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Electric, thermal, and thermoelectric response of a hot pion gas in a time dependent background magnetic field

Ankit Kumar1,*, K Gowthama2,†, Vinod Chandra1,‡, and Sadhana Dash2,§

  • *Contact author: kumar.ankit@iitgn.ac.in
  • †Contact author: k_gowthama@iitb.ac.in
  • ‡Contact author: vchandra@iitgn.ac.in
  • §Contact author: sadhana@phy.iitb.ac.in
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Phys. Rev. D 112, 096026 – Published 24 November, 2025

DOI: https://doi.org/10.1103/h9kt-bj75

Abstract

In this work, we investigate the electric, thermal, and thermoelectric response of a hot pion gas in the presence of a time-dependent background electromagnetic field. Using the relativistic Boltzmann equation within the relaxation time approximation, we evaluate the Ohmic and Hall conductivities, thermal and Hall-like thermal conductivities, and the magneto-Seebeck and Nernst coefficients, explicitly incorporating the effects of the magnetic field’s strength and decay dynamics. Unlike earlier studies restricted to static fields, our analysis accounts for the temporal evolution of the background magnetic field, capturing the nontrivial time dependence of transport coefficients and their sensitivity to the field profile. We further examine the elliptic flow coefficient, v2, linked to the Knudsen number through the thermal conductivity, and demonstrate its dependence on both the magnitude and decay of the magnetic field. This work provides the first systematic study of pion transport in a realistic, time-varying electromagnetic background and underscores the importance of including such effects in modeling the late stages of heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and LHC.

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References (55)

  1. J. Adams et al. (STAR Collaboration), Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A757, 102 (2005).
  2. K. Adcox et al. (PHENIX Collaboration), Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys. A757, 184 (2005).
  3. B. Back et al. (PHOBOS Collaboration), The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A757, 28 (2005).
  4. I. Arsene et al. (BRAHMS Collaboration), Quark gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys. A757, 1 (2005).
  5. K. Aamodt et al. (ALICE Collaboration), Charged-particle multiplicity density at mid-rapidity in central Pb-Pb collisions at sNN=2.76  TeV, Phys. Rev. Lett. 105, 252301 (2010).
  6. S. Turbide, R. Rapp, and C. Gale, Hadronic production of thermal photons, Phys. Rev. C 69, 014903 (2004).
  7. J. V. Steele, H. Yamagishi, and I. Zahed, Dilepton and photon emission rates from a hadronic gas, Phys. Lett. B 384, 255 (1996).
  8. A. Dash, S. Samanta, J. Dey, U. Gangopadhyaya, S. Ghosh, and V. Roy, Anisotropic transport properties of a hadron resonance gas in a magnetic field, Phys. Rev. D 102, 016016 (2020).
  9. A. Das, H. Mishra, and R. K. Mohapatra, Transport coefficients of hot and dense hadron gas in a magnetic field: A relaxation time approach, Phys. Rev. D 100, 114004 (2019).
  10. G. P. Kadam, H. Mishra, and L. Thakur, Electrical and thermal conductivities of hot and dense hadronic matter, Phys. Rev. D 98, 114001 (2018).
  11. D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, The effects of topological charge change in heavy ion collisions: “Event by event p and cp violation”, Nucl. Phys. A803, 227 (2008).
  12. V. Skokov, A. Illarionov, and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24, 5925 (2009).
  13. V. V. Skokov, A. Y. Illarionov, and V. D. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24, 5925 (2009).
  14. A. Huang, D. She, S. Shi, M. Huang, and J. Liao, Dynamical magnetic fields in heavy-ion collisions, Phys. Rev. C 107, 034901 (2023).
  15. G. Inghirami, M. Mace, Y. Hirono, L. Del Zanna, D. E. Kharzeev, and M. Bleicher, Magnetic fields in heavy ion collisions: Flow and charge transport, Eur. Phys. J. C 80, 293 (2020).
  16. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Chiral magnetic effect, Phys. Rev. D 78, 074033 (2008).
  17. D. Kharzeev, J. Liao, S. Voloshin, and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report, Prog. Part. Nucl. Phys. 88, 1 (2016).
  18. A. Sadofyev and M. Isachenkov, The chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697, 404 (2011).
  19. D. E. Kharzeev and H.-U. Yee, Chiral magnetic wave, Phys. Rev. D 83, 085007 (2011).
  20. K. Tuchin, Magnetic contribution to dilepton production in heavy-ion collisions, Phys. Rev. C 88, 024910 (2013).
  21. I. A. Shovkovy, Magnetic catalysis: A review, in Strongly Interacting Matter in Magnetic Fields, edited by D. Kharzeev, K. Landsteiner, A. Schmitt, and H.-U. Yee (Springer, Berlin, Heidelberg, 2013), pp. 13–49.
  22. V. Gusynin, V. Miransky, and I. Shovkovy, Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field, Nucl. Phys. B462, 249 (1996).
  23. G. Endrődi, M. Giordano, S. D. Katz, T. G. Kovacs, and F. Pittler, Magnetic catalysis and inverse catalysis for heavy pions, J. High Energy Phys. 07 (2019) 007.
  24. M. Bocquet, S. Bonazzola, E. Gourgoulhon, and J. Novak, Rotating neutron star models with magnetic field, Astron. Astrophys. 301, 757 (1995).
  25. G. Baym, D. Bödeker, and L. McLerran, Magnetic fields produced by phase transition bubbles in the electroweak phase transition, Phys. Rev. D 53, 662 (1996).
  26. K. Tuchin, Synchrotron radiation by fast fermions in heavy-ion collisions, Phys. Rev. C 82, 034904 (2010).
  27. K. Tuchin, Particle production in strong electromagnetic fields in relativistic heavy-ion collisions, Adv. High Energy Phys. 2013, 490495 (2013).
  28. E. Stewart and K. Tuchin, Continuous evolution of electromagnetic field in heavy-ion collisions, Nucl. Phys. A1016, 122308 (2021).
  29. D. Dey, G. K. K., S. Dash, and B. K. Nandi, Viscous effects of a hot QGP medium in a time dependent magnetic field and their phenomenological significance, Phys. Rev. D 111, 096014 (2025).
  30. G. K. K, M. Kurian, and V. Chandra, Electromagnetic response of hot QCD medium in the presence of background time-varying fields, Phys. Rev. D 104, 094037 (2021).
  31. K. Singh, J. Dey, and R. Sahoo, Thermal conductivity of evolving quark-gluon plasma in the presence of a time-varying magnetic field, Phys. Rev. D 109, 014018 (2024).
  32. K. Singh, J. Dey, and R. Sahoo, Electric field induction in quark-gluon plasma due to thermoelectric effects, Phys. Rev. D 110, 114051 (2024).
  33. R. Ghosh and M. Kurian, Magnetic-field-dependent electric-charge transport in hadronic medium at finite temperature, Phys. Rev. C 107, 034903 (2023).
  34. P. Kalikotay, S. Ghosh, N. Chaudhuri, P. Roy, and S. Sarkar, Medium effects on the electrical and Hall conductivities of a hot and magnetized pion gas, Phys. Rev. D 102, 076007 (2020).
  35. A. Das, H. Mishra, and R. K. Mohapatra, Magneto-seebeck coefficient and nernst coefficient of a hot and dense hadron gas, Phys. Rev. D 102, 014030 (2020).
  36. A. Das, H. Mishra, and R. K. Mohapatra, Electrical conductivity and Hall conductivity of a hot and dense hadron gas in a magnetic field: A relaxation time approach, Phys. Rev. D 99, 094031 (2019).
  37. K. Singh, K. K. Pradhan, D. Sahu, and R. Sahoo, Thermoelectric effects of an interacting hadron gas in the presence of an external magnetic field, Phys. Rev. D 111, 074033 (2025).
  38. P. Kalikotay, S. Ghosh, N. Chaudhuri, P. Roy, and S. Sarkar, Electrical conductivity and shear viscosity of a pion gas in a thermo-magnetic medium, Eur. Phys. J. A 60, 71 (2024).
  39. B. Feng, Electric conductivity and hall conductivity of the QGP in a magnetic field, Phys. Rev. D 96, 036009 (2017).
  40. D. Satow, Nonlinear electromagnetic response in quark-gluon plasma, Phys. Rev. D 90, 034018 (2014).
  41. S. Mitra and V. Chandra, Covariant kinetic theory for effective fugacity quasiparticle model and first order transport coefficients for hot qcd matter, Phys. Rev. D 97, 034032 (2018).
  42. S. R. Groot, W. A. Leeuwen, C. G. van Weert, and C. G. Weert, Relativistic Kinetic Theory: Principles and Applications (North Holland, Amsterdam 1980).
  43. K. K. Gowthama, M. Kurian, and V. Chandra, Thermal and thermoelectric responses of hot qcd medium in time-varying magnetic fields, Phys. Rev. D 106, 034008 (2022).
  44. S. Mitra and S. Sarkar, Medium effects on the thermal conductivity of a hot pion gas, Phys. Rev. D 89, 054013 (2014).
  45. S. Mitra and V. Chandra, Transport coefficients of a hot qcd medium and their relative significance in heavy-ion collisions, Phys. Rev. D 96, 094003 (2017).
  46. J. R. Bhatt, A. Das, and H. Mishra, Thermoelectric effect and Seebeck coefficient for hot and dense hadronic matter, Phys. Rev. D 99, 014015 (2019).
  47. S. Rath and S. Dash, Effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot qcd matter, Eur. Phys. J. A 59, 25 (2023).
  48. R. S. Bhalerao, J.-P. Blaizot, N. Borghini, and J.-Y. Ollitrault, Elliptic flow and incomplete equilibration at RHIC, Phys. Lett. B 627, 49 (2005).
  49. S. Rath and S. Dash, Momentum transport properties of a hot and dense qcd matter in a weak magnetic field, Eur. Phys. J. C 82, 797 (2022).
  50. P. Chakraborty and J. I. Kapusta, Quasiparticle theory of shear and bulk viscosities of hadronic matter, Phys. Rev. C 83, 014906 (2011).
  51. PHENIX Collaboration, Elliptic flow of identified hadrons in Au+Au collisions at sNN=200  GeV, Phys. Rev. Lett. 91, 182301 (2003).
  52. C. Gombeaud and J.-Y. Ollitrault, Elliptic flow in transport theory and hydrodynamics, Phys. Rev. C 77, 054904 (2008).
  53. F. L. Braghin, Low energy constituent quark and pion effective couplings in a weak external magnetic field, Eur. Phys. J. A 54, 45 (2018).
  54. S. Kumar Singh, S. Bhadury, M. Kurian, and V. Chandra, Particle number diffusion in second-order relativistic dissipative hydrodynamics with momentum-dependent relaxation time, Phys. Rev. D 111, 114007 (2025).
  55. S. K. Singh, M. Kurian, and V. Chandra, Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time, Phys. Rev. D 110, 014004 (2024).

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Phys. Rev. D 112, 096026– Published 24 November, 2025
  • Received 2 August 2025
  • Accepted 31 October 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. Funded by SCOAP3.

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