2008/06/30 by Frederico Brito, Amir O. Caldeira · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.mes-hall
paper · pdf · doi:10.1088/1367-2630/10/11/115014
published as New J. Phys. 10 (2008) 115014 · 12 pages, 2 figures; V2: Published version
arxiv created 2008/12/11 · arxiv updated 2009/12/01
We propose an approximation scheme to describe the dynamics of the spin-boson model when the spectral density of the environment shows a peak at a characteristic frequency Ω which can be very close (or even equal) to the spin Zeeman frequency Δ. Mapping the problem onto a two-state system (TSS) coupled to a harmonic oscillator (HO) with frequency ω0 we show that the representation of displaced HO states provides an appropriate basis to truncate the Hilbert space of the TSS-HO system and therefore a better picture of the system dynamics. We derive an effective Hamiltonian for the TSS-HO system, and show it furnishes a very good approximation for the system dynamics even when its two subsystems are moderately coupled. Finally, assuming the regime of weak HO-bath coupling and low temperatures, we are able to analytically evaluate the dissipative TSS dynamics.