Hypergeometric Generating Function of L-function, Slater's Identities, and Quantum Invariant

We study certain connections between the quantum invariants of the torus knots T_{3,2^k} and some q-series identities. In particular, we obtain new generalizations of Slater's identities (83) and (86).Comment: 18 page

Investigation of effectiveness of various methods with different unknown variables for 3-D eddy current analysis

Computer codes using the A-&#966;, A-&#966;-&#937;, A*-0&#937;-E, T-&#937;, and E-&#937; methods were developed. The effects of the volume ratio of the conductor region to the whole region, the shape of the conductor, and the ratio of the hole region to the conductor region on the computer storage, the CPU time, and the accuracy of the methods are investigated systematically using a few simple models. The effect of the conductivity of the conductor is also examined. The computer storage, the CPU time, and the error are found to increase with increase of the volume ratio of the conductor region to the whole region. The computer storage and the CPU time are affected by the shape of the conductor in some methods of analysis. The error of the A*-&#937;(E-&#937;) method is larger than that of the other methods</p

First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field

First-order quantum correction to the Larmor radiation is investigated on the basis of the scalar QED on a homogeneous background of time-dependent electric field, which is a generalization of a recent work by Higuchi and Walker so as to be extended for an accelerated charged particle in a relativistic motion. We obtain a simple approximate formula for the quantum correction in the limit of the relativistic motion when the direction of the particle motion is parallel to that of the electric field.Comment: 12 pages, 2 figures, accepted for publication in Physical Review

Astrophysical Condition on the attolensing as a possible probe for a modified gravity theory

We investigate the wave effect in the gravitational lensing by a black hole with very tiny mass less than 10^-19 solar mass, which is called attolensing, motivated by a recent report that the lensing signature might be a possible probe of a modified gravity theory in the braneworld scenario. We focus on the finite source size effect and the effect of the relative motion of the source to the lens, which are influential to the wave effect in the attolensing. Astrophysical condition that the lensed interference signature can be a probe of the modified gravity theory is demonstrated. The interference signature in the microlensing system is also discussed.Comment: Accepted for publication in IJMP

Quantum Larmor radiation in conformally flat universe

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics (SQED). A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the SQED. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e^2\hbar is determined by a non-local integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D80 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a non-relativistic motion in a homogeneous electric field.Comment: 12 pages, 4 figure, accepted for publication in Physical Review

The Subaru/XMM-Newton Deep Survey (SXDS) -VII. Clustering Segregation with Ultraviolet and Optical Luminosities of Lyman-Break Galaxies at z~3

We investigate clustering properties of Lyman-break galaxies (LBGs) at z~3 based on deep multi-waveband imaging data from optical to near-infrared wavelengths in the Subaru/XMM-Newton Deep Field. The LBGs are selected by U-V and V-z' colors in one contiguous area of 561 arcmin^2 down to z'=25.5. We study the dependence of the clustering strength on rest-frame UV and optical magnitudes, which can be indicators of star formation rate and stellar mass, respectively. The correlation length is found to be a strong function of both UV and optical magnitudes with brighter galaxies being more clustered than faint ones in both cases. Furthermore, the correlation length is dependent on a combination of UV and optical magnitudes in the sense that galaxies bright in optical magnitude have large correlation lengths irrespective of UV magnitude, while galaxies faint in optical magnitude have correlation lengths decreasing with decreasing UV brightness. These results suggest that galaxies with large stellar masses always belong to massive halos in which they can have various star formation rates, while galaxies with small stellar masses reside in less massive halos only if they have low star formation rates. There appears to be an upper limit to the stellar mass and the star formation rate which is determined by the mass of hosting dark halos.Comment: 16 pages, 15 figures, accepted for publication in Ap

Self-consistent calculation of nuclear photoabsorption cross section: Finite amplitude method with Skyrme functionals in the three-dimensional real space

The finite amplitude method (FAM), which we have recently proposed (T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)), simplifies significantly the fully self-consistent RPA calculation. Employing the FAM, we are conducting systematic, fully self-consistent response calculations for a wide mass region. This paper is intended to present a computational scheme to be used in the systematic investigation and to show the performance of the FAM for a realistic Skyrme energy functional. We implemented the method in the mixed representation in which the forward and backward RPA amplitudes are represented by indices of single-particle orbitals for occupied states and the spatial grid points for unoccupied states. We solve the linear response equation for a given frequency. The equation is a linear algebraic problem with a sparse non-hermitian matrix, which is solved with an iterative method. We show results of the dipole response for selected spherical and deformed nuclei. The peak energies of the giant dipole resonance agree well with measurements for heavy nuclei, while they are systematically underestimated for light nuclei. We also discuss the width of the giant dipole resonance in the fully self-consistent RPA calculation.Comment: 11 pages, 10 figure

Curvature effect on nuclear pasta: Is it helpful for gyroid appearance?

In supernova cores and neutron star crusts, nuclei are thought to deform to rodlike and slablike shapes, which are often called nuclear pasta. We study the equilibrium properties of the nuclear pasta by using a liquid drop model with curvature corrections. It is confirmed that the curvature effect acts to lower the transition densities between different shapes. We also examine the gyroid structure, which was recently suggested as a different type of nuclear pasta by analogy with the polymer systems. The gyroid structure investigated in this paper is approximately formulated as an extension of the periodic minimal surface whose mean curvature vanishes. In contrast to our expectations, we find from the present approximate formulation that the curvature corrections act to slightly disfavor the appearance of the gyroid structure. By comparing the energy corrections in the gyroid phase and the hypothetical phases composed of d-dimensional spheres, where d is a general dimensionality, we show that the gyroid is unlikely to belong to a family of the generalized dimensional spheres.Comment: 14 pages, 8 figure