647,603 research outputs found

### 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

### 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

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