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Relaxed hydrodynamic theory of electrically driven non-equilibrium steady states

Published 8 Apr 2024 in cond-mat.stat-mech, cond-mat.str-el, and hep-th | (2404.05568v2)

Abstract: The capability of hydrodynamics to accurately describe slow and long-wavelength fluctuations around non-equilibrium steady states (NESS), characterized by a stationary flow of energy or matter in the presence of a driving force, remains an open question. In this study, we explicitly construct a hydrodynamic description of electrically driven non-equilibrium charged steady states \new{in the limit in which the relaxation of the first non-hydrodynamic excitation is parametrically slow}. Our approach involves introducing gapped modes and extending the effective description into a relaxed hydrodynamic theory (RHT). Leveraging the gauge-gravity duality as a tool for controlled computations within non-equilibrium systems, we establish an ultraviolet complete model for these NESS that confirms the validity of our RHT. In summary, our findings provide a concrete realization of the validity of hydrodynamics beyond thermal equilibrium, offering valuable insights into the dynamics of non-equilibrium systems.

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References (51)
  1. Charge transport and hydrodynamics in materials. \JournalTitleNature Reviews Materials 8, 726–741, DOI: 10.1038/s41578-023-00597-3 (2023).
  2. Hydrodynamic theory of spin waves. \JournalTitlePhys. Rev. 188, 898–918, DOI: 10.1103/PhysRev.188.898 (1969).
  3. Hydrodynamics of solids. \JournalTitlePhys. Rev. B 13, 500–516, DOI: 10.1103/PhysRevB.13.500 (1976).
  4. Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids. \JournalTitlePhys. Rev. A 6, 2401–2420, DOI: 10.1103/PhysRevA.6.2401 (1972).
  5. Keizer, J. Thermodynamics at nonequilibrium steady states. \JournalTitleThe Journal of Chemical Physics 69, 2609–2620, DOI: 10.1063/1.436908 (2008).
  6. Qian, H. Open-system nonequilibrium steady state: Statistical thermodynamics, fluctuations, and chemical oscillations. \JournalTitleThe Journal of Physical Chemistry B 110, 15063–15074, DOI: 10.1021/jp061858z (2006). PMID: 16884217.
  7. Lax, M. Fluctuations from the nonequilibrium steady state. \JournalTitleRev. Mod. Phys. 32, 25–64, DOI: 10.1103/RevModPhys.32.25 (1960).
  8. Stochastic theory of nonequilibrium steady states and its applications. part i. \JournalTitlePhysics Reports 510, 1–86 (2012). Stochastic Theory of Nonequilibrium Steady States and Its Applications: Part I.
  9. Steady state thermodynamics. \JournalTitleProgress of Theoretical Physics Supplement 130, 29–44 (1998).
  10. Steady state thermodynamics. \JournalTitleJournal of Statistical Physics 125, 125–224, DOI: 10.1007/s10955-005-9021-7 (2006).
  11. Understanding non-equilibrium thermodynamics, vol. 295 (Springer, 2008).
  12. Fluctuations about simple nonequilibrium steady states. \JournalTitlePhys. Rev. A 23, 1451–1480, DOI: 10.1103/PhysRevA.23.1451 (1981).
  13. Statistical mechanics of stationary states. i. formal theory. \JournalTitlePhys. Rev. A 19, 1290–1306, DOI: 10.1103/PhysRevA.19.1290 (1979).
  14. Light scattering from nonequilibrium stationary states: The implication of broken time-reversal symmetry. \JournalTitlePhys. Rev. Lett. 42, 287–291, DOI: 10.1103/PhysRevLett.42.287 (1979).
  15. Fluctuations in fluids out of thermal equilibrium. \JournalTitleJournal of Statistical Physics 57, 531–547, DOI: 10.1007/BF01022821 (1989).
  16. Heat waves. \JournalTitleRev. Mod. Phys. 61, 41–73, DOI: 10.1103/RevModPhys.61.41 (1989).
  17. Maxwell, J. C. Iv. on the dynamical theory of gases. \JournalTitlePhilosophical transactions of the Royal Society of London 49–88 (1867).
  18. Cattaneo, C. Sur une forme de l’equation de la chaleur eliminant la paradoxe d’une propagation instantantee. \JournalTitleCompt. Rendu 247, 431–433 (1958).
  19. Holography and hydrodynamics with weakly broken symmetries. \JournalTitlePhys. Rev. D 99, 086012, DOI: 10.1103/PhysRevD.99.086012 (2019). 1810.10016.
  20. Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics. \JournalTitleJHEP 01, 162, DOI: 10.1007/JHEP01(2024)162 (2024). 2309.00511.
  21. Chandrasekharaiah, D. S. Hyperbolic Thermoelasticity: A Review of Recent Literature. \JournalTitleApplied Mechanics Reviews 51, 705–729, DOI: 10.1115/1.3098984 (1998).
  22. Heat conduction paradox involving second-sound propagation in moving media. \JournalTitlePhys. Rev. Lett. 94, 154301, DOI: 10.1103/PhysRevLett.94.154301 (2005).
  23. Christov, C. On frame indifferent formulation of the maxwell–cattaneo model of finite-speed heat conduction. \JournalTitleMechanics Research Communications 36, 481–486 (2009).
  24. Bissell, J. J. On oscillatory convection with the cattaneo–christov hyperbolic heat-flow model. \JournalTitleProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, 20140845, DOI: 10.1098/rspa.2014.0845 (2015).
  25. Straughan, B. Thermal convection with the cattaneo–christov model. \JournalTitleInternational Journal of Heat and Mass Transfer 53, 95–98 (2010).
  26. Analytical and numerical study of travelling waves using the maxwell-cattaneo relaxation model extended to reaction-advection-diffusion systems. \JournalTitlePhys. Rev. E 94, 042218, DOI: 10.1103/PhysRevE.94.042218 (2016).
  27. Turbulent transport in flames. \JournalTitleProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 451, 231–256, DOI: 10.1098/rspa.1995.0124 (1995).
  28. Bifurcations of travelling waves in population taxis models. \JournalTitlePhysics-Uspekhi 42, 917, DOI: 10.1070/PU1999v042n09ABEH000564 (1999).
  29. Jordan, P. Growth and decay of shock and acceleration waves in a traffic flow model with relaxation. \JournalTitlePhysica D: Nonlinear Phenomena 207, 220–229, DOI: https://doi.org/10.1016/j.physd.2005.06.002 (2005).
  30. Hydrodynamics of electrons in graphene. \JournalTitleJournal of Physics: Condensed Matter 30, 053001, DOI: 10.1088/1361-648x/aaa274 (2018).
  31. Tranquada, J. M. Cuprate superconductors as viewed through a striped lens. \JournalTitleAdvances in Physics 69, 437–509, DOI: 10.1080/00018732.2021.1935698 (2020).
  32. Principles of Condensed Matter Physics (Cambridge University Press, 2000).
  33. Yu, E. P. et al. Use of hydrodynamic theory to estimate electrical current redistribution in metals. \JournalTitlePhysics of Plasmas 27, 052703, DOI: 10.1063/1.5143271 (2020).
  34. Chen, L. et al. Shot noise in a strange metal. \JournalTitleScience 382, 907–911, DOI: 10.1126/science.abq6100 (2023).
  35. Kovtun, P. Thermodynamics of polarized relativistic matter. \JournalTitleJHEP 07, 028, DOI: 10.1007/JHEP07(2016)028 (2016). 1606.01226.
  36. Non-Boost Invariant Fluid Dynamics. \JournalTitleSciPost Phys. 9, 018, DOI: 10.21468/SciPostPhys.9.2.018 (2020). 2004.10759.
  37. Non-dissipative electrically driven fluids. \JournalTitleJHEP 05, 218, DOI: 10.1007/JHEP05(2023)218 (2023). 2211.05791.
  38. Adding flavor to AdS / CFT. \JournalTitleJHEP 06, 043, DOI: 10.1088/1126-6708/2002/06/043 (2002). hep-th/0205236.
  39. Origin of the Drude peak and of zero sound in probe brane holography. \JournalTitlePhys. Lett. B 774, 569–574, DOI: 10.1016/j.physletb.2017.10.023 (2017). 1709.01520.
  40. Kovtun, P. Lectures on hydrodynamic fluctuations in relativistic theories. \JournalTitleJ. Phys. A 45, 473001, DOI: 10.1088/1751-8113/45/47/473001 (2012). 1205.5040.
  41. Gauge/gravity duality: Foundations and applications (Cambridge University Press, Cambridge, 2015).
  42. Holographic systems far from equilibrium: a review. \JournalTitleReports on Progress in Physics 83, 016001, DOI: 10.1088/1361-6633/ab4f91 (2019).
  43. Metallic AdS/CFT. \JournalTitleJHEP 09, 024, DOI: 10.1088/1126-6708/2007/09/024 (2007). 0705.3870.
  44. Minkowski space correlators in AdS / CFT correspondence: Recipe and applications. \JournalTitleJHEP 09, 042, DOI: 10.1088/1126-6708/2002/09/042 (2002). hep-th/0205051.
  45. Holographic Spectral Functions in Metallic AdS/CFT. \JournalTitleJHEP 09, 032, DOI: 10.1088/1126-6708/2009/09/032 (2009). 0904.3905.
  46. Holographic Operator Mixing and Quasinormal Modes on the Brane. \JournalTitleJHEP 02, 021, DOI: 10.1007/JHEP02(2010)021 (2010). 0911.3610.
  47. Sulpizio, J. A. et al. Visualizing poiseuille flow of hydrodynamic electrons. \JournalTitleNature 576, 75–79, DOI: 10.1038/s41586-019-1788-9 (2019).
  48. Ku, M. J. H. et al. Imaging viscous flow of the dirac fluid in graphene. \JournalTitleNature 583, 537–541, DOI: 10.1038/s41586-020-2507-2 (2020).
  49. Mitrano, M. et al. Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La2−--xBaxCuO4. \JournalTitleScience Advances 5, eaax3346, DOI: 10.1126/sciadv.aax3346 (2019).
  50. Restoring time-reversal covariance in relaxed hydrodynamics. \JournalTitlePhys. Rev. D 108, 056003, DOI: 10.1103/PhysRevD.108.056003 (2023). 2304.01248.
  51. Dynamical stability and filamentary instability in holographic conductors. \JournalTitleJHEP 04, 173, DOI: 10.1007/JHEP04(2022)173 (2022). 2112.11677.
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