函数创新型问题的探究策略

与新课改接轨,近几年来全国以及各省市的高考题都或多或少地出现一些我们从未见过的题,面对这些'挑战',有些学生不知所措,发挥不出自己的水平.笔者认为:'没见过不等于难,新题型不等于新方法.'本文就函数的一些创新型问题作一下透析.

Transport Properties of Two Coupled Quantum Dots Under Optical Pumping

Using the Keldysh-Green function,we present a theoretical study on the electron transport properties of two coupled quantum dots under optical pumping. Plateaus in the I-V curve and resonant peaks in the transmission coefficient occur and can be explained by the local electron density of states in the quantum dots. The effects of the optical pumping frequency and intensity on the transport properties of the system are also discussed. The electron dynamical localization phenomenon occurs when the optical pumping frequency is equal to the discrete hole energy level. This result can be used to realize optical control switches.

The Roughness of Model Function to the Basis Functions

The roughness of the model function f（x） to the basis functions has been identified. When the model function is continuous segment, its roughness does not depend on the behavior of the first segment, but depends on ＂h＂, the shift in the slope of two consecutive segments. If the distribution of design is uniform, f（x） is continuous segment function, and h is constant, then the maximum roughness is h2/192 obtained at the midpoint of the observations. Suppose that we have a sequence of designs {Pn（x）} then its corresponding distribution {Fn （x）} converges weakly to some distribution F（x）. Let D（f） be a set of discontinuous points off（x）, it is possible to take the limit of the roughness if D（f） has zero （dF）-measure. The behavior of maximum roughness of the discontinuous segment function has been studied by using grid points.

Heat Generation by Electric Current in Normal-Metal-Molecular Quantum Dot-Superconductor System

We investigate the heat generation induced by electrical current in a normal-metal-molecular quantum dot-superconductor （NDS） system. By using nonequilibrium Green＇s function method, the heat generation Q is derived and studied in detail. The superconducting lead influences the heat generation significantly. An obvious step appears in Q - eV characteristics and the iocation of this step is related with the phonon frequency ωo. The heat generations exhibit very different behaviour in the condition eV 〈 △ and eV 〉 △ due to different tunneling mechanism. From the study of Q - eVg curves, there is an extra peak as eV 〉 △. The difference in this two cases is also shown in Q - ωo curve, an extra peak emerges as eV 〉 △.

Splitting and Restoration of Kondo Peak in a Deformed Molecule Quantum Dot Coupled to Ferromagnetic Electrodes

We adopt the nonequilibrium Green＇s function method to theoretically study the Kondo effect in a deformed molecule, which is treated as an electron-phonon interaction （EPI） system. The self-energy for phonon part is calculated in the standard many-body diagrammatic expansion up to the second order in EPI strength. We find that the multiple phonon-assisted Kondo satellites arise besides the usual Kondo resonance. In the antiparallel magnetic configuration the splitting of main Kondo peak and phonon-assisted satellites only happen for asymmetrical dot-lead couplings, but it is free from the symmetry for the parallel magnetic configuration. The EPI strength and vibrational frequency can enhance the spin splitting of both main Kondo and satellites. It is shown that the suppressed zero-bias Kondo resonance can be restored by applying an external magnetic field, whose magnitude is dependent on the phononic effect remarkably. Although the asymmetry in tunnel coupling has no contribution to the restoration of spin splitting of Kondo peak, it can shrink the external field needed to switch tunneling magnetoresistance ratio between large negative dip and large positive peak.

Kondo Resonance Splitting in a Quantum Dot with Perpendicular Magnetic Fields

Using the nonequilibrium Green＇s function technique, we investigate the Kondo effect in the quantum dot with perpendicular magnetic fields, in which one is the Zeeman splitting lies in the z-direction and the other is the spin flip points at the x-direction. It is found whatever one or two magnetic fields are applied, the local density of states （LDOS） will split into two peaks. The positions of two Kondo resonance peaks are determined by Zeeman energy △ when J = 0, and by √△^2＋J^2 when J≠0.

Influences of a Side-Coupled Triple Quantum Dot on Kondo Transport Through a Quantum Dot

Kondo transport properties through a Kondo-type quantum dot （QD） with a side-coupled triple-QD structure are systematically investigated by using the non-equilibrium Green＇s function method. We firstly derive the formulae of the current, the linear conductance, the transmission coefficient, and the local density of states. Then we carry out the analytical and numerical studies and some universal conductance properties are obtained. It is shown that the number of the conductance valleys is intrinsically determined by the side-coupled QDs and at most equal to the number of the QDs included in the side-coupled structure in the asymmetric limit. In the process of forming the conductance valleys, the side-coupled QD system plays the dominant role while the couplings between the Kondo-type QD and the side-coupled structure play the subsidiary and indispensable roles. To testify the validity of the universal conductance properties, another different kinds of side-coupled triple-QD structures are considered. It should be emphasized that these universal properties axe applicable in understanding this kind of systems with arbitrary many-QD side structures.

Heat Generation by Electrical Current in Quantum Dot System with Fano Resonance

We study the heat generation in quantum dot system with Fano resonance by nonequilibrium Green＇s functions method. The Fano resonance influences the heat generation significantly. As increases, the heat generation decreases gradually. From the study of Q-eV curves, we llnd that the linewidth function F has huge influence on the heat generation. The Q-eV curves display obvious steps when the linewidth function is small. However, these steps disappear with F increasing. As the source-drain bias eV increases, the Q-eVg curves also display interesting behaviors.