A note on localized transition in the spin-boson model by variational calculation

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(ω)= π∑k c2k = π/2 αωsω1s c ,there exists a universal s c for both kinds of variational schemes,the localized transition happens only for s ≤ sc ,moreover,the localized transition is discontinuous for s