ( 2019). 10.1063/1.5115042
L. M. C. Janssen and D. R. Reichman, Phys. Rev. Lett. 115, 205701 ( 2015). 10.1103/physrevlett.115.205701
G. Kotliar, S. Y. Savrasov, G. Pálsson, and G. Biroli, Phys. Rev. Lett. 87, 186401 ( 2001). 10.1103/physrevlett.87.186401
G. Biroli, P. Charbonneau, E. I. Corwin, Y. Hu, H. Ikeda, G. Szamel, and F. Zamponi, arXiv:2003.11179 ( 2020).
P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, Proc. Natl. Acad. Sci. U. S. A. 111, 15025 ( 2014). 10.1073/pnas.1417182111
S. M. Bhattacharyya, B. Bagchi, and P. G. Wolynes, Proc. Natl. Acad. Sci. U. S. A. 105, 16077 ( 2008). 10.1073/pnas.0808375105
T. Sarlat, A. Billoire, G. Biroli, and J.-P. Bouchaud, J. Stat. Mech.: Theory Exp. 2009, P08014. 10.1088/1742-5468/2009/08/p08014
S. Franz, G. Parisi, F. Ricci-Tersenghi, and T. Rizzo, Eur. Phys. J. E 34, 102 ( 2011). 10.1140/epje/i2011-11102-0
T. Rizzo and T. Voigtmann, Europhys. Lett. 111, 56008 ( 2015). 10.1209/0295-5075/111/56008
T. Rizzo and T. Voigtmann, arXiv:1903.01773 ( 2019).
J. A. Leegwater and H. van Beijeren, J. Stat. Phys. 57, 595 ( 1989). 10.1007/bf01022824
J. W. Dufty and M. H. Ernst, Mol. Phys. 102, 2123 ( 2004). 10.1080/00268970412331292858
T. W. Burkhardt, J. Stat. Phys. 133, 217 ( 2008). 10.1007/s10955-008-9615-y
H. P. J. McKean, J. Math. Kyoto Univ. 2, 227 ( 1962). 10.1215/kjm/1250524936