Explicit round fold maps on some fundamental manifolds

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of topological properties of smooth manifolds. Round fold maps were introduced as stable fold maps with singular value sets, defined as the set consisting of all the singular values, of concentric spheres by the author in 2013; for example, some special generic maps on spheres are regarded as round fold maps whose singular value sets are connected. Algebraic invariants such as homology and homotopy groups of manifolds admitting round fold maps and more precisely, the homeomorphism and diffeomorphism types of manifolds admitting such maps having appropriate differential topological structures were studied. Moreover, explicit round fold maps into the Eucidean space of dimension larger than $1$ are constructed on some fundamental manifolds such as manifolds having the structures of bundles over the standard sphere of dimension equal to the Euclidean space whose fibers are closed smooth manifolds and manifolds of dimension not smaller than twice the dimension of the Euclidean space represented as the connected sum of manifolds having the structures of bundles over the standard sphere of dimension equal to the Euclidean space whose fibers are diffeomorphic to standard spheres. In this paper, we construct new explicit fold maps on some fundamental manifolds including the manifolds before by using extended methods of ones used in the constructions before.Comment: arXiv admin note: substantial text overlap with arXiv:1305.1708, arXiv:1309.4854, arXiv:1304.061

Possibility of a coordinated signaling scheme in the Galaxy and SETI experiments

We discuss a Galaxy-wide coordinated signaling scheme with which a SETI observer needs to examine a tiny fraction of the sky. The target sky direction is determined as a function of time, based on high-precision measurements of a progenitor of a conspicuous astronomical event such as a coalescence of a double neutron star binary. In various respects, such a coordinated scheme would be advantageous for both transmitters and receivers, and might be widely prevailing as a tacit adjustment. For this scheme, the planned space gravitational-wave detector LISA and its follow-on missions have a potential to narrow down the target sky area by a factor of $10^{3\textit{-}4}$, and could have a large impact on future SETI experiments.Comment: 4 pages, 3 figures, accepted for publication in ApJ

Highly Eccentric Kozai Mechanism and Gravitational-Wave Observation for Neutron Star Binaries

The Kozai mechanism for a hierarchical triple system could reduce the merger time of inner eccentric binary emitting gravitational waves (GWs), and has been qualitatively explained with the secular theory that is derived by averaging short-term orbital revolutions. However, with the secular theory, the minimum value of the inner pericenter distance could be excessively limited by the averaging operation. Compared with traditional predictions, the actual evolution of an eccentric inner binary could be accompanied by (i) a higher characteristic frequency of the pulse-like GWs around its pericenter passages, and (ii) a larger residual eccentricity at its final inspiral phase. These findings would be important for GW astronomy with the forthcoming advanced detectors.Comment: 5 pages, 3 figures, revised versio

Heat kernel coefficients for compact fuzzy spaces

I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In continuum theory its asymptotic expansion for t -> +0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy spaces. For compact fuzzy spaces, however, an asymptotic expansion for t -> +0 is not appropriate because of their finiteness. It is shown that effective geometric quantities are found as coefficients of an approximate power-law expansion of the trace of a heat kernel valid for intermediate values of t. An efficient method to obtain these coefficients is presented and applied to some known fuzzy spaces to check its validity.Comment: Minor changes, 8 pages, 12 figures, LaTeX, JHEPclas

Hopf algebra description of quantum circuits

The controlled-NOT gate of qubit quantum circuits is shown to be described in terms of a Hopf algebra. Accordingly, any qubit quantum circuit can be expressed as the Hopf algebraic computations and unitary transformations on one qubit.Comment: 4 pages, 2 figures, some sentences and one reference adde

Generalized Bloch theorem and chiral transport phenomena

Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.Comment: 9 pages, 1 figure; v3: published versio

Polyhedral realizations of crystal bases and convex-geometric Demazure operators

The main object in this paper is a certain rational convex polytope whose lattice points give a polyhedral realization of a highest weight crystal basis. This is also identical to a Newton-Okounkov body of a flag variety, and it gives a toric degeneration. In this paper, we prove that a specific class of this polytope is given by Kiritchenko's Demazure operators on polytopes. This implies that polytopes in this class are all lattice polytopes. As an application, we give a sufficient condition for the corresponding toric variety to be Gorenstein Fano.Comment: 21 page

New Mixing Structures of Chiral Generations in a Model with Noncompact Horizontal Symmetry

New mixing structures between chiral generations of elementary particles at low energy are shown in a vectorlike model with a horizontal symmetry SU(1,1). In this framework the chiral model including odd number chiral generations is realized via the spontaneous symmetry breaking of the horizontal symmetry. It is shown that the Yukawa coupling matrices of chiral generations have naturally hierarchical patterns, and in some cases the overall factors of their Yukawa coupling matrices, e.g. the Yukawa coupling constants of the bottom quark and tau lepton are naturally suppressed.Comment: 22 pages, 7 figure

Estimating detection rates of compact binary inspirals for networks of ground-based gravitational-wave detectors

In a recent paper, Schutz proposed an analytical approximation for simplifying treatment of polarization angle and conveniently evaluating relative detection rates of compact binary inspirals for various networks of ground-based interferometers. We derived relative event rates by strictly handling polarization angle and quantitatively examine validity of Schutz's approximation. The associated error of the approximation is rigorously shown to be less than 1.02\%, irrespective of details of the detector networks.Comment: 2 pages, no figure, to appear in PR

Voter model on the two-clique graph

I examine the mean consensus time (i.e., exit time) of the voter model in the so-called two-clique graph. The two-clique graph is composed of two cliques interconnected by some links and considered as a toy model of networks with community structure or multilayer networks. I analytically show that, as the number of interclique links per node is varied, the mean consensus time experiences a crossover between a fast consensus regime [i.e., O(N)] and a slow consensus regime [i.e., O(N^2)], where N is the number of nodes. The fast regime is consistent with the result for homogeneous well-mixed graphs such as the complete graph. The slow regime appears only when the entire network has O(1) interclique links. The present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited.Comment: 4 figure