[Dynamique hors équilibre de systèmes complexes classiques et quantiques]
Lʼéquilibre est une situation plutôt idéale, lʼexception plutôt que la règle dans la Nature. Chaque fois que les paramètres externes ou internes dʼun système physique subissent une modification, sa relaxation subséquente vers lʼéquilibre peut, soit être impossible, soit prendre très longtemps. Du point de vue de la physique fondamentale, aucun principe générique tel que ceux de la thermodynamique ne permet de comprendre complètement son comportement. Lʼalternative consiste à traiter chaque cas séparément. Il est illusoire de tenter de donner, au moins à ce stade, une description complète de toutes les situations hors équilibre. Mais on peut essayer dʼidentifier et de caractériser quelques traits concrets, mais toujours généraux, dʼune classe de problèmes hors équilibre – restant à identifier – et de rechercher une description unifée de ceux-ci. Dans cette contribution, je décris brièvement le comportement et la théorie dʼun jeu de systèmes hors équilibre et je tente de mettre en lumière des traits communs et quelques lois générales qui ont vu le jour au cours des dernières années.
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied, its subsequent relaxation to equilibrium may be either impossible or take very long times. From the point of view of fundamental physics, no generic principle such as the ones of thermodynamics allows us to fully understand its behaviour. The alternative is to treat each case separately. It is illusionary to attempt to give, at least at this stage, a complete description of all non-equilibrium situations. Still, one can try to identify and characterise some concrete, but still general features of a class of out-of-equilibrium problems – yet to be identified – and search for a unified description of these. In this report, I briefly describe the behaviour and theory of a set of non-equilibrium systems and I try to highlight common features and some general laws that have emerged in recent years.
Mot clés : Dynamique hors équilibre, Systèmes désordonnés, Dynamique sous sollicitation
Leticia F. Cugliandolo 1
@article{CRPHYS_2013__14_8_685_0,
author = {Leticia F. Cugliandolo},
title = {Out-of-equilibrium dynamics of classical and quantum complex systems},
journal = {Comptes Rendus. Physique},
pages = {685--699},
publisher = {Elsevier},
volume = {14},
number = {8},
year = {2013},
doi = {10.1016/j.crhy.2013.09.004},
language = {en},
}
Leticia F. Cugliandolo. Out-of-equilibrium dynamics of classical and quantum complex systems. Comptes Rendus. Physique, Volume 14 (2013) no. 8, pp. 685-699. doi : 10.1016/j.crhy.2013.09.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.09.004/
[1] Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin, 1982
[2] Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press, Boston, 1989
[3] Nonlinear Dynamics and Chaos: With Applications to Physics, Biology Chemistry and Engineering, Westview Press, 1994
[4] Cellular Automata Modeling of Physical Systems, Cambridge University Press, 2005
[5] Complex Systems: Chaos and Beyond, a Constructive Approach with Applications in Life Sciences, Springer-Verlag, 2000
[6] Chaos, 15 (2005) (See the collection of articles published in)
[7] Mathematical Methods of Classical Mechanics, Springer, 1997
[8] Quantum Dissipative Systems, Series in Modern Condensed Matter Physics, vol. 10, World Scientific, Singapore, 1999
[9] Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford and New York, 1971
[10] Lectures on Phase Transitions and the Renormalization Group, Perseus Publishing, 1992
[11] Markov Process. Relat. Fields, 9 (2002), p. 243
[12] Phase transitions in two-dimensional random Potts models (Yu. Holovatch, ed.), Order, Disorder, and Criticality, World Scientific, Singapore, 2004
[13] Spin Glasses, Cambridge University Press, 1991
[14] Spin-Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications, World Scientific, Singapore, 1987
[15] Spin Glasses, a Challenge for Mathematicians: Cavity and Mean-Field Models, Springer-Verlag, Berlin, 2003
[16] Ann. Math., 163 (2006), p. 221
[17] Phys. Rev. Lett., 56 (1986), p. 1601
[18] Phys. Rep., 412 (2005), p. 277
[19] Exact results and open questions in first principle functional RG | arXiv
[20] An introduction to the nonperturbative renormalization group | arXiv
[21] The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials, Springer, 2011
[22] Glassy Materials and Disordered Solids: An Introduction to their Statistical Mechanics, World Scientific, Singapore, 2005
[23] Rev. Mod. Phys., 83 (2011), p. 587
[24] Dynamics of glassy systems, Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, Les Houches Session LXXVII (2003) (See e.g., Les Houches, 1–26 July 2002) | arXiv
[25] Non equilibrium statistical mechanics of systems with long-range interactions: ubiquity of core-halo distributions, Phys. Rep. (2013) (in press)
[26] Introduction to Frustrated Magnetism (C. Lacroix et al., eds.), Springer Series in Solid-State Sciences, vol. 164, 2011
[27] Information, Physics and Computation, Oxford University Press, 2009
[28] Phys. Rep., 195 (1990), p. 127
[29] Les Houches, 2008 (2010)
[30] Adv. Chem. Phys., 137 (2008), p. 31
[31] Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics, Leuven, Belgium (2005)
[32] Stochastic Energetics, Lecture Notes in Physics, vol. 799, Springer-Verlag, Berlin, 2010
[33] Rep. Prog. Phys., 75 (2012), p. 126001
[34] Phys. Rev. Lett., 98 (2007), p. 195702
[35] Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995
[36] Phys. Rep., 254 (1995), p. 215
[37] Rev. Mod. Phys., 66 (1994), p. 1125
[38] Statics and dynamics of disordered elastic systems | arXiv
[39] Adv. Phys., 49 (2000), p. 607
[40] Dynamics of disordered elastic systems | arXiv
[41] Phys. Rev. B, 80 (2009), p. 094201
[42] Crackling noise and avalanches: scaling, critical phenomena, and the renormalization group, Les Houches (2007)
[43] Avalanche dynamics of elastic interfaces | arXiv
[44] Growing length scales in aging systems (L. Berthier et al., eds.), Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, Oxford University Press, 2011
[45] Rev. Mod. Phys., 49 (1977), p. 435
[46] Z. Phys. B, Condens. Matter, 73 (1989), p. 539
[47] J. Phys. A, 38 (2005), p. R133
[48] J. Phys. A, 38 (2005), p. R133
[49] J. Stat. Mech. (2007), p. P07002
[50] Adv. Phys., 25 (1976), p. 343
[51] Spinodal decomposition versus nucleation and growth (S. Puri; V. Wadhawan, eds.), Kinetics of Phase Transitions, CRC Press, Boca Raton, FL, 2009, pp. 63-98
[52] Adv. Phys., 43 (1994), p. 357
[53] Slow dynamics and aging in spin-glasses, Complex Behaviour of Glassy Systems, Lecture Notes in Physics, vol. 492, Springer-Verlag, Berlin, 1997 | arXiv
[54] Analytical approaches to time and length scales in models of glasses (L. Berthier; G. Biroli; J.-P. Bouchaud; L. Cipelletti; W. van Saarloos, eds.), Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, Oxford University Press, 2011
[55] J. Stat. Mech. (L. Berthier; G. Biroli; J.-P. Bouchaud; L. Cipelletti; W. van Saarloos, eds.), Kinetically constrained models, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, P07017, Oxford University Press, 2007
[56] Statistical Mechanics of Driven Diffusive Systems (C. Domb; J.L. Lebowitz, eds.), Phase Transition and Critical Phenomena, vol. 17, Academic Press, London, 1995
[57] Adv. Phys., 50 (2001), p. 431
[58] Exactly solvable models for many-body systems far from equilibrium, Phase Transitions and Critical Phenomena, vol. 19, 2001
[59] J. Phys. A, 40 (2007), p. R333
[60] J. Phys. A, 38 (2005), p. R79
[61] Field-theoretic methods (R.A. Meyers, ed.), Encyclopedia of Complexity and Systems Science, Springer, New York, 2009
[62] Rev. Mod. Phys., 65 (1993), p. 851
[63] Annu. Rev. Phys. Chem., 60 (2009), p. 469
[64] J. Phys. A, 44 (2011), p. 483001
[65] Adv. Phys., 51 (2002), p. 1529
[66] Eur. Phys. J. B, 61 (2008), p. 1
[67] Rev. Mod. Phys., 80 (2008), p. 885
[68] Rev. Mod. Phys., 83 (2011), p. 863
[69] Quantum phase transitions in transverse field spin models: from statistical physics to quantum information | arXiv
[70] Nature, 452 (2008), p. 854
[71] Phys. Rev. B, 83 (2011), p. 094431
[72] Ann. Phys., 326 (2011), p. 96
[73] Les Houches IV, 2012 (2013) (in press)
[74] Phys. Rev. B, 83 (2011), p. 165105
[75] Phys. Rev. B, 87 (2013), p. 125113
[76] Rep. Prog. Phys., 75 (2012), p. 094501
[77] Phys. Rev. B, 84 (2011), p. 212404
[78] Rev. Mod. Phys., 59 (1987), p. 1
[79] Rev. Mod. Phys., 83 (2011), p. 1405
[80] Phys. Rep., 168 (1988), p. 115
[81] Phys. Rev. Lett., 102 (2009), p. 050404
[82] Dissipative quantum systems: from two to many atoms | arXiv
[83] Phases and phase transitions in disordered quantum systems (in: XVII Training Course in the Physics of Strongly Correlated Systems, Vietri sul Mare, Italy) | arXiv
[84] Adv. Phys., 58 (2009), p. 197
[85] Int. J. Mod. Phys. B, 20 (2006), p. 2795
[86] Phys. Rep., 523 (2013), p. 127
[87] Non-equilibrium steady-states in conformal field theory | arXiv
[88] Phys. Rev. B, 81 (2010), p. 041301(R)
[89] Extracting quantum work statistics and fluctuation theorems by single qubit interferometry | arXiv
[90] Ann. Phys., 318 (2005), p. 81
[91] Phys. Rep., 432 (2006), p. 115
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