Grand canonical partition function of a serial metallic island system

We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described using Grassmann numbers. The Coulomb charging energy of the system is represented in terms of phase fields conjugate to the island charges. By the large channel approximation, the tunneling action phase dependence can also be determined explicitly. Therefore, we represent the partition function as a path integral over phase fields with a path probability given in an analytically known effective action functional. Using the result, we also propose a calculation of the average electron number of the serial island system in terms of the expectation value of winding numbers. Finally, as an example, we describe the Coulomb blockade effect in the two-island system by the average electron number and propose a method to construct the quantum stability diagram.

Influence of the Distance between Focusing Lens and Target Surface on the Characteristics of Laser-excited Lead Plasma

The present work investigated the effect of distance from target surface on the parameters of lead plasma excited by 1064nm Q-switched Nd:YAG laser. The excitation was conducted in air, at atmospheric pressure, with pulse length of 5 ns, and at different pulse laser energies. Electron temperature was calculated by Boltzmann plot method based on the PbI emission spectral lines (369.03 nm, 416.98 nm, 523.48, and 561.94 nm). The PbI lines were recorded at different distances from the target surface at laser pulse energies of 260 and 280 mJ. The emission intensity of plasma increased with increasing the lens-to-target distance. The results also detected an increase in electron temperature with increasing the distance between the focal lens and the surface of the target in all laser energies under study. In addition, the electron number density was determined by using the Stark broadening method. The data illustrated that the electron number density was increased with increasing the distance from target surface, reaching the maximum at a distance of 11 cm for all pulse laser energy levels under study.

Measurements of electron number density and temperature in a supersonic plasma jet by optical emission spectroscopy

The results of experimental studies of the shock-wave region of the supersonic plasma jet flow formed by a pulsed capillary discharge with a polymeric wall are presented. Using optical emission spectroscopy of high spatial resolution, a detailed picture of the evolution of the radial profiles of the electron number density and temperature along the initial section of an underexpanded plasma jet, starting from the capillary outlet and ending with the flow stagnation zone, has been obtained. It was found that the profiles of the electron number density and temperature reflect all the features of the shock-wave flow region, tracing the influence of intercepting, central and reflected shock waves.

The Model of Multi Limits of the Quantity of Electrons in Central Coulomb force Field

Based on the theory of periodic bifurcation of iterative equation, a conjectural model of periodic bifurcation of number of electrons in a central Coulomb force field is proposed. After that with the help of the methods Zeng’s The Course of Quantum Mechanics and Wu’s Methods of Mathematical Physics, [1], [2] the wave function of the electrons under the approximate state is solved in the central Coulomb force field. By using the method of separating variables for solving partial differential equations and some transformation and construction techniques, the strict mathematical solution of the Schrödinger equation for the electron in the field of central Coulomb force is obtained, and the iterative formula of the level of electron number is given theoretically. And using MATLAB, the multi-limit model of electron number is simulated under different initial value problems, to explore the change of the limit with the initial value and the factors affecting the limit number to a certain extent. Some potential research value of this model is also proposed.

Effective π-electron number and Symmetry Perturbation Effect on the Two-photon Absorption of Oligofluorenes

Fluorene-based molecules present significant nonlinear optical responses, multiphoton absorption in the visible, which, combined with the high fluorescence quantum yield in organic solvents, could make this class of materials potentially...