Extended two-level quantum dissipative system from bosonization of the elliptic spin- Kondo model

Abstract

We study the elliptic spin- Kondo model (spin- fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion–boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.