Metastability Driven by Soft Quantum Fluctuation Modes

Abstract

The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which makes a saddle for the action, is derived in terms of Jacobian elliptic functions whose periodicity establishes the one-to-one correspondence between energy of the classical motion and temperature (inverse imaginary time) of the system. The quantum fluctuation contribution has been computed through the theory of the functional determinants for periodic boundary conditions. The decay rate shows a peculiar temperature dependence mainly due to the softening of the low lying quantum fluctuation eigenvalues. The latter are determined by solving the Lam\`{e} equation which governs the fluctuation spectrum around the time dependent classical bounce.