Tunneling in a quantum field theory on a compact one-dimensional space

Abstract

We compute tunneling in a quantum field theory in 1 + 1 dimensions for a field potential U(Φ) of the asymmetric double well type. The system is localized initially in the "false vacuum". We consider the case of a compact space (S 1 ) and study global tunneling. The process is studied in real-time simulations. The computation is based on the time-dependent Hartree-Fock variational principle with a product ansatz for the wave functions of the various normal modes. While the wave functions of the nonzero momentum modes are treated within the Gaussian approximation, the wave function of the zero mode that tunnels between the two wells is not restricted to be Gaussian, but evolves according to a standard Schrödinger equation. We find that in general tunneling occurs in a resonant way, the resonances being

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“…Tunneling processes in which the entire space tunnels at once certainly exist in gravitating field theories [27], but this was not included in our analysis. One may also consider tunneling in situations where the spatial sections are compact, then the results of simulations using the Hartree approximation [28] suggest that resonant tunneling can occur. Of course, there may well be other efficient tunneling mechanisms in field theory that bear no resemblance whatsoever to resonant tunneling in quantum mechanics, such as DBI tunneling [30].…”

Measures on Transitions for Cosmology from Eternal Inflation

“…For example, Tye [18] has recently argued that in a landscape like Fig. 1, very fast "resonant" tunneling from A → C can occur if (a) the (non-resonant) B → C transition rate approximately equals the A → B rate, and (b) the shape of the potential near vacuum B satisfies a "resonance condition" (see also [19]). Such tunneling in a general landscape can be accounted for consistently, but only if one allows the B → C transition rate to depend upon whether or not the previous transition was A → B.…”