The Influence Of Temperature On Quantum Tunneling In Spin-boson Model

The effect of temperature on quantum tunneling is an important issue in spin-boson model. In the present thesis,following the pioneer work by Silbey and Harris[R.Silbey and R.A.Harris, J.Chem.Phys.80,2615(1984)],we study this issue by employing two different variational calculations,i.e.,variational calculation based on displaced-oscillator-state(DOS) and variational calculation based on displaced-oscillator-state(DSS).Variational calculation based on DOS shows that,for both Ohmic and sub-Ohmic cases,tunneling splitting increases with temperature in low temperature regions.It is found that,Δ(T)∝T^1+s,here s=1 and 0＜s＜1 represent respectively the Ohmic and sub-Ohmic case.It turns out that,the dressing factor of the frequency modes with frequency(κ_BT＜ω＜Δ) decreases with increasing temperature,leading to the increase of tunneling splitting with temperature.On the other hand,variational calculation based on DSS tells that,for both Ohmic and sub-Ohmic cases,tunneling splitting decreases with increasing temperature in low temperature regions.It is found that,Δ(T)∝1-αT^(n+s)/2,here a＞0 and n is the degree of dimension of the phonon bath in the long wave approximation.In order to find out the origin of different temperature dependence,we also make variational calculation for the single mode case.It tums out that,for phonon modes with with frequency(κ_BT＜ω＜Δ), tunneling splitting of the DSS ground state shows opposite temperature dependence to that of the DOS ground state,leading to a different temperature dependence in multi-mode case.Since the DSS ground state is stable in the strong coupling regime,the present result indicates that temperature dependence on tunneling splitting in weak coupling regime is different from that in strong coupling regime.