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Wave turbulence and the kinetic equation beyond leading order (2212.02555v2)

Published 5 Dec 2022 in cond-mat.stat-mech, hep-th, nlin.CD, and physics.flu-dyn

Abstract: We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method, and is based on an analogy between the Liouville equation in infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: a broad class of nonlinear classical field theories are believed to have a stationary turbulent state -- a far-from-equilibrium state, even at weak coupling. Our method provides an efficient way to derive properties of the weak wave turbulent state. A central object in these studies, which is a reduction of the Liouville equation, is the kinetic equation, which governs the occupation numbers of the modes. All properties of wave turbulence to date are based on the kinetic equation found at leading order in the weak nonlinearity. We explicitly obtain the kinetic equation to next-to-leading order.

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References (39)
  1. V. Zakharov, “Weak turbulence in media with a decay spectrum,” J Appl Mech Tech Phys 6 (1965) 22–24.
  2. Springer-Verlag, 1992.
  3. S. Nazarenko, Wave Turbulence. Springer-Verlag Berlin Heidelberg, 2011.
  4. M. Shavit and G. Falkovich, “Singular Measures and Information Capacity of Turbulent Cascades,” Phys. Rev. Lett. 125 (2020) 104501, arXiv:1911.12670 [physics.flu-dyn].
  5. V. Rosenhaus and M. Smolkin, “Feynman rules for forced wave turbulence,” arXiv:2203.08168 [cond-mat.stat-mech].
  6. C. Rodda, C. Savaro, G. Davis, J. Reneuve, P. Augier, J. Sommeria, T. Valran, S. Viboud, and N. Mordant, “Experimental observations of internal wave turbulence transition in a stratified fluid,” Physical Review Fluids 7 (2022) no. 9, 094802, arXiv:2209.03616 [physics.flu-dyn].
  7. E. Falcon and N. Mordant, “Experiments in Surface Gravity – Capillary Wave Turbulence,”Annual Review of Fluid Mechanics 54 (Jan, 2022) 1–25, arXiv:2107.04015 [physics.flu-dyn].
  8. E. Kochurin, G. Ricard, N. Zubarev, and E. Falcon, “Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence,” Physical Review E 105 (2022) no. 6, L063101, arXiv:2205.11516 [physics.plasm-ph].
  9. G. Düring, C. Josserand, and S. Rica, “Wave turbulence theory of elastic plates,” Physica D: Nonlinear Phenomena 347 (2017) 42–73.
  10. A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, “Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves,”Physical Review Letters 92 (Apr, 2004) .
  11. J. Orosco, W. Connacher, and J. Friend, “Identification of weakly-to strongly-turbulent three-wave processes in a micro-scale system,” arXiv:2205.01803 [physics.flu-dyn].
  12. J. Guioth, F. Bouchet, and G. L. Eyink, “Path large deviations for the kinetic theory of weak turbulence,” arXiv:2203.11737 [cond-mat.stat-mech].
  13. M. Gałka, P. Christodoulou, M. Gazo, A. Karailiev, N. Dogra, J. Schmitt, and Z. Hadzibabic, “Emergence of isotropy and dynamic self-similarity in the birth of two-dimensional wave turbulence,” arXiv:2203.09514 [cond-mat.quant-gas].
  14. N. Vladimirova, M. Shavit, and G. Falkovich, “Fibonacci Turbulence,”Physical Review X 11 (Jun, 2021) , arXiv:2101.10418 [nlin.CD].
  15. G. Falkovich, Y. Kadish, and N. Vladimirova, “Multi-mode correlations and the entropy of turbulence,” arXiv:2209.05816 [nlin.CD].
  16. J. W. Banks, T. Buckmaster, A. O. Korotkevich, G. Kovacic, and J. Shatah, “Direct verification of the kinetic description of wave turbulence,” arXiv:2109.02477 [physics.flu-dyn].
  17. S. Schlichting and D. Teaney, “The First fm/c of Heavy-Ion Collisions,” Ann. Rev. Nucl. Part. Sci. 69 (2019) 447–476, arXiv:1908.02113 [nucl-th].
  18. A. Chatrchyan, K. T. Geier, M. K. Oberthaler, J. Berges, and P. Hauke, “Analog cosmological reheating in an ultracold Bose gas,” Phys. Rev. A 104 (2021) no. 2, 023302, arXiv:2008.02290 [cond-mat.quant-gas].
  19. Y. Zhu, B. Semisalov, G. Krstulovic, and S. Nazarenko, “Direct and inverse cascades in turbulent Bose-Einstein condensate,” arXiv:2208.09279 [cond-mat.quant-gas].
  20. G. Dematteis and Y. V. Lvov, “The Structure of Energy Fluxes in Wave Turbulence,” arXiv:2205.12899 [physics.flu-dyn].
  21. V. David and S. Galtier, “Wave turbulence in inertial electron magnetohydrodynamics,” Journal of Plasma Physics 88 (2022) no. 5, 905880509, arXiv:2209.08577 [physics.plasm-ph].
  22. Y. Sano, N. Navon, and M. Tsubota, “Emergent isotropy of a wave-turbulent cascade in the Gross-Pitaevskii model,” arXiv:2209.08973 [cond-mat.quant-gas].
  23. N. Berti, K. Baudin, A. Fusaro, G. Millot, A. Picozzi, and J. Garnier, “Interplay of thermalization and strong disorder: Wave turbulence theory, numerical simulations, and experiments in multimode optical fibers,” Phys. Rev. Lett. 129 (2022) no. 6, 063901, arXiv:2207.08680 [physics.optics].
  24. K. Kawasaki and I. Oppenheim, “Logarithmic term in the density expansion of transport coefficients,”Phys. Rev. 139 (Sep, 1965) A1763–A1768.
  25. J. R. Dorfman and E. G. D. Cohen, “Velocity correlation functions in two and three dimensions,”Phys. Rev. Lett. 25 (Nov, 1970) 1257–1260.
  26. J. R. Dorfman, T. R. Kirkpatrick, and J. V. Sengers, “Why Non-equilibrium is Different,” arXiv:1512.02679 [cond-mat.stat-mech].
  27. Cambridge University Press, 2021.
  28. M. S. Green, “Boltzmann equation from the statistical mechanical point of view,” The Journal of Chemical Physics 25 (1956) no. 5, 836–855.
  29. E. Cohen, “On the generalization of the boltzmann equation to general order in the density,” Physica 28 (1962) no. 10, 1025–1044.
  30. R. Zwanzig, “Method for finding the density expansion of transport coefficients of gases,” Physical Review 129 (1963) no. 1, 486.
  31. J. Brocas, “On the comparison between two generalized boltzmann equations,” Advances in Chemical Physics (1967) 317–381.
  32. R. Balescu, “Irreversible processes in ionized gases,” The Physics of Fluids 3 (1960) no. 1, 52–63.
  33. I. Prigogine, Non-equilibrium Statistical Mechanics. Interscience Publishers, 1962. Reprint: Dover Publications, 2017.
  34. Springer, 2003.
  35. R. Peierls, “On the kinetic theory of heat conduction in crystals,” Ann. Phys. 395 (1929) no. 8, 1055.
  36. J. J. Sakurai, Modern Quantum Mechanics. Addison-Wesley, 1994.
  37. A. Polyakov unpublished
  38. V. Gurarie, Statistics without thermodynamic equilibrium. PhD thesis, Princeton University, 1996. https://scholar.google.com/citations?view_op=view_citation&hl=en&user=lX4Ods8AAAAJ&cstart=100&pagesize=100&sortby=pubdate&citation_for_view=lX4Ods8AAAAJ:f2IySw72cVMC.
  39. V. Gurarie, “Probability density, diagrammatic technique, and epsilon expansion in the theory of wave turbulence,” Nucl. Phys. B 441 (1995) 569–594, arXiv:hep-th/9405077.
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