arXiv subjects

Xiao-Jing Liu

Publications and source records attributed to Xiao-Jing Liu.

At least 55 records · Page 3Linked to original sources

arXiv2013

Quantum theory of light double-slit diffraction

In this paper, we study the light double-slit diffraction experiment with quantum theory approach. Firstly, we calculate the light wave function in slits by quantum theory of photon. Secondly, we calculate the diffraction wave function with Kirchhoff's law. Thirdly, we give the diffraction intensity of light double-slit diffraction, which is proportional to the square of diffraction wave function. Finally, we compare calculation result of quantum theory and classical electromagnetic theory with the experimental data. We find the quantum calculate result is accordance with the experiment data, and the classical calculation result with certain deviation. So, the quantum theory is more accurately approach for studying light diffraction.

quant-ph↗

arXiv2013

Full Quantum Theory of ${C_{60}}$ Double-slit Diffraction

In this paper, we apply the full new method of quantum theory to study the double-slit diffraction of ${C_{60}}$ molecules. We calculate the double-slit wave functions of ${C_{60}}$ molecules by Schrödinger equation, and calculate the diffraction wave function behind the slits with the Feynman path integral quantum theory, and then give the relation between the diffraction intensity of double-slit and diffraction pattern position. We compare the calculation results with two different double-slit diffraction experiments. When the decoherence effects are considered, the calculation results are in good agreement with the two experimental data.

quant-ph↗

arXiv2012

Spinor wave equation of photon

In this paper, we give the spinor wave equations of free and unfree photon, which are the differential equation of space-time one order. For the free photon, the spinor wave equations are covariant, and the spinors $ψ$ are corresponding to the the reducibility representations $D^{10}+D^{01}$ and $D^{10}+D^{01}+D^{1/2 1/2}$ of the proper Lorentz group.

physics.gen-ph↗

arXiv2012

Non-relativistic quantum theory at finite temperature

We propose the non-relativistic finite temperature quantum wave equations for a single particle and multiple particles. We give the relation between energy eigenvalues, eigenfunctions, transition frequency and temperature, and obtain some results: (1) when the degeneracies of two energy levels are same, the transition frequency between the two energy levels is unchanged when the temperature is changed. (2) When the degeneracies of two energy levels are different, the variance of transition frequency at two energy levels is direct proportion to temperature difference.

quant-ph↗

arXiv2012

The effect of defect layer on transmissivity and light field distribution in general function photonic crystals

We have theoretically investigated a general function photonic crystals (GFPCs) with defect layer, and choose the line refractive index function for two mediums $A$ and $B$, and analyze the effect of defect layer's position, refractive indexes and period numbers on the transmission intensity and the electric field distribution. We obtain some new characters that are different from the conventional PCs, which should be helpful in the design of photonic crystals.

physics.optics↗

arXiv2012

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.

quant-ph↗

arXiv2012

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.

physics.gen-ph↗

arXiv2012

Function Photonic Crystals

In the paper, we present a new kind of function photonic crystals, which refractive index is a function of space position. Unlike conventional PCs, which structure grow from two materials, A and B, with different dielectric constants $ε_{A}$ and $ε_{B}$. By 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 study the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals. By choosing various refractive index distribution function $n(z)$, we can obtain more width or more narrow band gap structure than conventional photonic crystals.

physics.gen-ph↗

arXiv2012

A study on quantum mechanical approach for $C_{60}$ diffraction analysis

Diffraction phenomena of large molecules have been studied in many experiments, and these experiments are described by many theoretical works. In this paper, we study $C_{60}$ molecules single and double-slit diffraction with quantum theory approach, and we pay close attention to the $C_{60}$ diffraction experiment carried out by A.Zeilinger et.at in 1999. In double-slit diffraction, we consider the decoherence effect, and find the theoretical results are good agreement with experimental data.

quant-ph↗

arXiv2012

Transmission Character of General Function Photonic Crystals

In the paper, we present a new general function photonic crystals (GFPCs), which refractive index of medium is a arbitrary function of space position. Unlike conventional photonic crystals (PCs), which structure grow from two mediums $A$ and $B$, with different constant refractive indexes $n_{a}$ and $n_{b}$. Based on Fermat principle, we give the motion equations of light in one-dimensional GFPCs, and calculate its transfer matrix, which is different from the conventional PCs. We choose the linearity refractive index function for two mediums $A$ and $B$, and find the transmissivity of one-dimensional GFPCs can be much larger or smaller than 1 for different slope linearity refractive index function, which is different from the transmissivity of conventional PCs (its transmissivity is in the range of 0 and 1). Otherwise, we study the effect of different incident angles, the number of periods and optical thickness on the transmissivity, and obtain some new results different from the conventional PCs.

physics.optics↗

arXiv2012

Light field distribution of general function photonic crystals

In this paper, We have presented a new general function photonic crystals (GFPCs), which refractive indexes are line functions of space position in two mediums $A$ and $B$, and obtain new results: (1) when the line function of refractive indexes is up or down, the transmissivity can be far larger or smaller than 1. (2) when the refractive indexes function increase or decrease along the direction of incident light, the light intensity should be magnified or weaken, which can be made optical magnifier or attenuator. (3) The GFPCs can be made optical diode when the light positive and negative incident the GFPCs.

physics.optics↗

arXiv2012

Schrödinger equation of general potential

It is well known that the Schrödinger equation is only suitable for the particle in common potential $V(\vec{r},t)$. In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave equation can describe the particle which is in general potential $V(\vec{r}, \dot{\vec{r}}, t)$. We think these new quantum wave equations can be applied in many fields.

quant-ph↗

arXiv2012

An optical diode and magnifier from a general function photonic crystals

We have presented a new general function photonic crystals (GFPCs), which refractive index is a function of space position. Based on Fermat principle, we achieve the motion equations of light in one-dimensional general function photonic crystals, and calculate its transfer matrix. In this paper, we choose the line refractive index function for two mediums $A$ and $B$, and obtain new results: (1) when the line function of refractive indexes is up or down, the transmissivity can be far larger or smaller than 1. (2) when the refractive indexes function increase or decrease at the direction of incident light, the light intensity should be magnified or weaken, which can be made light magnifier or attenuator. (3) The GFPCs can also be made optical diode. The new general function photonic crystals can be applied to design more optical instruments.

physics.optics↗

arXiv2012

Quantum theory of two-photon interference

In this paper, we study two-photon interference with the approach of photon quantum theory, with specific attention to the two-photon interference experiment carried out by Milena D'Angelo et al. (Phys. Rev. Lett 87:013602, 2001). We find the theoretical result is accordance with experiment data.

quant-ph↗

arXiv2011

Special Theory for Superluminal Particle

The OPERA collaboration reported evidence for muonic neutrinos travelling faster than light in vacuum. In this paper, an extended relativity theory is proposed. We think all particles can be divided into three kinds: The first kind of particle is its velocity in the range of $0\leq v < c$, e.g. electron, atom, molecule and so on ($c$ is light velocity, i.e., the limit velocity of the first kind of particle). The second kind of particle is its velocity in the range of $0\leq v < c_{m1}$, e.g. photon ($c_{m1}$ is the limit velocity of the second kind of particle). The third kind of particle is its velocity in the range of $c\leq v < c_{m2}$, e.g. tachyon, and muonic neutrinos ($c_{m2}$ is the limit velocity of the third kind of particle). The first kind of particle is described by the special relativity. With the extended relativity theory, we can describe the second and third kinds particles, and can analysis the OPERA experiment results and calculate the muonic neutrinos mass.

physics.gen-ph↗

arXiv2011

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.

physics.gen-ph↗

arXiv2011

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.

math-ph↗

arXiv2011

Quantum Theory Approach for Neutron Single and Double-Slit Diffraction

We provide a quantum approach description of neutron single and double-slit diffraction, with specific attention to the cold neutron diffraction ($λ\approx 20$Å) carried out by Zeilinger et al. in 1988. We find the theoretical results are good agreement with experimental data.

quant-ph↗