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

Electronic structures of [001]- and [111]-oriented InSb and GaSb free-standing nanowires

We report on a theoretical study of the electronic structures of InSb and GaSb nanowires oriented along the [001] and [111] crystallographic directions. The nanowires are described by atomistic, spin-orbit inteaction included, tight-binding models, and the band structures and the wave functions of the nanowires are calculated by means of a Lanczos iteration algorithm. For the [001]-oriented InSb and GaSb nanowires, the systems with both square and rectangular cross sections are considered. Here, it is found that all the energy bands are double degenerate. Furthermore, although the lowest conduction bands in these nanowires show good parabolic dispersions, the top valence bands show rich and complex structures. In particular, the topmost valence bands of these nanowires with a square cross section show a double maximum structure. In the nanowires with a rectangular cross section, this double maximum structure is suppressed and top valence bands gradually develop into parabolic bands as the aspect ratio of the cross section is increased. For the [111]-oriented InSb and GaSb nanowires, the systems with hexagonal cross sections are considered. It is found that all the bands at the \Gamma-point are again double degenerate. However, some of them will split into non-degenerate bands when the wave vector moves away from the \Gamma-point. Furthermore, although the lowest conduction bands again show good parabolic dispersions, the topmost valence bands do not show the double maximum structure but, instead, a single maximum structure with its maximum at a wave vector slightly away from the \Gamma-point. We also investigate the effects of quantum confinement on the band structures of the [001]- and [111]-oriented InSb and GaSb nanowires and present an empirical formula for the description of quantization energies of the band edge states in the nanowires.Comment: 17 pages, 19 figure

In-medium Properties of Θ+\Theta^{+} as a Kπ\piN structure in Relativistic Mean Field Theory

The properties of nuclear matter are discussed with the relativistic mean-field theory (RMF).Then, we use two models in studying the in-medium properties of $\Theta^+$: one is the point-like $\Theta^*$ in the usual RMF and the other is a K$\pi$N structure for the pentaquark. It is found that the in-medium properties of $\Theta^+$ are dramatically modified by its internal structure. The effective mass of $\Theta^+$ in medium is, at normal nuclear density, about 1030 MeV in the point-like model, while it is about 1120 MeV in the model of K$\pi$N pentaquark. The nuclear potential depth of $\Theta^+$ in the K$\pi$N model is approximately -37.5 MeV, much shallower than -90 MeV in the usual point-like RMF model.Comment: 8 pages, 5 figure

Chiral Condensates in Quark and nuclear Matter

We present a novel treatment for calculating the in-medium quark condensates. The advantage of this approach is that one does not need to make further assumptions on the derivatives of model parameters with respect to the quark current mass. The normally accepted model-independent result in nuclear matter is naturally reproduced. The change of the quark condensate induced by interactions depends on the incompressibility of nuclear matter. When it is greater than 260 MeV, the density at which the condensate vanishes is higher than that from the linear extrapolation. For the chiral condensate in quark matter, a similar model-independent linear behavior is found at lower densities, which means that the decreasing speed of the condensate in quark matter is merely half of that in nuclear matter if the pion-nucleon sigma commutator is six times the average current mass of u and d quarks. The modification due to QCD-like interactions is found to slow the decreasing speed of the condensate, compared with the linear extrapolation.Comment: 12 pages, 7 figures, revtex4 styl

Models of Social Groups in Blogosphere Based on Information about Comment Addressees and Sentiments

This work concerns the analysis of number, sizes and other characteristics of groups identified in the blogosphere using a set of models identifying social relations. These models differ regarding identification of social relations, influenced by methods of classifying the addressee of the comments (they are either the post author or the author of a comment on which this comment is directly addressing) and by a sentiment calculated for comments considering the statistics of words present and connotation. The state of a selected blog portal was analyzed in sequential, partly overlapping time intervals. Groups in each interval were identified using a version of the CPM algorithm, on the basis of them, stable groups, existing for at least a minimal assumed duration of time, were identified.Comment: Gliwa B., Ko\'zlak J., Zygmunt A., Models of Social Groups in Blogosphere Based on Information about Comment Addressees and Sentiments, in the K. Aberer et al. (Eds.): SocInfo 2012, LNCS 7710, pp. 475-488, Best Paper Awar

Theoretical Triple-Differential Cross Sections of a Methane Molecule By a Proper-Average Method

For the last few years, our group has calculated cross sections for electron-impact ionization of molecules using the molecular three-body distorted-wave approximation coupled with the orientation-averaged molecular orbital (OAMO) approximation. This approximation was very successful for calculating ionization cross sections for hydrogen molecules and to a lesser extent nitrogen molecules. Recently we used the approximation to calculate single ionization cross sections for the 1t2 state of methane (CH4) and we found major discrepancies with the experimental data. Here we investigate the validity of the OAMO approximation by calculating cross sections that have been properly averaged over all molecular orientations. These calculations with proper averages are in much better agreement with experiment than the OAMO calculations

The hyperon mean free paths in the relativistic mean field

The $\Lambda$- and $\Xi^-$-hyperon mean free paths in nuclei are firstly calculated in the relativistic mean field (RMF) theory. The real parts of the optical potential are derived from the RMF approach, while the imaginary parts are obtained from those of nucleons with the relations: $U^{\mathrm{IY}}_{\mathrm{S}} = \alpha_{\sigma \mathrm{Y}}\cdot U_{\mathrm{S}}^{\mathrm{IN}}$ and $U^{\mathrm{IY}}_{\mathrm{V}} = \alpha_{\omega \mathrm{Y}}\cdot U_{\mathrm{V}}^{\mathrm{IN}}$ . With the assumption, the depth of the imaginary potential for $\Xi^-$ is $W_{\Xi}\simeq-$ 3.5 MeV, and for $\Lambda$ is $W_{\Lambda}\simeq-$ 7 MeV at low incident energy. We find that, the hyperon mean free path decreases with the increase of the hyperon incident energies, from 200 MeV to 800 MeV; and in the interior of the nuclei, the mean free path is about $2\sim 3$ fm for $\Lambda$, and about $4\sim 8$ fm for $\Xi^-$, depending on the hyperon incident energy.Comment: 5 figures, 6 page

The properties of kaonic nuclei in relativistic mean-field theory

The static properties of some possible light and moderate kaonic nuclei, from C to Ti, are studied in the relativistic mean-field theory. The 1s and 1p state binding energies of $K^-$ are in the range of $73\sim 96$ MeV and $22\sim 63$ MeV, respectively. The binding energies of 1p states increase monotonically with the nucleon number A. The upper limit of the widths are about $42\pm 14$ MeV for the 1s states, and about $71\pm 10$ MeV for the 1p states. The lower limit of the widths are about $12\pm 4$ MeV for the 1s states, and $21\pm 3$ MeV for the 1p states. If $V_{0}\leq 30$ MeV, the discrete $K^-$ bound states should be identified in experiment. The shrinkage effect is found in the possible kaonic nuclei. The interior nuclear density increases obviously, the densest center density is about $2.1\rho_{0}$.Comment: 9 pages, 2 tables and 1 figure, widths are considered, changes a lo