摘要
We present mathematical analyses of the evolution of solutions of the self-consistent equation derived from variational calculations based on the displaced-oscillator-state and the displaced-squeezed-state in spin-boson model at a zero temperature and a finite temperature. It is shown that, for a given spectral function defined as J（w） = π∑k Ck^2 = π/2αw^8w^1-s, there exists a universal sc for both kinds of variational schemes, the localized transition happens only for 2 s ≤ sc, moreover, the localized transition is discontinuous for s 〈 sc while a continuous transition always occurs when s = sc. At T = 0, we have sc = 1, while for T ≠ 0, sc = 2 which indicates that the localized transition in super-Ohmic case still exists, manifesting that the result is in discrepancy with the existing result.
We present mathematical analyses of the evolution of solutions of the self-consistent equation derived from variational calculations based on the displaced-oscillator-state and the displaced-squeezed-state in spin-boson model at a zero temperature and a finite temperature. It is shown that, for a given spectral function defined as J（w） = π∑k Ck^2 = π/2αw^8w^1-s, there exists a universal sc for both kinds of variational schemes, the localized transition happens only for 2 s ≤ sc, moreover, the localized transition is discontinuous for s 〈 sc while a continuous transition always occurs when s = sc. At T = 0, we have sc = 1, while for T ≠ 0, sc = 2 which indicates that the localized transition in super-Ohmic case still exists, manifesting that the result is in discrepancy with the existing result.
基金
supported by the National Natural Science Foundation of China (Grant No 10575045)
