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

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 (S1) 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 evolves according to a standard Schrödinger equation. We find that in general tunneling occurs in a resonant way. If the nonzero momentum modes are excited efficiently, they react back onto the zero mode causing an effective dissipation. In some region of parameter space this back-reaction causes the tunneling being replaced by a sliding of the wave function.