Dynamics of a Two-Level System Coupled to Ohmic Bath: A Perturbation Approach

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The physics of a two-level system coupled to Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. Our main results are: The coherence-incoherence transition is at αc=1 2[1+Δᵣ/ωc]; for α<αc the dynamical quantity P(t)=(ω₀ t)(-γt); the sussceptibility χ′′(ω)/ω is of a double peak structure for α<αc and the Shiba's relation is exactly satisfied; at the transition point α=αc the real time correlation function C(t)≈ -1/γ²c t² in the long time limit.