45,786 research outputs found

    Dyonic (A)dS Black Holes in Einstein-Born-Infeld Theory in Diverse Dimensions

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    We study Einstein-Born-Infeld gravity and construct the dyonic (A)dS planar black holes in general even dimensions, that carry both the electric charge and magnetic fluxes along the planar space. In four dimensions, the solution can be constructed with also spherical and hyperbolic topologies. We study the black hole thermodynamics and obtain the first law. We also classify the singularity structure.Comment: Latex, 21 pages, typos corrected and references adde

    Godel Metrics with Chronology Protection in Horndeski Gravities

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    G\"odel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the G\"odel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.Comment: Latex, 11 pages, references adde

    Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm

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    A misunderstanding that an arbitrary phase rotation of the marked state together with the inversion about average operation in Grover's search algorithm can be used to construct a (less efficient) quantum search algorithm is cleared. The π\pi rotation of the phase of the marked state is not only the choice for efficiency, but also vital in Grover's quantum search algorithm. The results also show that Grover's quantum search algorithm is robust.Comment: 5 pages, 5 figure

    Diamond-free Families

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    Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of [n]:={1,...,n}[n]:=\{1,...,n\} that contains no subposet P. This problem has been studied intensively in recent years, and it is conjectured that π(P):=limnLa(n,P)/nchoosen/2\pi(P):= \lim_{n\rightarrow\infty} La(n,P)/{n choose n/2} exists for general posets P, and, moreover, it is an integer. For k2k\ge2 let \D_k denote the kk-diamond poset {A<B1,...,Bk<C}\{A< B_1,...,B_k < C\}. We study the average number of times a random full chain meets a PP-free family, called the Lubell function, and use it for P=\D_k to determine \pi(\D_k) for infinitely many values kk. A stubborn open problem is to show that \pi(\D_2)=2; here we make progress by proving \pi(\D_2)\le 2 3/11 (if it exists).Comment: 16 page
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