Quantum coherence and phase diffusion

Abstract
Simonius has shown this remarkable result that if the coherence of wavefunctions is destroyed after a sufficiently short time by interaction with some « heat bath », the quantum tunnelling may become much slower than without heat bath. We consider the situation where the phase coherence is destroyed by weak interaction either with a classical noise or with a continuum of quantum harmonic oscillators in thermal equilibrium. In both cases the coherence is destroyed by a phase diffusion process « à la Stratonovich ». We analyse this process for single level systems diagonally coupled to the noise and for two level systems with an off diagonal coupling