Quantum Inequality for Negative Energy Density States of Massive Dirac Field in Four-Dimensional Spacetime

Negative energy density and the quantum inequality are examined for the Dirac field. A proof is given of the quantum inequality for negative energy densities in the massive Dirac field produced by the superposition of two single particle electron states.     

Restrictions on negative energy density for the Dirac field in flat spacetime

This paper investigates the quantum Dirac field in n+1-dimensional flat spacetime and derives a lower bound in the form of quantum inequality on the energy density averaged against spacetime sampling functions. The state-independent quantum inequality derived in the present paper is similar to the temporal quantum energy inequality and it is stronger for massive field than for massless one. It also presents the concrete results of the quantum inequality in 2 and 4-dimensional spacetimes.     

Atomic population oscillations between two coupled Bose——Einstein condensates with time-dependent nonlinear interaction

The atomic population oscillations between two Bose--Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.     

Relic Gravitational Waves and Trans-Planckian Physics

Assuming that the effects of trans-Planckian physics are encoded in the choice of initial conditions, mode by mode, for vacuum states at the time when its wavelength becomes equal to the scale of new physics （Planck＇s scale for example）, we calculate the spectrum of energy densities of total relic gravitational waves from de Sitter inflation to the matter dominated universe. Our results show that the spectrum acquires corrections due to the consideration of trans-Planckian physics and these corrections depend sensitively on the vacuum state that was actually realized at the beginning of the inflation.     

Vacuum polarization of scalar electrodynamics in flat space－time with nontrivial topology

The one-loop vacuum polarization is calculated for scalar electrodynamics in a flat space－time with the topology S¹×R³. The effect of vacuum polarization upon photon propagation is considered. It is found that photon propagation becomes anisotropic with some photon modes acquiring a positive topological mass and thus travelling at a subluminal speed.     

Inflationary dynamics in the braneworld scenarios

We analyze the attractor behaviour of the inflation field in braneworld scenarios using the Hamilton-Jacobi formalism, where the Friedmann equation has the form of H2 = ρ + ε(2ρ0ρ)~(1/2) or H2 = ρ + ερ2/2σ , with ε = ±1. We find that in all models the linear homogeneous perturbation can decay exponentially as the scalar field rolls down its potential. However, in the case of a -ρ2 correction to the standard cosmology with ρ σ , the existence of an attractor solution requires (σρ)/φ2 1. Our results show that the perturbation decays more quickly in models with positive-energy correction than in the standard cosmology, which is opposite to the case of negative-energy correction. Thus, the positive-energy modification rather than the negative one can assist the inflation and widen the range of initial conditions.     

电偶极子与单摆

电偶极子是电磁学基本模型之一,其电场强度分布颇有特点.通常教材要么给出电势然后做梯度计算,要么通过矢量叠加直接给出场强,推导比较数学化,学生难以对偶极子场强特点和物理图像获得直观理解.本文把熟知的力学单摆和偶极子联系起来,通过力电类比给出偶极子电场的两种形式,特别是不依赖坐标的场强形式,清楚阐明了各分量特点,还给出类比方法的应用实例.这种方法有助于初学者从不同角度体会知识点联系,深入理解偶极子物理图像,强化类比思维.     

Lower Bounds on Negative Energy Densities for the Scalar Field in Flat Spacetime

We obtain a lower bound on the spacetime-weighted average of the energy density for the scalar field in four-dimensional flat spacetime. The bound takes the form of a quantum inequality. The inequality does not rely on the quantum state and its form is only related to the weights, namely the spacetime sampling functions which are assumed to be smooth, positive and compactly supported. It is found that the inequality is just equal to the temporal quantum energy inequality. When the characteristic length of the temporal sampling function tends to zero, the lower bound becomes divergent. This is consistent with the fact that the spatial restriction on negative energy density does not exist in four-dimensional spacetime.     

Vacuum Polarization of Twisted Scalars in a Non—simply Connected Space—time and Its Effects

The vacuum polarization due to twisted scalar fields is investigated in a non-simply connected space-time,It is found that some photon modes acpuire an imaginary topological mass,thus travelling at a superluminal speed.Topological bi-refringence is expected for photons propagating perpendicularly to the compactification direction.The effect of a topological photom mass on the static properties of electromagnetic fields is also considered for the cases of both twisted and untwisted scalar fields,Our result shows that in the untwisted case the magnetic field is screened along the radial dirction for massive photon modes.while in the twisted case no screening occurs and the magnetic fields merely oscillate.     

Observational Constraints on the Unified Dark-Energy--Dark-Matter Model

We investigate the constraints on a generalized Chaplygin gas （GCG） model using the gold sample type-Ia supernovae （She Ia） data, the new Supernova Legacy Survey （SNLS） Sne Ia data and the size of baryonic acoustic oscillation peak found in Sloan Digital Sky Survey （SDSS）. In a spatially flat universe case we obtain, at a 95.4% confidence level, A8 = 0.76^＋0.07 -0.07 and α= 0.028^＋0.322 -0.2382 Our results are consistent with the ACDM model （α= 0）, but rule out the standard Chaplygin gas model （α= 1）.