Mechanism of Gravity Impulse

It is well-known that energy-momentum is the source of gravitational field. For a long time, it is generally believed that only stars with huge masses can generate strong gravitational field. Based on the unified theory of gravitational interactions and electromagnetic interactions, a new mechanism of the generation of gravitational field is studied. According to this mechanism, in some special conditions, electromagnetic energy can be directly converted into gravitational energy, and strong gravitational field can be generated without massive stars. Gravity impulse found in experiments is generated by this mechanism.Comment: 10 page

Ballistic transport: A view from the quantum theory of motion

Ballistic transport of electrons through a quantum wire with a constriction is studied in terms of Bohm's interpretation of quantum mechanics, in which the concept of a particle orbit is permitted. The classical bouncing ball trajectories, which justify the name ``ballistic transport'', are established in the large wave number limit. The formation and the vital role of quantum vortices is investigated.Comment: 14 pages, revtex, 4 postscript figure

Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems

In a recent paper, wavelet analysis was used to perturb the coupling matrix in an array of identical chaotic systems in order to improve its synchronization. As the synchronization criterion is determined by the second smallest eigenvalue $\lambda_2$ of the coupling matrix, the problem is equivalent to studying how $\lambda_2$ of the coupling matrix changes with perturbation. In the aforementioned paper, a small percentage of the wavelet coefficients are modified. However, this result in a perturbed matrix where every element is modified and nonzero. The purpose of this paper is to present some results on the change of $\lambda_2$ due to perturbation. In particular, we show that as the number of systems $n \to \infty$, perturbations which only add local coupling will not change $\lambda_2$. On the other hand, we show that there exists perturbations which affect an arbitrarily small percentage of matrix elements, each of which is changed by an arbitrarily small amount and yet can make $\lambda_2$ arbitrarily large. These results give conditions on what the perturbation should be in order to improve the synchronizability in an array of coupled chaotic systems. This analysis allows us to prove and explain some of the synchronization phenomena observed in a recently studied network where random coupling are added to a locally connected array. Finally we classify various classes of coupling matrices such as small world networks and scale free networks according to their synchronizability in the limit.Comment: 7 pages, 2 figures, 1 tabl

When Locally Linear Embedding Hits Boundary

Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. Particularly, LLE converges to a mixed-type differential operator with degeneracy. This study leads to an alternative boundary detection algorithm and two potential approaches to recover the Dirichlet Laplace-Beltrami operator.Comment: 11 Figure

Non-disturbance criteria of quantum measurements

Using the general sequential product proposed by Shen and Wu in [J. Phys. A: Math. Theor. 42, 345203, 2009], we derive three criteria for describing non-disturbance between quantum measurements that may be unsharp with such new sequential products, which generalizes Gudder's results

Non-Relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in earth's gravitational field may form a gravitationally bound quantized state, which had already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are discussed in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.Comment: 12 pages, no figur