A covariantly foliated higher dimensional space-time: Implications for short distance gravity and BSM physics

We consider the space-time at short distances in which it is described by a $D$-dimensional manifold (bulk) carrying out the principal bundle structure. As a result, this space-time manifold is foliated in the covariant way by the $(D-4)$-dimensional submanifolds, realized as the space-like internal spaces, that are smooth copies of the Lie group $G$ considered in this paper as the special unitary group. The submanifolds being transversal to the internal spaces are realized as the external spaces and in fact identified as the usual $4$-dimensional world. The fundamental degrees of freedom determining the geometrical dynamics of the bulk corresponding with short distance gravity are given by the gauge fields, the external metric field and the modulus fields setting dynamically the volume of the internal spaces. These gauge fields laying the bulk is to point precisely out the local directions of the external spaces which depend on the topological non-triviality of the space-time principal bundle. The physical size of the internal spaces is fixed dynamically by the moduli stabilization potential which completely arise from the intrinsic geometry of the bulk. A detail description of the low energy bulk gravity in the weak field limit is given around the classical ground state of the bulk. Additionally, we investigate the dynamics of the fundamentally $4$-dimensional Weyl spinor fields and the fields of carrying out the non-trivial representations of the Lie group $G$ propagating in the bulk in a detail study. These results suggest naturally the possible solutions to some the experimental problems of Standard Model, the smallness of the observed neutrino masses and a dark matter candidate.Comment: 33 pages, 1 figure. Improved version with some rewriting, title change

Gauge theory of quantum gravity

The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great challenge in physics. Here we present an alternative construction of quantum gravity in which the quantum gravitational degrees of freedom are described by the non-Abelian gauge fields characterizing topological non-triviality of the space-time. The quantum dynamics of the space-time thus corresponds to the superposition of the distinct topological states. Its unitary time evolution is described by the path integral approach. This result will also be suggested to solve some major problems in physics of the black holes.Comment: 11 pages, discussions and references added, a mistake of Eq. (10) corrected, results unchange

Statistics of random lasing modes and amplified spontaneous emission spikes in weakly scattering systems

We have measured the spectral correlations and intensity statistics of random lasing modes in weakly scattering systems, and compared them to those of the amplified spontaneous emission spikes. Their dramatic differences revealed the distinct physical mechanisms. We find that local excitation of a weakly scattering system may greatly reduce the number of lasing modes even without absorption outside the pumped region. The lasing modes can be very different from the quasimodes of the passive system due to selective amplification of the feedback from the scatterers within the local gain region

Charmonium resonances and Fano line shapes

Anomalous line shapes of quarkonia are explained naturally as an interference effect of a $c\bar c$ confined closed channel with the surrounding continua, well established in other fields of physics as Fano-resonances. We discuss a quark model coupled-channel analysis describing quarkonium as a mixing of closed $Q\bar Q$ and molecular-like $D\bar D$ open channels. The asymmetric line shapes observed in $\psi(3770)$ production cross sections in $e^+e^-$ annihilation to $D^0\bar{D}^0$ and $D^+ D^-$, respectively, are described very well. The method allows to extract directly from the data the amount of $Q\bar Q \leftrightarrow D\bar D$ configuration mixing.Comment: 4 pages, 4 figure

Some new bounds of placement delivery arrays

Coded caching scheme is a technique which reduce the load during peak traffic times in a wireless network system. Placement delivery array (PDA in short) was first introduced by Yan et al.. It can be used to design coded caching scheme. In this paper, we prove some lower bounds of PDA on the element and some lower bounds of PDA on the column. We also give some constructions for optimal PDA.Comment: Coded caching scheme, placement delivery array, optima

Completing the spectrum of almost resolvable cycle systems with odd cycle length

In this paper, we construct almost resolvable cycle systems of order $4k+1$ for odd $k\ge 11$. This completes the proof of the existence of almost resolvable cycle systems with odd cycle length.Comment: k-cycle system; almost resolvable cycle system. arXiv admin note: substantial text overlap with arXiv:1605.0081

Almost resolvable kk-cycle systems with k≡2(mod4)k\equiv 2\pmod 4

In this paper, we show that if $k\geq 6$ and $k \equiv 2 \pmod 4$, then there exists an almost resolvable $k$-cycle system of order $2kt+1$ for all $t\ge 1$ except possibly for $t=2$ and $k\geq 14$. Thus we give a partial solution to an open problem posed by Lindner, Meszka, and Rosa (J. Combin. Des., vol. 17, pp.404-410, 2009).Comment: cycle system; almost resolvable cycle system. arXiv admin note: substantial text overlap with arXiv:1706.05958, arXiv:1605.0081

The nature and line shapes of charmonium in the e+e−→DDˉe^+e^- \to D\bar{D} reactions

We explore the nature of sharp resonances with asymmetric line shape observed in cross section data, a general physical phenomenon produced by the interference of continuum background and resonances. A Fano scheme and the coupled-channel T-matrix approach are employed to this aim and their close relationship is present. As a typical example, we point out that the $\psi(3770)$ state observed in the $e^+e^-$ reactions with an anomalous line shape can be explained naturally as a resonance embedded in the $D\bar{D}$ continuum. From a coupled-channels analysis the background of $\psi(3770)$ resonance is found to originate from a pole at $\sqrt{s}=3716.0 \pm$ 30.0~MeV. As a by-product, the broad structure $X(3900)/G(3900)$ seen in the Belle data, is found to be the tail of the $\psi(3770)$ state, distorted by the opening of the $D^*\bar{D} + c.c$ channel and the onset of the $\psi(4040)$ spectral distribution, thus making the assignment as a genuine charmonium state unlikely.Comment: 11 pages, 4 figures, extended versio

Wave interference effect on polymer microstadium laser

We investigate the lasing modes in fully chaotic polymer microstadiums under optical pumping. The lasing modes are regularly spaced in frequency, and their amplitudes oscillate with frequency. Our numerical simulations reveal that the lasing modes are multi-orbit scar modes. The interference of partial waves propagating along the constituent orbits results in local maxima of quality factor at certain frequencies. The observed modulation of lasing mode amplitude with frequency results from the variation of quality factor, which provides the direct evidence of wave interference effect in open chaotic microcavities

About the Calabi problem: a finite dimensional approach

Let us consider a projective manifold and $\Omega$ a volume form. We define the gradient flow associated to the problem of $\Omega$-balanced metrics in the quantum formalism, the \Omega$-balacing flow. At the limit of the quantization, we prove that the$\Omega$-balacing flow converges towards a natural flow in K\"ahler geometry, the$\Omega$-K\"ahler flow. We study the existence of the$\Omega$-K\"ahler flow and proves its long time existence and convergence towards the solution to the Calabi problem of prescribing the volume form in a given K\"ahler class. We derive some natural geometric consequences of our study.Comment: 38 pages. Revised version with improved expositio