Abstract
Classical-statistical lattice simulations provide a useful approximation to out-of-equilibrium quantum field theory, but only for systems exhibiting large occupation numbers, and only for phenomena that are not intrinsically quantum mechanical in nature. In certain special circumstances, it can be appropriate to initialize such real-time simulations with quantum-like zero-point fluctuations. We will revisit these points, and investigate reports that quantum bubble nucleation rates in 1+1 dimensions can be computed through the classical evolution of such a quantum-like initial condition [1]. We find that although intriguing, the reported numerical agreement between classical-statistical simulations and the quantum nucleation rate in 1+1 dimensions is a coincidence, which is not specific to this choice of initialisation, is parameter and lattice cut-off dependent and disappears as the number of space-dimensions increases from 1+1 to 2+1.
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References
J. Braden et al., New semiclassical picture of vacuum decay, Phys. Rev. Lett. 123 (2019) 031601 [Erratum ibid. 129 (2022) 059901] [arXiv:1806.06069] [INSPIRE].
M.P. Hertzberg, Quantum and classical behavior in interacting bosonic systems, JCAP 11 (2016) 037 [arXiv:1609.01342] [INSPIRE].
G. Aarts and J. Smit, Classical approximation for time dependent quantum field theory: diagrammatic analysis for hot scalar fields, Nucl. Phys. B 511 (1998) 451 [hep-ph/9707342] [INSPIRE].
G. Aarts and J. Berges, Classical aspects of quantum fields far from equilibrium, Phys. Rev. Lett. 88 (2002) 041603 [hep-ph/0107129] [INSPIRE].
A. Rajantie and A. Tranberg, Looking for defects in the 2PI correlator, JHEP 11 (2006) 020 [hep-ph/0607292] [INSPIRE].
A. Arrizabalaga, J. Smit and A. Tranberg, Equilibration in ϕ4 theory in 3 + 1 dimensions, Phys. Rev. D 72 (2005) 025014 [hep-ph/0503287] [INSPIRE].
Z.-G. Mou, P.M. Saffin and A. Tranberg, Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles, JHEP 11 (2019) 135 [arXiv:1909.02488] [INSPIRE].
P. Millington, Z.-G. Mou, P.M. Saffin and A. Tranberg, Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation, JHEP 03 (2021) 077 [arXiv:2011.02657] [INSPIRE].
M.P. Hertzberg, F. Rompineve and N. Shah, Quantitative analysis of the stochastic approach to quantum tunneling, Phys. Rev. D 102 (2020) 076003 [arXiv:2009.00017] [INSPIRE].
G.D. Moore and K. Rummukainen, Classical sphaleron rate on fine lattices, Phys. Rev. D 61 (2000) 105008 [hep-ph/9906259] [INSPIRE].
J. Berges, S. Scheffler and D. Sexty, Bottom-up isotropization in classical-statistical lattice gauge theory, Phys. Rev. D 77 (2008) 034504 [arXiv:0712.3514] [INSPIRE].
A. Rajantie and A. Tranberg, Counting defects with the two-point correlator, JHEP 08 (2010) 086 [arXiv:1005.0269] [INSPIRE].
M. D’Onofrio, K. Rummukainen and A. Tranberg, Sphaleron rate in the minimal standard model, Phys. Rev. Lett. 113 (2014) 141602 [arXiv:1404.3565] [INSPIRE].
A. Rajantie, P.M. Saffin and E.J. Copeland, Electroweak preheating on a lattice, Phys. Rev. D 63 (2001) 123512 [hep-ph/0012097] [INSPIRE].
P.B. Greene, L. Kofman, A.D. Linde and A.A. Starobinsky, Structure of resonance in preheating after inflation, Phys. Rev. D 56 (1997) 6175 [hep-ph/9705347] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258 [hep-ph/9704452] [INSPIRE].
G.N. Felder, J. García-Bellido, P.B. Greene, L. Kofman, A.D. Linde and I. Tkachev, Dynamics of symmetry breaking and tachyonic preheating, Phys. Rev. Lett. 87 (2001) 011601 [hep-ph/0012142] [INSPIRE].
D. Bödeker and K. Rummukainen, Non-Abelian plasma instabilities for strong anisotropy, JHEP 07 (2007) 022 [arXiv:0705.0180] [INSPIRE].
A. Rebhan, P. Romatschke and M. Strickland, Hard-loop dynamics of non-Abelian plasma instabilities, Phys. Rev. Lett. 94 (2005) 102303 [hep-ph/0412016] [INSPIRE].
A. Tranberg and J. Smit, Baryon asymmetry from electroweak tachyonic preheating, JHEP 11 (2003) 016 [hep-ph/0310342] [INSPIRE].
J. García-Bellido, D.Y. Grigoriev, A. Kusenko and M.E. Shaposhnikov, Nonequilibrium electroweak baryogenesis from preheating after inflation, Phys. Rev. D 60 (1999) 123504 [hep-ph/9902449] [INSPIRE].
J. García-Bellido, M. Garcia Perez and A. Gonzalez-Arroyo, Symmetry breaking and false vacuum decay after hybrid inflation, Phys. Rev. D 67 (2003) 103501 [hep-ph/0208228] [INSPIRE].
J. Smit and A. Tranberg, Chern-Simons number asymmetry from CP-violation at electroweak tachyonic preheating, JHEP 12 (2002) 020 [hep-ph/0211243] [INSPIRE].
A. Arrizabalaga, J. Smit and A. Tranberg, Tachyonic preheating using 2PI-1/N dynamics and the classical approximation, JHEP 10 (2004) 017 [hep-ph/0409177] [INSPIRE].
V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rept. 215 (1992) 203 [INSPIRE].
M.A. Amin, M.P. Hertzberg, D.I. Kaiser and J. Karouby, Nonperturbative dynamics of reheating after inflation: a review, Int. J. Mod. Phys. D 24 (2014) 1530003 [arXiv:1410.3808] [INSPIRE].
S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
G.D. Moore and K. Rummukainen, Electroweak bubble nucleation, nonperturbatively, Phys. Rev. D 63 (2001) 045002 [hep-ph/0009132] [INSPIRE].
G.D. Moore, K. Rummukainen and A. Tranberg, Nonperturbative computation of the bubble nucleation rate in the cubic anisotropy model, JHEP 04 (2001) 017 [hep-lat/0103036] [INSPIRE].
O. Gould, S. Güyer and K. Rummukainen, First-order electroweak phase transitions: a nonperturbative update, arXiv:2205.07238 [INSPIRE].
C.L. Wainwright, CosmoTransitions: computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183 (2012) 2006 [arXiv:1109.4189] [INSPIRE].
J. Braden, M.C. Johnson, H.V. Peiris, A. Pontzen and S. Weinfurtner, Mass renormalization in lattice simulations of false vacuum decay, arXiv:2204.11867 [INSPIRE].
J. Berges and J. Cox, Thermalization of quantum fields from time reversal invariant evolution equations, Phys. Lett. B 517 (2001) 369 [hep-ph/0006160] [INSPIRE].
J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739 (2004) 3 [hep-ph/0409233] [INSPIRE].
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Tranberg, A., Ungersbäck, G. Bubble nucleation and quantum initial conditions in classical statistical simulations. J. High Energ. Phys. 2022, 206 (2022). https://doi.org/10.1007/JHEP09(2022)206
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DOI: https://doi.org/10.1007/JHEP09(2022)206