Abstract
Localised heterogeneities have been recently discovered to act as bubble-nucleation sites in nonlinear field theories. Vacuum decay seeded by black holes is one of the most remarkable applications. This article proposes a simple and exactly solvable ϕ4 model to study bubble evolution about a localised heterogeneity. Bubbles with a rich dynamical behaviour are observed depending on the topological properties of the heterogeneity. The linear stability analysis of soliton-bubbles predicts oscillating bubbles and the insertion of new bubbles inside an expanding precursor bubble. Numerical simulations in 2+1 dimensions are in good agreement with theoretical predictions.
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References
R. Gregory, I.G. Moss and B. Withers, Black holes as bubble nucleation sites, JHEP 03 (2014) 081 [arXiv:1401.0017] [INSPIRE].
P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [arXiv:1503.07331] [INSPIRE].
P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [arXiv:1501.04937] [INSPIRE].
P. Burda, R. Gregory and I. Moss, The fate of the Higgs vacuum, JHEP 06 (2016) 025 [arXiv:1601.02152] [INSPIRE].
M.S. Turner and F. Wilczek, Is our vacuum be metastable?, Nature 298 (1982) 633 [INSPIRE].
E.J. Weinberg, Classical solutions in quantum field theory: Solitons and Instantons in High Energy Physics, Cambridge University Press, (2012).
T.W.B. Kibble, Some Implications of a Cosmological Phase Transition, Phys. Rept. 67 (1980) 183 [INSPIRE].
I.G. Moss, Black hole bubbles, Phys. Rev. D 32 (1985) 1333 [INSPIRE].
W.A. Hiscock, Can black holes nucleate vacuum phase transitions?, Phys. Rev. D 35 (1987) 1161 [INSPIRE].
V.A. Berezin, V.A. Kuzmin and I.I. Tkachev, Black holes initiate false vacuum decay, Phys. Rev. D 43 (1991) R3112 [INSPIRE].
J.A. González et al., Fate of the true-vacuum bubbles, JCAP 06 (2018) 033 [arXiv:1710.05334] [INSPIRE].
R. Gregory, K.M. Marshall, F. Michel and I.G. Moss, Negative modes of Coleman-De Luccia and black hole bubbles, Phys. Rev. D 98 (2018) 085017 [arXiv:1808.02305] [INSPIRE].
L. Cuspinera, R. Gregory, K. Marshall and I.G. Moss, Higgs Vacuum Decay from Particle Collisions?, Phys. Rev. D 99 (2019) 024046 [arXiv:1803.02871] [INSPIRE].
T.P. Billam, R. Gregory, F. Michel and I.G. Moss, Simulating seeded vacuum decay in a cold atom system, Phys. Rev. D 100 (2019) 065016 [arXiv:1811.09169] [INSPIRE].
C. Cheung and S. Leichenauer, Limits on New Physics from Black Holes, Phys. Rev. D 89 (2014) 104035 [arXiv:1309.0530] [INSPIRE].
M. Nach, Hawking’s radiation of sine-Gordon black holes in two dimensions, Int. J. Mod. Phys. A 34 (2019) 1950086 [INSPIRE].
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York (1986).
P.L. Christiansen and P.S. Lomdahl, Numerical study of 2+1 dimensional sine-Gordon solitons, Physica D 2 (1981) 482.
J. González, A. Marcano, B. Mello and L. Trujillo, Controlled transport of solitons and bubbles using external perturbations, Chaos Soliton Fract. 28 (2006) 804.
A.G. Castro-Montes, J.F. Marín, D. Teca-Wellmann, J.A. González and M.A. García-Ñustes, Stability of bubble-like fluxons in disk-shaped josephson junctions in the presence of a coaxial dipole current, Chaos 30 (2020) 063132.
B. Felsager, Geometry, particles, and fields, Springer Science & Business Media (2012).
T. Vachaspati, Kinks and domain walls: An introduction to classical and quantum solitons, Cambridge University Press (2006).
N. Manton and P. Sutcliffe, Topological solitons, Cambridge University Press (2004).
K. Javidan, Analytical formulation for soliton-potential dynamics, Phys. Rev. E 78 (2008) 046607 [arXiv:0805.2676] [INSPIRE].
G. Kälbermann, Soliton interacting as a particle, Phys. Lett. A 252 (1999) 37 [INSPIRE].
G. Kälbermann, A model for soliton trapping in a well, Chaos Solitons Fract. 12 (2001) 2381.
K. Javidan, Interaction of topological solitons with defects: Using a nontrivial metric, J. Phys. A 39 (2006) 10565 [INSPIRE].
M.A. Lizunova, J. Kager, S. de Lange and J. van Wezel, Kinks and realistic impurity models in φ4-theory, arXiv:2007.04747 [INSPIRE].
M. Peyrard and T. Dauxois, Physique des Solitons, Savoirs actuels (2004).
I. Barashenkov, A. Gocheva, V. Makhankov and I. Puzynin, Stability of the soliton-like bubbles, Physica D 34 (1989) 240.
I.V. Barashenkov and E.Y. Panova, Stability and evolution of the quiescent and travelling solitonic bubbles, Physica D 69 (1993) 114.
J.A. González and J.A. Hołyst, Behavior of φ4 kinks in the presence of external forces, Phys. Rev. B 45 (1992) 10338.
J.A. González, S. Cuenda and A. Sánchez. Kink dynamics in spatially inhomogeneous media: The role of internal modes, Phys. Rev. E 75 (2007) 036611.
J.A. González, M.A. García-Ñustes, A. Sánchez and P.V. McClintock, Hawking-like emission in kink-soliton escape from a potential well, New J. Phys. 10 (2008) 113015.
A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Solitons in conducting polymers, Rev. Mod. Phys. 60 (1988) 781 [INSPIRE].
M. Peyrard and A.R. Bishop, Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett. 62 (1989) 2755.
J.A. González and B. de A Mello, Kink catastrophes, Phys. Scripta 54 (1996) 14.
J.A. González and F.A. Oliveira, Nucleation theory, the escaping processes and nonlinear stability, Phys. Rev. B 59 (1999) 6100.
J. González, A. Bellorín and L. Guerrero, How to excite the internal modes of sine-gordon solitons, Chaos Solitons Fract. 17 (2003) 907.
M.A. García-Ñustes, J.A. González and J.F. Marín, Bubble-like structures generated by activation of internal shape modes in two-dimensional sine-Gordon line solitons, Phys. Rev. E 95 (2017) 032222 [arXiv:1605.04990] [INSPIRE].
J.F. Marín, Generation of soliton bubbles in a sine-gordon system with localised inhomogeneities, J. Phys. Conf. Ser. 1043 (2018) 012001.
J.A. Hołyst, Kink solitons of the double-quadratic model in the presence of an external spatially inhomogeneous force, Phys. Rev. E 57 (1998) 4786.
D.K. Campbell and M. Peyrard, Solitary wave collisions revisited, Physica D 18 (1986) 47.
M. Chirilus-Bruckner, C. Chong, J. Cuevas-Maraver and P.G. Kevrekidis, Sine-Gordon Equation: From Discrete to Continuum, pp. 31–57, Springer International Publishing, Cham (2014).
P.G. Kevrekidis and J. Cuevas-Maraver, A Dynamical Perspective on the φ4 model: Past, present and future, Springer (2019).
S. Flügge, Practical quantum mechanics, Springer Science & Business Media (2012).
J.A. Hołyst and H. Benner, Universal family of kink-bearing models reconstructed from a Pöschl-Teller scattering potential, Phys. Rev. B 43 (1991) 11190.
J.A. González, A. Bellorín and L.E. Guerrero, Internal modes of sine-gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65 (2002) 065601.
G. Lythe, Stochastic Dynamics of ϕ4 Kinks: Numerics and Analysis, pp. 93–110, Springer International Publishing, Cham (2019).
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Marín, J.F. Bubble evolution around heterogeneities in ϕ4-field theories. J. High Energ. Phys. 2021, 198 (2021). https://doi.org/10.1007/JHEP02(2021)198
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DOI: https://doi.org/10.1007/JHEP02(2021)198