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The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonic oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoscopic circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schr?dinger equation of the system is a four-order difference equation in representation. Using the extended perturbative method, the detail energy spectrum and wave functions are obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopic circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.

The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior: conductance oscillations. In this paper, using an improved quantum theory to mesoscopic circuits developed recently by Li and Chen, the mesoscopic electron resonator is quantized based on the fundamental fact that the electric charge takes discrete value. With presentation transformation and unitary transformation, the Schrodinger equation becomes an standard Mathieu equation. Then, the detailed energy spectrum and wave functions in the system are obtained, which will be helpful to the observation of other characters of electron resonator. The average of currents and square of the current are calculated, the results show the existence of the current fluctuation, which causes the noise in the circuits, the influence of inductance to the noise is discussed. With the results achieved, the stability characters of mesoscopic electron resonator are studied firstly, these works would be benefit to the design and control of integrate circuit.

Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrodinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrodinger equation can be divided into two Mathieu equations in representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.

We present a study of associated ηc and γ double diffractive production in p-p collision based on Ingelman-Schlein model, and the framework of non-relativistic QCD factorization formalism for quarkonia production. The predic-tion of ηc and γ is more reliable than J/ψ production, because the associated ηc and γ production is a pure color-octetprocess, and the dominant contribution comes from color octet 1So(8) subprocess, which is related to the color octet matrixelement of 1So(8) of J/ψ by the heavy quark spin symmetry and the large PT J/ψ production data. We find that the ratioof diffractive to inclusive cross sections is independent of the values of color octet matrix elements, but is sensitive to thegluon factor of the Pomeron and renormalized Pomeron flux factors. So experimental measurement of this ratio can giveus more information of the nature of Pomeron and test the assumption of hard diffractive factorization in hadron-hadron collisions.

Using three sets of Pomeron structure functions, the cross sections of J/ψ and γ associated production via resolved photon and proton diffractive scatting in ep collision are investigated. It is found that the cross sections calculated with various gluon distribution functions of Pomeron are different. The discrepancy is about 1.8 times for differential cross sections and 1.7 times for total cross sections. The experimental studies of the process could give valuable insight in the diffractive production mechanism and test the color-octet mechanism for heavy quarkonium production in a new environment.

The extended x-rescaling model can explain the quark's nuclear effect very well. Weather it can also explain the gluon's nuclear effect should be investigated further. Associated J/ψ and γ production with large PT is a very clean channel to probe the gluon distribution in proton or nucleus. In this paper, using the extended x-rescaling model, the PT distribution of the nuclear effect factors of process is calculated and discussed. Comparing our theoretical results with the future experimental data, the extended x-rescaling model can be examined.

We present a study of $J/��+ jet$ diffractive production in the direct photon process at HERA based on the factorization theorem for lepton-induced hard diffractive scattering and the factorization formalism of the nonrelativistic QCD (NRQCD) for quarkonia production. Using the diffractive gluon distribution function extracted from HERA data on diffractive deep inelastic scattering and diffractive dijet photon production, we show that this process can be studied at HERA with present integrated luminosity, and can give valuable insights in the color-octet mechanism for heavy quarkonia production., Revtex, 21 pages, 7 EPS figures

Based on the character in which both the intermediate and final states are intimately related with the vacuum properties of strong-interactions,we have discussed from an alternative point of view the processes of both the radiative production of glueball and the annihilation into electron-positron pair in J/ψ decays.Using the modified field theory model of pomeron in high-energy soft strong processes and the consequent hypothesis of the maximum non-perturbative strong interaction as well as the relevant changes of parameters of the model connecting with the large inner-structure difference between light and heavy constituent quarks,we proposed another mechanism for these two decay processes and calculated their partial width.The coupling constant between the glueballs and the non-perturbative gluons has been estimated.