Bai-Jun Zhang

Function photonic crystals

Abstract In this paper, we present a new kind of function photonic crystals (PCs), whose refractive index is a function of space position. Conventional PCs structure grows from two materials, A and B, with different dielectric constants e A and e B . Based on Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we give the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals, and we find the following: (1) For the vertical and non-vertical incidence light of function photonic crystals, there are band gap structures, and for only the vertical incidence light, the conventional PCs have band gap structures. (2) By choosing various refractive index distribution functions n(z), we can obtain more wider or more narrower band gap structure than conventional photonic crystals.

Finite Temperature Schrödinger Equation

We know Schrödinger equation describes the dynamics of quantum systems, which don’t include temperature. In this paper, we propose finite temperature Schrödinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shrödinger equation.

Quantum Wave Equation of Non-conservative System

It is well known that Schrödinger’s equation is only suitable for the particle in conservative force field. In atomic and molecular field, a particle can suffer the action of non-conservative force. In this paper, a new quantum wave equation is proposed, which can describe the particle in non-conservative force field. We think the new quantum wave equation can be used in many fields.

Quantum theory of light diffraction

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.

Quantum Theory of Electronic Multiple-Slit Diffraction

We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.

Quantum Theory of Atom Laser Cooling

In this paper, we study the laser cooling mechanisms with new Schrodinger quantum wave equation, which can describe a particle in conservative and non-conservative force field. We prove the atom in laser field can be cooled with the new theory, and predict that the atom cooling temperature T is directly proportional to the atom vibration frequency ω, which is in accordance with experiment result. PACS: 03.65.-w, 37.10.De, 37.10.Mn

Derivation of Nonlinear Schrödinger Equation

We propose some nonlinear Schrödinger equations by adding some higher order terms to the Lagrangian density of Schrödinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schrödinger equation is weak.

Dirac Equation at Finite Temperature

In this paper, we propose finite temperature Dirac equation, which can describe the quantum systems in an arbitrary temperature for a relativistic particle of spin-1/2. When the temperature T=0, it become Dirac equation. With the equation, we can study the relativistic quantum systems in an arbitrary temperature.

Non-factorization contributions in D → π K , K K decay

Abstract We have analyzed the D → π K , K K decay with the naive factorization (NF), QCD factorization (QCDF) and QCD factorization including soft-gluon exchanges ( QCDF + SGE ). In these decay channels, the soft-gluon effects are firstly calculated with light cone QCD sum rules. Comparing the three kind approaches, we can find the calculation results have made much more improved QCD factorization (QCDF) than the naive factorization (NF), and the calculation results have also made improved QCD factorization including soft-gluon exchanges ( QCDF + SGE ) than the QCD factorization (QCDF) in the color-suppressed decay channels. In addition, we find the soft-gluon effects are larger than the leading order contributions, and the calculation results are close to the experimental data for the color-suppressed decay channels. In color-allowed decay channel D 0 → π + K − , the soft-gluon effects are small and we should consider other power terms, such as final state interaction and annihilation effects.

QUANTUM THEORY OF NEUTRON DIFFRACTION

Phenomena of electron, neutron, atomic, and molecular diffraction have been studied in many experiments, and these experiments have been explained by some theoretical works. We study neutron single and double-slit diffraction with a new quantum mechanical approach. The calculation results are compared with the experimental data obtained with cold neutrons.