- Physical Review Journals
All JournalsPhysics Magazine

Physical Review C

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

Magnetized charged boson gas and two-step condensation in neutron-star matter

Amanda Castillo Ayón1,*, Gabriel Gil Perez1, A. Pérez Martínez1,†, H. Pérez Rojas1,‡, Gabriella Piccinelli Bocchi2,§, Adriel Ernesto Rodríguez Concepción1,∥, and Angel Sanchez3,¶

  • *Contact author: amandac@icimaf.cu
  • †Contact author: aurora@icimaf.cu
  • ‡Contact author: hugo@icimaf.cu
  • §Contact author: itzamna@unam.mx
  • ∥Contact author: adrielerdz@icimaf.cu
  • Contact author: ansac@ciencias.unam.mx
PDF

Phys. Rev. C 113, 015802 – Published 7 January, 2026

DOI: https://doi.org/10.1103/bz7h-rv7g

Abstract

We study the thermodynamic properties of a noninteracting, relativistic gas of charged scalar bosons in a uniform magnetic field, including both statistical and vacuum contributions at arbitrary field strengths. Focusing on the low-temperature regime and separating the lowest Landau level (LLL) from excited states provides a clearer view of the magnetic field’s impact on thermodynamic quantities. We revisit Bose-Einstein condensation (BEC), specific heat, magnetization, and the equation of state (EoS). A central result is the diffuse character of BEC induced by the magnetic field, reflected in the specific heat, which exhibits two plateaus: the first appears when the system becomes effectively one-dimensional through magnetic confinement, while the second—associated with the true one-particle ground state—is suppressed by the field. Consequently, no critical condensation temperature arises. For magnetization, the LLL contribution shifts from diamagnetic to paramagnetic. As the field strengthens with the inclusion of the excited states, the statistical magnetization remains negative. In contrast, the vacuum contribution dominates at strong fields, driving paramagnetism. We also show that antiparticles increase specific heat, magnetization, and total pressure. These effects are illustrated for a pion gas under neutron star conditions and compared with previous results for a neutral vector boson system.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. J. Chadwick, Proc. R. Soc. Lond. Ser. A 136, 692 (1932).
  2. M. Camenzind, Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes, Astronomy and Astrophysics Library (Springer, Berlin, 2007).
  3. J. M. Lattimer and M. Prakash, Phys. Rep. 442, 109 (2007).
  4. D. Page, M. Prakash, J. M. Lattimer, and A. W. Steiner, PoS XXXIVBWNP, 005 (2011).
  5. A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins, Nature (London) 217, 709 (1968).
  6. C. Kouveliotou, M. K. Briggs, G. J. Fishman, L. J. Dershem, W. S. Paciesas, J. A. Pendleton, and K. Hurley, Nature (London) 355, 607 (1992).
  7. R. L. Delgado, P. Bargueño, and F. Sols, Phys. Rev. E 86, 031102 (2012).
  8. N. Bigagli, C. Warner, W. Yuan, S. Zhang, I. Stevenson, T. Karman, and S. Will, Nat. Phys. 19, 1579 (2023).
  9. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Nature (London) 631, 289 (2024).
  10. H. Pérez Rojas, Phys. Lett. B 379, 148 (1996).
  11. H. Pérez Rojas, Phys. Lett. A 234, 13 (1997).
  12. H. Pérez and L. Villegas, arXiv:cond-mat/9911227.
  13. J. Daicic and N. E. Frankel, Phys. Rev. D 53, 5745 (1996).
  14. V. Khalilov, C. L. Ho, and C. Yang, Mod. Phys. Lett. A 12, 1973 (1997).
  15. V. R. Khalilov and C. L. Ho, Phys. Rev. D 60, 033003 (1999).
  16. G. B. Standen and D. J. Toms, Phys. Rev. E 60, 5275 (1999).
  17. A. Ayala, M. Loewe, J. C. Rojas, and C. Villavicencio, Phys. Rev. D 86, 076006 (2012).
  18. G. Quintero Angulo, A. Pérez Martínez, and H. Pérez Rojas, Phys. Rev. C 96, 045810 (2017).
  19. G. Quintero Angulo, A. Pérez Martínez, and H. Pérez Rojas, Int. J. Mod. Phys. Conf. Ser. 45, 1760047 (2017).
  20. G. Quintero Angulo, L. C. Suarez González, A. Pérez Martínez and H. Pérez Rojas, Phys. Rev. C 104, 035803 (2021).
  21. G. Quintero Angulo, L. C. Suarez González, A. Pérez Martínez and H. Pérez Rojas, Phys. Rev. C 108, 015806 (2023).
  22. A. E. Rodríguez Concepción and G. Quintero Angulo, Astron. Nachr. 345, e240009 (2024).
  23. G. Quintero Angulo, A. Pérez Martínez, H. Pérez Rojas, Astron. Nachr. 344, e220082 (2023).
  24. M. A. A. Hernández, arXiv:2507.19507.
  25. A. E. R. Concepcion, Charged scalar bosons, Version 1 (2025), https://doi.org/10.17605/OSF.IO/GMFYV.
  26. E. J. Ferrer, V. de la Incera, D. M. Paret, A. Pérez Martínez, and A. Sanchez, Phys. Rev. D 91, 085041 (2015).
  27. V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Nucl. Phys. B 462, 249 (1996).
  28. M. Chaichian, S. S. Masood, C. Montonen, A. Pérez Martinez, and H. Pérez Rojas, Phys. Rev. Lett. 84, 5261 (2000).
  29. J. Schwinger, Phys. Rev. 82, 664 (1951).
  30. W. Dittrich and H. Gies, Probing the Quantum Vacuum: Perturbative Effective Action Approach in Quantum Electrodynamics and Its Application, Springer Tracts in Modern Physics, Vol. 166 (Springer, Berlin, 2000).
  31. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier, Amsterdam, 2005).
  32. S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (Wiley, New York, 1983).
  33. R. K. Pathria, Statistical Mechanics, 2nd ed. (Butterworth-Heinemann, Oxford, 1996).
  34. M. R. Schafroth, Phys. Rev. 100, 463 (1955).
  35. R. C. Duncan and C. Thompson, Astrophys. J. 392, L9 (1992).
  36. J. Mei, R. Wen, S. Mao, M. Huang, and K. Xu, Phys. Rev. D 110, 034024 (2024).
  37. L. H. Ryder, Quantum Field Theory, 2nd ed. (Cambridge University Press, Cambridge, 1996).
  38. V. I. Ritus, Ann. Phys. 69, 555 (1972).
  39. V. I. Ritus, Zh. Eksp. Teor. Fiz. 75, 1560 (1978) [Sov. Phys. JETP 48, 788 (1978)].
  40. A. Das, Finite Temperature Field Theory, 1st ed. (World Scientific, Singapore, 1997).
  41. J. I. Kapusta and C. Gale, Finite-Temperature Field Theory: Principles and Applications, 1st ed. (Cambridge University Press, Cambridge, 2006).

Outline

Information

Phys. Rev. C 113, 015802– Published 7 January, 2026
  • Received 15 July 2025
  • Accepted 5 November 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation