Quantum decay into a continuum at weak bias

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Abstract
We consider the quantum decay from the locally stable ground state of a one-dimensional metastable potential. We consider the case where the metastable minimum is almost degenerate with the vacuum level. In this case, the quantum decay probability is influenced by backscattering from the continuum states; a feature which is not accounted for in standard WKB theory. We evaluate the decay rates, from the ground state and the higher-resonance states, by the use of complex-time path-integral methods. The decay rate from the low-lying states of the metastable well is characterized by two quasi-zero-modes and a transmission factor, which approaches zero proportional to the square root of the potential drop. Moreover, we present a useful set of rules for the complex-time path-integral phase factors. These rules considerably simplify the calculation of decay rates (i.e., the pole condition of the Fourier-transformed Green’s function).