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

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

2005-05-13

arxiv.org/abs/hep-th/0505118v2

Nucl.Phys.B745:142-164,2006

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, 13 figures, substantial changes in the text, conclusions based on a much larger set of parameters and simulations

Scientific paper

10.1016/j.nuclphysb.2006.03.031

We compute tunneling in a quantum field theory in 1+1 dimensions for a field potential $U(\Phi)$ of the asymmetric double well type. The system is localized initially in the ``false vacuum''. We consider the case of a {\em compact space} ($S_1$) and study {\em 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 {\em 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 Schr\"odinger equation. We find that in general tunneling occurs in a resonant way, the resonances being associated with degeneracies of the approximate levels in the two separated wells. If the nonzero momentum modes of the quantum field are excited only weakly, the phenomena resemble those of quantum mechanics with the wave function of the zero mode oscillating forth and back between the wells. 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 potential barrier to disappear temporarily or definitely, the tunneling towards the ``true vacuum'' is then replaced by a sliding of the wave function.

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