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The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems. On this basis, we have given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, we have given the generalized Hamiltonian function for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics.

The optical bistability have been studied theoretically in a multi-mode optomechanical system with two mechanical oscillators independently coupled to two cavities in addition to direct tunnel coupling between cavities. It is proved that the bistable behavior of mean intracavity photon number in the right cavity can be tuned by adjusting the strength of the pump laser beam driving the left cavity. And the mean intracavity photon number is relatively larger in the red sideband regime than that in the blue sideband regime. Moreover, we have shown that the double optical bistability of intracavity photon in the right cavity and the two steady-state positions of mechanical resonators can be observed when the control field power is increased to a critical value. Besides, the critical values for observing bistability and double bistability can be tuned by adjusting the coupling coefficient between two cavities and the coupling rates between cavities mode and mechanical mode.

In this paper, we have firstly proposed a new one-dimensional varied-time photonic crystals, i.e., the refractive indices of media $A$ and $B$ are the time functions. We consider the varied-time photonic crystals of refractive indices period variation and calculate the transmissivity and electronic field distribution with and without defect layer, which are different from the conventional photonic crystals, which transmissivity and electronic field distribution are static, but the varied-time photonic crystals transmissivity and electronic field distribution are dynamic. We have obtained some new results for the varied-time photonic crystals, which should be help to design new type dynamic optical devices, such as the accurate optical switch and so on., Comment: There are errors in Fig. 8

In this paper, we have studied the quantum transmission characteristics of one-dimensional photonic crystal with and without defect layer by the quantum theory approach, and compared the calculation results of classical with quantum theory. We have found some new quantum effects in the one-dimensional photonic crystal. When the incident angle $\theta=0$, there is no quantum effect. When the incident angle $\theta\neq0$, we find there are obvious quantum effect with the incident angle increase. At the incident angle $\theta\neq0$, there are also quantum effect with the change of thickness and refractive indexes of medium $B$ or $A$. We think the new quantum effect of photonic crystal shall help us to design optical devices.

In this paper, we have given the symmetrical and antisymmetrical spin and space wave functions of three-electron, and further given the full total entanglement states for the three-electron, which are related to their space and spin wave function. When we study particles entanglement we not only consider their spin entanglement and also consider their space entanglement. Otherwise, we find that electrons entanglement are restricted to the teeny range, when electrons exceed the space range, their entanglement should be broken down even disappearance, which is accordance with the experiments results.

In this paper, we have given the spin states of two-photon, which are expressed by the quadratic combination of two single photon spin states, they are a kind of quantum expression. Otherwise, we give all entanglement states of two-photon, which are different from the xanzsd classical polarization vector expression of two-photon entanglement state., Comment: arXiv admin note: text overlap with arXiv:1303.3406 by other authors

In this paper, we have proposed the spiron equation of free and non-free photon, and give the spin operator and spin wave function of photon. We calculate the helicity of photon and prove there are left-handed and right-handed photon. By the spiron equation of non-free photon, we can study the quantum property of photon in medium, which can be used in quantum optics, photonic crystals and so on.

In this paper, we have proposed $SU(2)$ non-Abelian electromagnetism gauge theory. In the theory, photon has self-interaction and interaction, which can explain photon entanglement phenomenon in quantum information. Otherwise, we find there are three kinds photons $\gamma^{+}$, $\gamma^{-}$ and $\gamma^{0}$, and they have electric charge $+e_{\gamma}$, $-e_{\gamma}$ and $0$, respectively, which are accordance with some experiment results., Comment: arXiv admin note: text overlap with arXiv:1310.4610 by other authors