在一個部份相干且由變化磁通量推動的環中能量散逸的研究

Abstract

我們研究被隨時間成線性增加的磁通量穿透的中觀環。這環是部分同調以致環中之傳導電子將遭遇非同調之散射。除此之外，我們也考慮由於環中含有雜質，導致電子受到彈性散射對這中觀環的影響。在這種和時間有關得情形下，我們採取由Buttiker提出的散設矩陣模型，去處理不同調散射。這使得我們可以在相同的立足點，同等處理不同調散射、彈性散射和同調非彈性過程。我們精確解決了隨時間變化的磁通量，導致同調非彈性過程這個問題。我們的結果清楚說明了： 1. 當沒有雜質時，從非同調散射射出的電子中，能量愈低的，它們對感 應電流之直流成份貢獻愈大。 2. 當有雜質時， (a) 在弱雜質情形時，從非同調散射射出的電子中，能量愈低的，它們對感應電流之直流成份貢獻愈大，就像沒有雜質的情形。 (b) 但在強雜質情形時，當化學位增加時，感應電流之直流成份在零和非零區交替出現，其在非零區之峰值隨化學位增加而增加。我們發現零和非零區分別對應到一維能帶結構□的能隙和能帶。這些特性之所以如此，是因為電子環繞這環時，它的能量會漸漸偏移直至它碰到禁帶－在那裡它將遭到全反射。這種全反射並不會發生在固定磁通量的環中。因此，在部份同調的環中，有關散逸的的研究，我們的結果包含了非緩變效應。我們同時也探討了介於強弱雜質之中間範疇非緩變特色的漸次發展行為。

We have studied a mesoscopic ring threaded by a magnetic flux that increases linearly with time. The ring is partially coherent such that conduction electrons in the ring will encounter incoherent scatterings. Besides, we have also considered the behavior of the ring when the electrons encounter elastic scatterings due to the presence of an impurity in the ring. We have adopted a S-matrix model, as proposed by Buttiker, for the incoherent scatterings in this time-dependent situation. This allows us to treat the incoherent scatterings, the elastic scatterings and the coherent inelastic processes on the same footing. We have solved exactly the problem that the coherent inelastic processes caused by the time-varying magnetic flux. Our results demonstrate unequivocally that, 1.When there is no impurity, for the electrons emanating out of incoherent scatterings, the lower the energies of these electrons, the greater will be their net contribution to the dc component of the induced current. 2. When there is an impurity : (a)In the case of a weak impurity, the lower the energies of the electrons that emanate out of incoherent scatterings, the greater will be their net contribution to the dc component I_{dc} of the induced current just like the situation of no impurity. (b)In the case of a strong impurity, however, I_{dc} alternates between regions of zero and nonzero values as the chemical potential \mu increases. The peak value of I_{dc} in the nonzero region increases with \mu. We find that these regions of zero I_{dc}, and nonzero I_{dc}, correspond closely with the gaps, and the bands, respectively, of a one dimensional energy band. These characteristics arise from the fact that the electrons traversing the ring have their {\it energies} shifted gradually until their {\it energies} fall upon a forbidden region, where they suffer total reflection. This kind of total reflection does not occur in a ring with a constant flux. Our results thus contain the nonadiabatic effects of the changing flux on the dissipation in a partially coherent ring. The evolution of these nonadiabatic features in the intermediate impurity regime is also investigated.