Noncommutative Deformation of Spinor Zero Mode and ADHM Construction

A method to construct noncommutative instantons as deformations from commutative instantons was provided in arXiv:0805.3373. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton background on noncommutative R^4, and we modify the index of the Dirac operator on the noncommutative space slightly and show that the number of the zero mode of the Dirac operator is preserved under the noncommutative deformation. We prove the existence of the Green's function associated with instantons on noncommutative R^4, as a smooth deformation of the commutative case. The feature of the zero modes of the Dirac operator and the Green's function derives noncommutative ADHM equations which coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one correspondence between the instantons on noncommutative R^4 and ADHM data. An example of a noncommutative instanton and a spinor zero mode are also given.Comment: 34 pages, no figures, v3: an appendix and some definitions added,typos correcte

Physical Relation of Source I to IRc2 in the Orion KL Region

We present mid-infrared narrow-band images of the Orion BN/KL region, and N-band low-resolution spectra of IRc2 and the nearby radio source "I." The distributions of the silicate absorption strength and the color temperature have been revealed with a sub-arcsecond resolution. The detailed structure of the 7.8 micron/12.4 micron color temperature distribution was resolved in the vicinity of IRc2. A mid-infrared counterpart to source I has been detected as a large color temperature peak. The color temperature distribution shows an increasing gradient from IRc2 toward source I, and no dominant temperature peak is seen at IRc2. The spectral energy distribution of IRc2 could be fitted by a two-temperature component model, and the "warmer component" of the infrared emission from IRc2 could be reproduced by scattering of radiation from source I. IRc2 itself is not self-luminous, but is illuminated and heated by an embedded luminous young stellar object located at source I.Comment: 20 pages, 11 figures. Minor corrections had been done in the ver.2. Accepted for publication in PAS

Instanton Number of Noncommutative U(n) gauge theory

We show that the integral of the first Pontrjagin class is given by an integer and it is identified with instanton number of the U(n) gauge theory on noncommutative ${\bf R^4}$. Here the dimension of the vector space $V$ that appear in the ADHM construction is called Instanton number. The calculation is done in operator formalism and the first Pontrjagin class is defined by converge series. The origin of the instanton number is investigated closely, too.Comment: 6 color figures, 27 pages, some comments and references are added,typos fixe

The flux of noncommutative U(1) instanton through the fuzzy spheres

From the ADHM construction on noncommutative $R_{\theta}^4$ we investigate different U(1) instanton solutions tied by isometry trasformations. These solutions present a form of vector fields in noncommutative $R_{\theta}^3$ vector space which makes possible the calculus of their fluxes through fuzzy spheres. We establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under isometry transformations.Comment: 18 pages, new version to appear in Int. Jour. of Mod. Phys.

Euler number of Instanton Moduli space and Seiberg-Witten invariants

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish. The partition function is the sum of Euler number of instanton moduli space when it is possible to apply the vanishing theorem. And we get a relation of Euler number labeled by the instanton number $k$ with Seiberg-Witten invariants, too. All calculation in this paper is done without assuming duality.Comment: LaTeX, 34 page

Quantum protocols for anonymous voting and surveying

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a N-fold reduction in computational complexity, where N is the number of voters.Comment: 8 pages. V2 includes the modifications made for the published versio

Earthquake Induced Slope Failure Simulation by SPH

Majority of slope stability, slope displacement and soil liquefaction analyses subjected to earthquake loading condition employed the finite element method (FEM) as the standard numerical tool. However, mechanism of soil failure in such condition often involved extremely large deformation and failure behaviors, which were unable to be modeled by FEM since this method was suffered from the grid distortion. In an attempt to overcome this limitation, we present herein our first attempt to extend the smoothed particle hydrodynamics (SPH) method to analyze slope failure behavior due to seismic shaking. For the sake of simplicity, effect of pore-water pressure was not taken into consideration. The numerical framework was then applied to simulate the failure behavior of a slope subjected to a seismic loading. Experimental model was also conducted to verify the numerical performance. It is shown that SPH can simulate fairly well the slope failure behavior in the model test, especially in prediction of the failure surface. The paper suggests that SPH should be considered as a powerful alternative for computation of geomaterials subjected to earthquake loading conditions