Quantum mechanical barrier problems: II. Dissipative tunnelling at finite temperatures for the unbiased oscillator

Abstract

The decay rate for an unbiased local quasi-equilibrium oscillator, leaking through a quartic potential energy barrier into free space and weakly coupled to an ohmic thermal environment, is calculated in the low temperature quantum tunnelling regime. The imaginary part of the free energy is determined by a bound kink-antikink pair. It is found that the limits of zero dissipation (λ → 0) and zero temperature ( T → 0) do not commute. In the limit λ → 0 (for nonzero T) one recovers the finite nondissipative quantum tunnelling rate obtained in a previous paper (I), whereas in the limit T → 0 (for nonzero λ) a freezing phenomenon occurs.