- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Particle number diffusion in second-order relativistic dissipative hydrodynamics with momentum-dependent relaxation time

Sunny Kumar Singh1,*, Samapan Bhadury2,†, Manu Kurian3,‡, and Vinod Chandra1,§

  • *Contact author: sunny.singh@iitgn.ac.in
  • †Contact author: samapan.bhadury@uj.edu.pl
  • ‡Contact author: manukurian@iitism.ac.in
  • §Contact author: vchandra@iitgn.ac.in
PDF

Phys. Rev. D 111, 114007 – Published 10 June, 2025

DOI: https://doi.org/10.1103/sf5m-87w7

Abstract

This article explores particle number diffusion in relativistic hydrodynamics using kinetic theory with a modified collision kernel that incorporates the momentum dependence of the particle relaxation time. Starting from the Boltzmann equation within the extended relaxation time approximation (ERTA), we derive second-order evolution equations for the dissipative number current and calculate the associated transport coefficients. The sensitivity of transport coefficients to the particle momentum dependence of the collision timescale of the microscopic interactions in the hot QCD medium is analyzed. For a conformal, number-conserving system, we compare the ERTA-modified transport coefficients for particle diffusion with exact results derived from scalar field theory. With an appropriate parametrization of the relaxation time, we demonstrate the consistency of our analysis and assess the degree of agreement of the results with the exact solutions from scalar field theory. The relaxation times for the shear and number diffusion evolution equations are seen to be distinct in general when the momentum dependence of the relaxation time is taken into consideration.

View figure in article

Physics Subject Headings (PhySH)

See Also

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

Sunny Kumar Singh, Manu Kurian, and Vinod Chandra
Phys. Rev. D 110, 014004 (2024)

Article Text

References (75)

  1. U. Heinz and R. Snellings, Annu. Rev. Nucl. Part. Sci. 63, 123 (2013).
  2. C. Gale, S. Jeon, and B. Schenke, Int. J. Mod. Phys. A 28, 1340011 (2013).
  3. A. Jaiswal and V. Roy, Adv. High Energy Phys. 2016, 9623034 (2016).
  4. W. Florkowski, M. P. Heller, and M. Spalinski, Rep. Prog. Phys. 81, 046001 (2018).
  5. D. Teaney, Phys. Rev. C 68, 034913 (2003).
  6. P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99, 172301 (2007).
  7. J. Noronha-Hostler, G. S. Denicol, J. Noronha, R. P. G. Andrade, and F. Grassi, Phys. Rev. C 88, 044916 (2013).
  8. S. Ryu, J. F. Paquet, C. Shen, G. S. Denicol, B. Schenke, S. Jeon, and C. Gale, Phys. Rev. Lett. 115, 132301 (2015).
  9. M. R. Heffernan, C. Gale, S. Jeon, and J.-F. Paquet, Phys. Rev. Lett. 132, 252301 (2024).
  10. D. Wagner, Phys. Rev. D 111, 016008 (2025).
  11. P. Palni et al., in Proceedings of the 2nd Hot QCD Matter Conference 2024 (2024), arXiv:2412.10779.
  12. G. Pichon, Ann. Inst. Henri Poincaré. A. Phys. Théor. 2, 21 (1965), https://www.numdam.org/item/AIHPA_1965__2_1_21_0/.
  13. W. A. Hiscock and L. Lindblom, Phys. Rev. D 31, 725 (1985).
  14. G. S. Denicol, T. Kodama, T. Koide, and P. Mota, J. Phys. G 35, 115102 (2008).
  15. I. Muller, Z. Phys. 198, 329 (1967).
  16. W. Israel, Ann. Phys. (N.Y.) 100, 310 (1976).
  17. W. Israel and J. M. Stewart, Ann. Phys. (N.Y.) 118, 341 (1979).
  18. F. S. Bemfica, F. S. Bemfica, M. M. Disconzi, M. M. Disconzi, J. Noronha, and J. Noronha, Phys. Rev. D 100, 104020 (2019); 105, 069902(E) (2022).
  19. R. E. Hoult and P. Kovtun, J. High Energy Phys. 06 (2020) 067.
  20. A. Pandya and F. Pretorius, Phys. Rev. D 104, 023015 (2021).
  21. A. Jaiswal, Phys. Rev. C 87, 051901 (2013).
  22. A. K. Panda, A. Dash, R. Biswas, and V. Roy, J. High Energy Phys. 03 (2021) 216.
  23. G. S. Denicol, T. Koide, and D. H. Rischke, Phys. Rev. Lett. 105, 162501 (2010).
  24. G. S. Denicol, H. Niemi, E. Molnar, and D. H. Rischke, Phys. Rev. D 85, 114047 (2012); 91, 039902(E) (2015).
  25. A. Jaiswal, B. Friman, and K. Redlich, Phys. Lett. B 751, 548 (2015).
  26. J. A. Fotakis, M. Greif, C. Greiner, G. S. Denicol, and H. Niemi, Phys. Rev. D 101, 076007 (2020).
  27. A. Dash, M. Shokri, L. Rezzolla, and D. H. Rischke, Phys. Rev. D 107, 056003 (2023).
  28. A. Daher, L. Tinti, A. Jaiswal, and R. Ryblewski, Phys. Rev. D 111, 074011 (2025).
  29. G. S. Denicol, C. Gale, S. Jeon, A. Monnai, B. Schenke, and C. Shen, Phys. Rev. C 98, 034916 (2018).
  30. L. Du and U. Heinz, Comput. Phys. Commun. 251, 107090 (2020).
  31. X. An et al., Nucl. Phys. A1017, 122343 (2022).
  32. J. L. Anderson and H. R. Witting, Physica (Amsterdam) 74, 466 (1974).
  33. A. Jaiswal, R. Ryblewski, and M. Strickland, Phys. Rev. C 90, 044908 (2014).
  34. G. S. Denicol, U. W. Heinz, M. Martinez, J. Noronha, and M. Strickland, Phys. Rev. Lett. 113, 202301 (2014).
  35. J.-P. Blaizot and L. Yan, J. High Energy Phys. 11 (2017) 161.
  36. J.-P. Blaizot and L. Yan, Phys. Lett. B 780, 283 (2018).
  37. M. Kurian, S. Mitra, S. Ghosh, and V. Chandra, Eur. Phys. J. C 79, 134 (2019).
  38. S. Bhadury, M. Kurian, V. Chandra, and A. Jaiswal, J. Phys. G 48, 105104 (2021).
  39. S. Rath and B. K. Patra, Phys. Rev. D 102, 036011 (2020).
  40. K. K. Gowthama, M. Kurian, and V. Chandra, Phys. Rev. D 103, 074017 (2021).
  41. R. Ghosh and N. Haque, Phys. Rev. D 105, 114029 (2022).
  42. J. Dey, S. Samanta, S. Ghosh, and S. Satapathy, Phys. Rev. C 106, 044914 (2022).
  43. R. Ghosh and M. Kurian, Phys. Rev. C 107, 034903 (2023).
  44. N. Weickgenannt and J.-P. Blaizot, Phys. Rev. D 111, 056006 (2025).
  45. M. P. Heller, R. A. Janik, and P. Witaszczyk, Phys. Rev. Lett. 110, 211602 (2013).
  46. A. Buchel, M. P. Heller, and J. Noronha, Phys. Rev. D 94, 106011 (2016).
  47. S. Jaiswal, C. Chattopadhyay, L. Du, U. Heinz, and S. Pal, Phys. Rev. C 105, 024911 (2022).
  48. S. Jaiswal, J.-P. Blaizot, R. S. Bhalerao, Z. Chen, A. Jaiswal, and L. Yan, Phys. Rev. C 106, 044912 (2022).
  49. N. Vyas, S. Jaiswal, and A. Jaiswal, Phys. Lett. B 841, 137943 (2023).
  50. W. Florkowski, E. Maksymiuk, R. Ryblewski, and M. Strickland, Phys. Rev. C 89, 054908 (2014).
  51. C. Chattopadhyay, U. Heinz, S. Pal, and G. Vujanovic, Phys. Rev. C 97, 064909 (2018).
  52. G. S. Rocha, G. S. Denicol, and J. Noronha, Phys. Rev. Lett. 127, 042301 (2021).
  53. S. Mitra, Phys. Rev. C 103, 014905 (2021).
  54. G. S. Rocha, M. N. Ferreira, G. S. Denicol, and J. Noronha, Phys. Rev. D 106, 036022 (2022).
  55. A. Shaikh, S. Rath, S. Dash, and B. Panda, Phys. Rev. D 111, 096011 (2025).
  56. D. Teaney and L. Yan, Phys. Rev. C 89, 014901 (2014).
  57. D. Dash, S. Bhadury, S. Jaiswal, and A. Jaiswal, Phys. Lett. B 831, 137202 (2022).
  58. D. Dash, S. Jaiswal, S. Bhadury, and A. Jaiswal, Phys. Rev. C 108, 064913 (2023).
  59. S. K. Singh, M. Kurian, and V. Chandra, Phys. Rev. D 110, 014004 (2024).
  60. S. Bhadury, Phys. Rev. C 111, 034909 (2025).
  61. S. Kamata, Phys. Rev. D 110, 116020 (2024).
  62. K. Dusling, G. D. Moore, and D. Teaney, Phys. Rev. C 81, 034907 (2010).
  63. G. S. Denicol and J. Noronha, Phys. Lett. B 850, 138487 (2024).
  64. G. S. Rocha, C. V. P. de Brito, and G. S. Denicol, Phys. Rev. D 108, 036017 (2023).
  65. S. R. Groot, W. A. Leeuwen, C. G. van Weert, and C. G. Weert, Relativistic Kinetic Theory: Principles and Applications (North-Holland, Amsterdam, 1980).
  66. C. Cercignani and G. M. Kremer, The Relativistic Boltzmann Equation: Theory and Applications (Birkhäuser Basel, 2002), Vol. 22, p. 384.
  67. D. Wagner, A. Palermo, and V. E. Ambruş, Phys. Rev. D 106, 016013 (2022).
  68. P. Chakraborty and J. I. Kapusta, Phys. Rev. C 83, 014906 (2011).
  69. K. Dusling and T. Schäfer, Phys. Rev. C 85, 044909 (2012).
  70. A. Kurkela and U. A. Wiedemann, Eur. Phys. J. C 79, 776 (2019).
  71. D. Wagner, V. E. Ambrus, and E. Molnar, Phys. Rev. D 109, 056018 (2024).
  72. S. Banerjee, S. Bhadury, W. Florkowski, A. Jaiswal, and R. Ryblewski, arXiv:2405.05089.
  73. J. Adam et al. (STAR Collaboration), Phys. Rev. Lett. 123, 132301 (2019).
  74. A. Das, H. Mishra, and R. K. Mohapatra, Phys. Rev. D 106, 014013 (2022).
  75. S. Dey, A. Jaiswal, and H. Mishra, J. High Energy Phys. 12 (2024) 192.

Outline

Information

Phys. Rev. D 111, 114007– Published 10 June, 2025
  • Received 3 February 2025
  • Accepted 20 May 2025
Crossmark - Check for updates button
Creative Commons Logo

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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation