The quantum transport in a narrow channel (NC) is studied in the presence of a time-dependent delta-profile electric field. The electric field is taken to be transversely polarized, with frequency ω, causing inter-subband and inter-sideband transitions. Suppression in the dc conductance G is found, which escalates with the chemical potential. There are structures in G which are related to the quasi-bound states (QBS) features. Major dip, and dip-and-peak, structures occur when an incident electron makes transition to a subband edge by absorbing or emitting one, and two,hω, respectively. Structures associated with threehω processes are recognized. The QBS are closely associated with the singular density of states (DOS) at subband bottoms. Our results indicate that, due to this singular features of the DOS, the interaction of the electron with the electric field has to be treated beyond finite order perturbation.PACS numbers: 72.10. -d, 72.40.+w, 73.35. Quantum transport in NC has received a lot of attention in recent years. These channels can be realized experimentally within a split-gate configuration. 1,2 The channels connect adiabatically on each side to a twodimensional electron gas. Energy levels of the channels are quantized into one-dimensional subbands which give rise, in the ballistic regime, to a quantized G. 1,2 The singular feature of the DOS near a subband edge leads to impurity-induced dip structures in G when the scatterer is attractive. 3,4,5,6,7,8,9 These dip structures are associated with the formation of impurity-induced QBS. 4 More recently, there are growing interest in the timedependent phenomena in quantum point contact (QPC) systems. 10,11,12,13,14,15 Firstly, the optical absorption coefficient of a QPC has been calculated 10 , up to secondorder in the electron-photon coupling, and a proposal is made that the optical absorption in the QPC can be used to characterize the lateral confining potential of the QPC. Secondly, the photon-assisted quantum transport in QPC systems 11,12,13,14,15 has been studied while ministeps are predicted to appear in G versus µ. 12 On the other hand, QBS features are found in G when a point barrier oscillates in a narrow channel. 16 These features, that the dc conductance G exhibits dip, or peak structures when the chemical potential µ is at nhω above the threshold energy of a subband, persists even in the case of a finite-range oscillating barrier, including the case when the barrier range a ≫ λ F . 17 The oscillating barrier is uniform in the transverse direction and does not induce inter-subband transitions. However, the presence of the oscillating barrier, as long as it has a longitudinal profile, breaks the longitudinal translational invariance. Thus the electrons are relieved from conserving the longitudinal momentum, making the inter-sideband transitions possible. The sideband index n labels those electrons which net energy change is nhω, as a result of interacting with the oscillating barrier. The physical origin of these QBS, as pointed out by Bagwell...
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