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Emergence of Navier-Stokes Hydrodynamics in Chaotic Quantum Circuits

Hansveer Singh1,2, Ewan McCulloch3, Sarang Gopalakrishnan3, and Romain Vasseur1,4

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Phys. Rev. Lett. 134, 230401 – Published 10 June, 2025

DOI: https://doi.org/10.1103/z9ym-kqln

Abstract

We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the incompressible Navier-Stokes equations. By analyzing circuit-to-circuit fluctuations in the ensemble we argue that these are negligible, so the circuit-averaged value of transport coefficients like the viscosity is also (in the long-time limit) the value in a typical circuit. The circuit-averaged transport coefficients can be mapped onto a classical irreversible Markov process. Therefore, remarkably, our construction allows us to efficiently compute the viscosity of a family of strongly interacting chaotic two-dimensional quantum systems.

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References (40)

  1. F. Bonetto, J. L. Lebowitz, and L. Rey-Bellet, arXiv:math-ph/0002052.
  2. V. Khemani, A. Vishwanath, and D. A. Huse, Phys. Rev. X 8, 031057 (2018).
  3. T. Rakovszky, F. Pollmann, and C. von Keyserlingk, Phys. Rev. X 8, 031058 (2018).
  4. A. J. Friedman, A. Chan, A. D. Luca, and J. Chalker, Phys. Rev. Lett. 123, 210603 (2019).
  5. E. McCulloch, J. D. Nardis, S. Gopalakrishnan, and R. Vasseur, Phys. Rev. Lett. 131, 210402 (2023).
  6. H. Singh, B. Ware, R. Vasseur, and A. J. Friedman, Phys. Rev. Lett. 127, 230602 (2021).
  7. J. Feldmeier, W. Witczak-Krempa, and M. Knap, Phys. Rev. B 106, 094303 (2022).
  8. J. Feldmeier, P. Sala, G. D. Tomasi, F. Pollmann, and M. Knap, Phys. Rev. Lett. 125, 245303 (2020).
  9. J. Iaconis, A. Lucas, and R. Nandkishore, Phys. Rev. E 103, 022142 (2021).
  10. A. Morningstar, V. Khemani, and D. A. Huse, Phys. Rev. B 101, 214205 (2020).
  11. S. Moudgalya, A. Prem, D. A. Huse, and A. Chan, Phys. Rev. Res. 3, 023176 (2021).
  12. J. Lehmann, P. S. de Torres-Solanot, F. Pollmann, and T. Rakovszky, SciPost Phys. 14, 140 (2023).
  13. A. Gromov, A. Lucas, and R. M. Nandkishore, Phys. Rev. Res. 2, 033124 (2020).
  14. J. Iaconis, S. Vijay, and R. Nandkishore, Phys. Rev. B 100, 214301 (2019).
  15. J. Guo, P. Glorioso, and A. Lucas, Phys. Rev. Lett. 129, 150603 (2022).
  16. O. Hart and R. Nandkishore, Phys. Rev. B 106, 214426 (2022).
  17. A. Lucas and K. C. Fong, J. Phys. Condens. Matter 30, 053001 (2018).
  18. L. Fritz and T. Scaffidi, arXiv:2303.14205.
  19. U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505 (1986).
  20. U. Frisch, D. d’Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet, Lattice Gas Hydrodynamics in Two and Three Dimensions (Complex Systems Publications, Inc., Champaign, IL, 1990).
  21. C. Q. Cook and A. Lucas, Phys. Rev. B 99, 235148 (2019).
  22. A. J. Friedman, C. Q. Cook, and A. Lucas, SciPost Phys. 14, 137 (2023).
  23. M. Qi, J. Guo, and A. Lucas, Phys. Rev. B 107, 144305 (2023).
  24. S. Palpacelli and S. Succi, Commun. Comput. Phys. 4, 980 (2008).
  25. D. Forster, D. R. Nelson, and M. J. Stephen, Phys. Rev. A 16, 732 (1977).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/z9ym-kqln for a detailed derivation of the effective two copy Markov process, provides a brief review of the derivation for lattice gas hydrodynamics and details about numerical simulations.
  27. B. Doyon, SciPost Phys. Lect. Notes 18 (2020).
  28. L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1959).
  29. M. Kardar, Statistical Physics of Particles (Cambridge University Press, Cambridge, England, 2007).
  30. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
  31. M. P. Fisher, V. Khemani, A. Nahum, and S. Vijay, Annu. Rev. Condens. Matter Phys. 14, 335 (2023).
  32. U. Agrawal, A. Zabalo, K. Chen, J. H. Wilson, A. C. Potter, J. Pixley, S. Gopalakrishnan, and R. Vasseur, Phys. Rev. X 12, 041002 (2022).
  33. A. Nahum, S. Vijay, and J. Haah, Phys. Rev. X 8, 021014 (2018).
  34. T. Zhou and A. Nahum, Phys. Rev. B 99, 174205 (2019).
  35. R. Vasseur, A. C. Potter, Y.-Z. You, and A. W. W. Ludwig, Phys. Rev. B 100, 134203 (2019).
  36. C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Phys. Rev. B 101, 104302 (2020).
  37. Y. Bao, S. Choi, and E. Altman, Phys. Rev. B 101, 104301 (2020).
  38. Y. Li, R. Vasseur, M. P. A. Fisher, and A. W. W. Ludwig, Phys. Rev. B 109, 174307 (2024).
  39. G. R. McNamara and G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988).
  40. L. P. Kadanoff, G. R. McNamara, and G. Zanetti, Phys. Rev. A 40, 4527 (1989).

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Phys. Rev. Lett. 134, 230401– Published 10 June, 2025
  • Received 2 July 2024
  • Revised 29 September 2024
  • Accepted 14 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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