Absence of asymptotic-time symmetry breaking in zero-bias spin-boson model with partial relaxation

Abstract

The symmetric spin-boson model without external field is treated for any type of coupling to the boson bath and any initial bath density matrix. With initially fully aligned spin (〈σ_z〉 (0)= =1), the proof is given that a partial relaxation (〈σ_z〉 (+∞) t1<) implies that there is no asymptotic-time (up-and-down) symmetry breaking (i.e. that 〈σ_z〉 (+∞)=0). For the problem of a particle (interacting with free bosons) in a symmetric double well without spatial symmetry breaking before the infinite time limit, this means that att→ + ∞ the particle distribution becomes symmetric (irrespective of the full initial asymmetry) unless the particle fully remains (att→ + ∞) in Ihe starting well.