Path integral study of phase transitions for thermons in macroscopic quantum tunneling

A study of the escape rate for several potentials and thermon periods by means of a path integral approach is presented. The period of the thermons and the escape rate exponent have been characterized for different cases. As the temperature diminishes, the crossing from purely thermal activation to thermally assisted tunneling is characterized by phase transitions, which can be of first or second order. In the quantum regime, first order transitions can be also found. Besides, different periods with adequate behavior for both low and limiting upper temperature shows that escape rate and escape temperature present degeneracies for the same temperature depending on the numbers of maximal points in the thermon periods.