Interaction transform for bi-set functions over a finite set

Set functions appear as a useful tool in many areas of decision making and operations research, and several linear invertible transformations have been introduced for set functions, such as the Möbius transform and the interaction transform. The present paper establish similar transforms and their relationships for bi-set functions, i.e. functions of two disjoint subsets. Bi-set functions have been recently introduced in decision making (bi-capacities) and game theory (bi-cooperative games), and appear to open new areas in these fields.Set function; Bi-set function; Möbius transform; Interaction transform

Quantum spin-Hall effect on the M\"obius graphene ribbon

Topological phases of matter have revolutionized quantum engineering. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we study the topological and geometrical transport properties of a M\"obius graphene ribbon. In the absence of a magnetic field, we measure a quantum spin-Hall current on the graphene strip, originating from topology and curvature, whereas a quantum Hall current is not observed. In the torus geometry a Hall current is measured. Additionally, a specific illustration of the equivalence between the Berry and Ricci curvature is presented through a travelling wave-packet around the M\"obius band.Comment: arXiv admin note: substantial text overlap with arXiv:1810.0210

Assessment of detectability of neutral interstellar deuterium by IBEX observations

The abundance of deuterium in the interstellar gas in front of the Sun gives insight into the processes of filtration of neutral interstellar species through the heliospheric interface and potentially into the chemical evolution of the Galactic gas. We investigate the possibility of detection of neutral interstellar deuterium at 1 AU from the Sun by direct sampling by the Interstellar Boundary Explorer (IBEX). We simulate the flux of neutral interstellar D at IBEX for the actual measurement conditions. We assess the number of interstellar D atom counts expected during the first three years of IBEX operation. We also simulate observations expected during an epoch of high solar activity. In addition, we calculate the expected counts of D atoms from the thin terrestrial water layer, sputtered from the IBEX-Lo conversion surface by neutral interstellar He atoms. Most D counts registered by IBEX-Lo are expected to originate from the water layer, exceeding the interstellar signal by 2 orders of magnitude. However, the sputtering should stop once the Earth leaves the portion of orbit traversed by interstellar He atoms. We identify seasons during the year when mostly the genuine interstellar D atoms are expected in the signal. During the first 3 years of IBEX operations about 2 detectable interstellar D atoms are expected. This number is comparable with the expected number of sputtered D atoms registered during the same time intervals. The most favorable conditions for the detection occur during low solar activity, in an interval including March and April each year. The detection chances could be improved by extending the instrument duty cycle, e.g., by making observations in the special deuterium mode of IBEX-Lo.Comment: Accepted for Astronomy & Astrophysic

Axial U(1)U(1) symmetry at high temperature in 2-flavor lattice QCD

We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical M\"obius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 \, \mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.Comment: 8 pages, 4 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spai