A Study On The Temperature Effect In Nano-electromechanical System(NEMS)

With the criterion reduces to the nano-scale,some macroscopic properties of objects will change,and there will be some new characteristics.In NEMS,the nano-structure will have some new effects,such as quantum effects,interface effects and effects of the nanometer scale and so on.For the development of NEMS,the in-depth study of the new nature is the key.But in those new effects,the temperature is always a crucial factor. Therefore,in this article we study the temperature effect of NEMS,that is,the impact of the temperature on split tunneling.First of all,we introduce the physical model of NEMS,that is,the single-mode situation of the spin-boson model.Through carrying on the strict numerical solution to the model,we obtain the tunneling splitting along with temperature changes.The results show that:as the temperature rose,split tunneling is decline first and then rise,and there exists a temperature change point T_t in the middle.In addition,we also give the results of the adiabatic approximation,used for the comparison to the strict numerical solution, in order to determine the applicable conditions of the adiabatic approximation.Second,we use the small-polaron theory to analyze the single-mode sitiuation.According to small-polaron theory,split tunneling is composed of two parts:Diagonal transition and non-diagonal transitions.On one hand,the tunneling splitting caused by diagonal transition drops along with the rising temperature and can only exist in the weak coupling region.On the other hand,the tunneling splitting caused by non-diagonal transition rises along with increasing temperature,and becomes the major contribution part only when the coupling strength is strong.Thus,in low-temperature weak-coupling region,diagonal transition is the main contributor to the split tunneling;in the strong coupling Region,the diagonal contribution is to be suppressed,non-diagonal transition becomes the main contribution part of the split tunneling;When the coupling strength tends to the middle value,the split tunneling presents a coherent-incoherent changes along with the rising temperature.Therefore,we use the small polaron theory to analyze temperature transition point T_t which generated by the strict numerical solution, and we discover that small-polaron analytical solution and rigorous numerical solution have consistent trend with the temperature changes.Therefore,small-polaron theory can give a good analysis to the spin-boson model.At the same time,we also analyze the reasons for the deviation between small-polaron analytical solution and strict numerical solution.Finally,we extend to the multi-mode case by the single-mode case(i.e.spin-boson model).According to the influence functional theory,the entire system phonon tunneling splitting can be expressed as the simple product of the tunneling splitting of each single-mode case,so we can get the system's tunneling splitting trends as a function of temperature.We use a two-mode case as a simple test to confirm the effectiveness of this assumption of simple Product.The results show that:In the weak-coupling region,the impact of all the phonon mode on the two-level tunneling splitting is the same,that is, coupling to any phonon will suppress the tunneling splitting,so the total system's tunneling splitting has suppress effect with the rising temperature.This result indicated that in the sub-ohm,the ohm,ultra-ohm situation,the tunneling splitting decreases along with the increasing temperature.But in the strong-coupling region,split tunneling presents the opposite temperature effect phenomenon.Therefore,in the spin-boson model,the tunneling splitting as a function of temperature is first decreased and then increased,and this is our innovation of this paper.