Instanton approach to the decay of a metastable quantum state

Abstract

The escape transition due to quantum tunnelling of a particle from a metastable region, created by a cubic potential, is studied. Finding this amplitude is reduced to the computation of a Feynman path integral. This calculus has been carried out using the instanton method, which demands to rotate the time coordinate along the imaginary plane. The results obtained show that the ground state energy has actually an imaginary part (fact that is actually related to the metastability of the system) and allows to find the decaying rate of the metastable state