We discuss the capacitance of a coherent mesoscopic parallel-plate capacitor based on the self-consistent theory of dynamic response for mesoscopic systems. The results show that the capacitance is a complex function of frequency which is strongly dependent on the frequency of the external field. The capacitance-frequency curve shows a significant characteristic that a peak in the imaginary part of the capacitance corresponds to the minimum in the real part, and further study shows that they are related to a plasmon-like excitation. In addition,we discuss the size effect of the capacitor, and find that the capacitance approaches geometric capacitance when the distance between two plates of the capacitor is very large.

Using a three dimensional-quasi-one dimensional-three dimensional model to depict the point contact between a scanning tunneling microscope tip and a metal crystal, by indenting the tip into a metal surface and then withdrawing we have studied the electron transport properties of the microstructure. By means of the single electron approximation and the transfer matrix method, we solve the Schr?dinger equation for this three dimensional system, and calculate the variation regularity of its conductance by quantum mechanics method. The variation of the conductance with constricting and stretching of the constriction is studied, and the quantization of the conductance in units of 2e2/h and 2×2e2/h are obtained.

In order to study the role of contacts in the coherent transport of mesoscopic structure systems, a 2D-1D-2D model of nano-sized single-barrier system is considered, which includes a single-barrier structure conductor with two reservoirs. Basing on the scattering-matrix method and the Thomas-Fermi approximation, we have calculated the transmission probability and the distribution of internal potential when a dc voltage is applied to the system. The results show that: (1) the contacts can produce significant effects on the transmission probability; (2) the behaviors of conductance and the distribution of internal potential differ from the usual transport conductance give by the Kirchhoff's laws. Therefore we conclude that since contacts and the mesocopic systems are quantum coherent, the role of contacts is important for in-depth investigation of the transport in mesoscopic systems.

Plasmonic excitations in mesoscopic-sized atomic chains are investigated by employing the tight-binding model. Based on the quantum response theory and random phase approximation, a plasma oscillation eigen-frequency equation is derived for calculation of the plasmon energy spectrum. The plasmon energy spectrum has been numerically calculated, and the eigen-oscillation of the system and the resonance behavior under the external electric field applied on the atom chain are investigated, respectively. Dependence of plasmonic excitation energy on the length of systems and electron density has been discussed. Results suggest that in the case of resonance, the resonant peak of dipole moment is corresponding to the plasmonic excitation, and this indicates that the external electric field excites the plasmon of the system. In resonance the oscillation amplitude of the charge is much larger than that in the case of non-resonance, especially the imaginary part of the charge has a more obvious enhancement. For the eigen-oscillations, the plasmonic excitation energy is greater than the single-particle excitation state at the same level; the length of atomic chains, the electron density, and the strength of Coulomb correlation have significant effects on the plasmon spectroscopy. For the given atom-chain length, with variation of number of electrons, the plasmonic excitation energy varies symmetrically around the half-filling. This indicates that the plasmon spectrum of the system is symmetrical for the electrons and holes.

In recent years considerable attention is being paid to the blue-shift of photoluminescence due to quantum confinement in the nanostructure. By employing two simple models of one-dimensional crystal potential，we study the electronic energy spectra and confinement energies by solving the Schrdinger equation for the models. Based on the calculation of the confinement energies in the nanostructures，the size- and potential-dependence of the confinement energy and the blue shift are investigated. The results suggest that: with creasing size of the system the energy of electrons at the bottom of the conduction band decreases，but increases at the top of the valence band. Therefore，the confinement energies increased abruptly as the size of nano-particle (or nanostructures) decreases. Meanwhile，our results for the confinement energies show obvious difference from the ones calculated by the effective-mass approximation of ten used in the literature. Moreover，we also find that the band gap and blue shift depend on the crystal potential in the systems，and the confinement energies decrease as the potential increases.