438,729 research outputs found

    Hodge metrics and positivity of direct images

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    Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle EE on a complex manifold, and every positive integer kk, the vector bundle SkEdetES^kE\otimes\det E has a continuous metric with Griffiths semi-positive curvature. If EE is ample on a projective manifold, the metric can be made smooth and Griffiths positive.Comment: revised and expanded version of "A positivity property of ample vector bundles

    Comment on "A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems" by A. H. Castro-Neto and B. A. Jones

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    In a recent paper Castro-Neto and Jones argue that because the observability of quantum Griffiths-McCoy effects in metals is controlled by non-universal quantities, the quantum Griffiths-McCoy scenario may be a viable explanation for the non-fermi-liquid behavior observed in heavy fermion compounds. In this Comment we point out that the important non-universal quantity is the damping of the spin dynamics by the metallic electrons; quantum Griffiths-McCoy effects occur only if this is parametrically weak relative to other scales in the problem, i.e. if the spins are decoupled from the carriers. This suggests that in heavy fermion materials, where the Kondo effect leads to a strong carrier-spin coupling, quantum Griffiths-McCoy effects are unlikely to occur.Comment: 2 page

    Quantum Locality?

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    Robert Griffiths has recently addressed, within the framework of a 'consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths' rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his 'consistent quantum theory' shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths' reply, which cites general possibilities of ambiguities that make what is to be proved ill-defined, and hence render the pertinent 'consistent framework' ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that framework is used. The section also shows, in response to Griffiths' challenge, why a putative proof of locality that he has described is flawed.Comment: This version adds a response to Griffiths' reply to my original. It notes that Griffiths confirms the validity of my argument if one uses the framework that I use. Griffiths' objection that other frameworks exist is not germaine, because I use the unique one that satisfies the explicitly stated conditions that the choices be macroscopic choices of experiments and outcomes in a specified orde

    Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath

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    We study the effect of dissipation on the infinite randomness fixed point and the Griffiths-McCoy singularities of random transverse Ising systems in chains, ladders and in two-dimensions. A strong disorder renormalization group scheme is presented that allows the computation of the finite temperature behavior of the magnetic susceptibility and the spin specific heat. In the case of Ohmic dissipation the susceptibility displays a crossover from Griffiths-McCoy behavior (with a continuously varying dynamical exponent) to classical Curie behavior at some temperature TT^*. The specific heat displays Griffiths-McCoy singularities over the whole temperature range. For super-Ohmic dissipation we find an infinite randomness fixed point within the same universality class as the transverse Ising system without dissipation. In this case the phase diagram and the parameter dependence of the dynamical exponent in the Griffiths-McCoy phase can be determined analytically.Comment: 23 pages, 12 figure

    The Appointment of Dr. Jose-Marie Griffiths to the Position of Vice President for Academic Affairs

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    Bryant University President Ronald K. Machtley is proud to announce the appointment of Dr. Jośe-Marie Griffiths to the distinguished position of Vice President for Academic Affairs and requests that you join him in welcoming Dr. Griffiths to the Bryant University communit

    On the Griffiths numbers for higher dimensional singularities

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    We show that Yau's conjecture on the inequalities for (n-1)-th Griffiths number and (n-1)-th Hironaka number does not hold for isolated rigid Gorenstein singularities of dimension greater than 2. But his conjecture on the inequality for (n-1)-th Griffiths number is true for irregular singularities.Comment: to appear in Annales de l'Institut Fourie
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