Gravity, antimatter and the Dirac-Milne universe

We review the main arguments against antigravity, a different acceleration of antimatter relative to matter in a gravitational field, discussing and challenging Morrison's, Good's and Schiff's arguments. Following Price, we show that, very surprisingly, the usual expression of the Equivalence Principle is violated by General Relativity when particles of negative mass are supposed to exist, which may provide a fundamental explanation of MOND phenomenology, obviating the need for Dark Matter. Motivated by the observation of repulsive gravity under the form of Dark Energy, and by the fact that our universe looks very similar to a coasting (neither decelerating nor accelerating) universe, we study the Dirac-Milne cosmology, a symmetric matter-antimatter cosmology where antiparticles have the same gravitational properties as holes in a semiconductor. Noting the similarities with our universe (age, SN1a luminosity distance, nucleosynthesis, CMB angular scale), we focus our attention on structure formation mechanisms, finding strong similarities with our universe. Additional tests of the Dirac-Milne cosmology are briefly reviewed, and we finally note that a crucial test of the Dirac-Milne cosmology will be soon realized at CERN next to the ELENA antiproton decelerator, possibly as early as fall 2018, with the AEgIS, ALPHA-g and Gbar antihydrogen gravity experiments.Comment: Proceedings of the Low Energy Antiproton Physics Conference (LEAP), Sorbonne University, Paris, March 12th to 16th, 201

Disproof of the List Hadwiger Conjecture

The List Hadwiger Conjecture asserts that every $K_t$-minor-free graph is $t$-choosable. We disprove this conjecture by constructing a $K_{3t+2}$-minor-free graph that is not $4t$-choosable for every integer $t\geq 1$

Spectral Metric Spaces on Extensions of C*-Algebras

We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect to summability and produces new spectral quantum metric spaces out of given ones. Using our construction we find new spectral triples on the quantum 2- and 3-spheres giving a new perspective on these algebras in noncommutative geometry.Comment: 29 pages, extensively revised, corrected and improved versio

Independent Sets in Graphs with an Excluded Clique Minor

Let $G$ be a graph with $n$ vertices, with independence number $\alpha$, and with with no $K_{t+1}$-minor for some $t\geq5$. It is proved that $(2\alpha-1)(2t-5)\geq2n-5$

Circumference and Pathwidth of Highly Connected Graphs

Birmele [J. Graph Theory, 2003] proved that every graph with circumference t has treewidth at most t-1. Under the additional assumption of 2-connectivity, such graphs have bounded pathwidth, which is a qualitatively stronger result. Birmele's theorem was extended by Birmele, Bondy and Reed [Combinatorica, 2007] who showed that every graph without k disjoint cycles of length at least t has bounded treewidth (as a function of k and t). Our main result states that, under the additional assumption of (k + 1)- connectivity, such graphs have bounded pathwidth. In fact, they have pathwidth O(t^3 + tk^2). Moreover, examples show that (k + 1)-connectivity is required for bounded pathwidth to hold. These results suggest the following general question: for which values of k and graphs H does every k-connected H-minor-free graph have bounded pathwidth? We discuss this question and provide a few observations.Comment: 11 pages, 4 figure

Propagation of Vortex Electron Wave Functions in a Magnetic Field

The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent prefactor. Hence adding OAM and propagating can in this case be replaced by first propagating then adding OAM. Also, the results shown provide an explicit illustration of the fact that the gyromagnetic ratio for OAM is unity. We also propose a novel version of the Bohm-Aharonov effect using vortex electron beams.Comment: 14 pages, 2 figures, submitted to Phys Rev

Spin Wave Diffraction Control and Read-out with a Quantum Memory for Light

A scheme for control and read-out of diffracted spins waves to propagating light fields is presented. Diffraction is obtained via sinusoidally varying lights shifts and ideal one-to-one mapping to light is realized using a gradient echo quantum memory. We also show that dynamical control of the diffracted spin waves spatial orders can be implemented to realize a quantum pulse sequencer for temporal modes that have high time-bandwidth products. Full numerical solutions suggest that both co-propagating and couterpropagating light shift geometries can be used, making the proposal applicable to hot and cold atomic vapours as well as solid state systems with two-level atoms.Comment: 5 pages, 3 figure

Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter--BPS black holes in N=4 supergravity and one--eighth BPS black holes in N=8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half--BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of SL(2,R), a result which is of possible mathematical interest.Comment: 40 page