Effect of dissipation on the decay-rate transition on a circle

The effect of dissipation on the rate of decay from the quantum tunneling regime to the classical regime is investigated in (1+1)-dimensional scalar field theory when the spatial coordinate is compactified. Especially, two potential models, i.e., the inverted double-well potential and the cubic potential, are discussed. In the case of Ohmic dissipation, the value of the critical parameter distinguishing the types of transition is increased for both potential models. In the case of super-Ohmic dissipation, the critical parameter decreases for both potential models.