Baryogenesis from Dark Sector

We propose a novel mechanism to generate a suitable baryon asymmetry from dark (hidden) sector. This is a Baryogenesis through a reverse pathway of the "asymmetric dark matter" scenario. In the mechanism, the asymmetry of dark matter is generated at first, and it is partially transferred into a baryon asymmetry in the standard model sector. This mechanism enables us not only to realize the generation of the baryon asymmetry but also to account for the correct amount of dark matter density in the present universe within a simple framework.Comment: 7 page

Moments of a single entry of circular orthogonal ensembles and Weingarten calculus

Consider a symmetric unitary random matrix $V=(v_{ij})_{1 \le i,j \le N}$ from a circular orthogonal ensemble. In this paper, we study moments of a single entry $v_{ij}$. For a diagonal entry $v_{ii}$ we give the explicit values of the moments, and for an off-diagonal entry $v_{ij}$ we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size $N$. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.Comment: 17 page

Generalized β\beta-conformal change and special Finsler spaces

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.Comment: References added, some modifications are performed, LateX file, 24 page

Three-Dimensional Evolution of the Parker Instability under a Uniform Gravity

Using an isothermal MHD code, we have performed three-dimensional, high-resolution simulations of the Parker instability. The initial equilibrium system is composed of exponentially-decreasing isothermal gas and magnetic field (along the azimuthal direction) under a uniform gravity. The evolution of the instability can be divided into three phases: linear, nonlinear, and relaxed. During the linear phase, the perturbations grow exponentially with a preferred scale along the azimuthal direction but with smallest possible scale along the radial direction, as predicted from linear analyses. During the nonlinear phase, the growth of the instability is saturated and flow motion becomes chaotic. Magnetic reconnection occurs, which allows gas to cross field lines. This, in turn, results in the redistribution of gas and magnetic field. The system approaches a new equilibrium in the relaxed phase, which is different from the one seen in two-dimensional works. The structures formed during the evolution are sheet-like or filamentary, whose shortest dimension is radial. Their maximum density enhancement factor relative to the initial value is less than 2. Since the radial dimension is too small and the density enhancement is too low, it is difficult to regard the Parker instability alone as a viable mechanism for the formation of giant molecular clouds.Comment: 8 pages of text, 4 figures (figure 2 in degraded gif format), to appear in The Astrophysical Journal Letters, original quality figures available via anonymous ftp at ftp://ftp.msi.umn.edu/pub/users/twj/parker3d.uu or ftp://canopus.chungnam.ac.kr/ryu/parker3d.u

Uncertainty principle for proper time and mass

We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this uncertainty relation can be derived if only we take the fundamental point of view that the proper time should be included as a dynamic variable in the Lagrangian describing the system of the clock. Some problems and some positive aspects of our approach are then discussed.Comment: 15 pages, accepted for publication in J. Math. Phy

Multiple finite Riemann zeta functions

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite counterparts in connection with symmetric polynomials and some arithmetic quantities called powerful numbers.Comment: 19 page