Instability of the asymptotic-time-symmetry-breaking in the second order in quantum tunneling

Abstract

We apply a previous analysis of the dependence of the dynamic time-convolution equations and their solution on the degree λ of the initial strength of the polaron cloud to the usual zero-bias spin-boson model and standard second order (i.e. Born) approximation (in tunneling, i.e. the standard dilute blip approximation at λ=1). At temperatureT=0 and for the usual Ohmic type spin-boson coupling, the asymptotic-time-symmetry-breaking phenomenon as a function of the coupling strentghg can be analyzed, in the above Born approximation, in the wholeg-λ plane. A hardly interpretable conclusion is found that the symmetry breaking in the above approximation appears just at discrete lines in the plane. This implies instability of the phenomenon in the second-order theory with respect to arbitrarily small perturbations of the initial state and complies with exact proofs of absence of the partial symmetry-breaking phenomenon in analogous symmetric models.