Quantum tunnelling in non-relativistic quantum mechanics of a single particle is a distinguishing feature from the classical mechanics where surmounting a potential barrier requires large enough energy instead of quantum mechanically penetrating the potential barrier with lower energy.
This feature persists when generalized into the case of relativistic field theory with multiple potential minimums, one of which is absolute minimum in both classical and (perturbative) quantum sense, while the rest of which is still classically stable but metastable by barrier penetration in quantum field theory.
Vacuum decay in field theory proceeds via sudden nucleations of true vacuum bubbles in the false vacuum environment, which is essentially a quantum phenomenon without classical analog. The decay rate is estimated by Euclidean instanton as an analog to the WKB approximation in nonrelativistic quantum mechanics.
Recently, semiclassical vacuum decay was found in Phys. Rev. Lett. 123 no. 3, (2019) that vacuum decay in field theory could proceed via classical evolution of the equation of motion for some initial configurations of false vacuum fluctuations. In particular, flyover vacuum decay was suggested in arXiv:1906.09657 that, a sufficiently large local initial fluctuation in field velocity could carry the field value directly flying over the potential barrier.
In our paper, we found that condition for semiclassical vacuum decay is rather loose, even allowing for the dubbed pop-up vacuum decay, where the semiclassical vacuum decay could still occur even if the initial energy density is everywhere insufficient to classically overcome the potential barrier.
gif : The time evolution of field profile for the last example of Fig.4 in the mentioned paper. The initial profile for field velocity is everywhere below the threshold for a classical surmounting over the potential barrier, however, after gathering energy through the gradient term in the equation of motion, a true vacuum bubble (red) is eventually formed out of the false vacuum background (blue), and then expands as usual but with oscillating feature inside the bubble.
It is worth noting that, the semiclassical vacuum decay is not only entirely motivated from the numerical simulations [ Phys.Rev. D100 (2019) 065016 , JHEP 1910 (2019) 174 , Phys.Rev.Lett. 123 (2019) 031601 ], but also from some theoretical considerations [ JHEP 1807 (2018) 014 , Phys.Rev. D100 (2019) 016011 ] and even experimential (cold atom) interest [ EPL 110 (2015) 56001 , J.Phys. B50 (2017) 024003].
值得注意的是，半经典真空衰变不只全出于数值模拟 [ Phys.Rev. D100 (2019) 065016 , JHEP 1910 (2019) 174 , Phys.Rev.Lett. 123 (2019) 031601 ] 的动机，还有来自理论上的考量 [ JHEP 1807 (2018) 014 , Phys.Rev. D100 (2019) 016011 ]，甚至是实验（冷原子）上的兴趣[ EPL 110 (2015) 56001 , J.Phys. B50 (2017) 024003]。