22,811 research outputs found

    Cooperation between Top-Down and Bottom-Up Theorem Provers

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    Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches

    Castaing's instability in a trapped ultra-cold gas

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    We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to an experiment at JILA. It shows the presence of Castaing's instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.Comment: 5 pages, 3 figures; equation (8) corrected; submitted to EPJ

    Large amplitude spin waves in ultra-cold gases

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    We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped Rb87 atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence.Comment: To appear in Eur. Phys. J.

    Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem

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    Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show that the SIC existence problem is equivalent to three other, on the face of it quite different problems. Although it is still not clear whether these reformulations of the problem will make it more tractable, we believe that the fact that SICs have these connections to other areas of mathematics is of some intrinsic interest. Specifically, we reformulate the SIC problem in terms of (1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result being a greatly strengthened version of one previously obtained by Appleby, Flammia and Fuchs). The connection between these three reformulations is non-trivial: It is not easy to demonstrate their equivalence directly, without appealing to their common equivalence to SIC existence. In the course of our analysis we obtain a number of other results which may be of some independent interest.Comment: 36 pages, to appear in Quantum Inf. Compu

    Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory

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    The flow curves, viz. the curves of stationary stress under steady shearing, are obtained close to the glass transition in dense colloidal dispersions using asymptotic expansions in a schematic model of mode coupling theory. The shear thinning of the viscosity in fluid states and the yielding of glassy states is discussed. At the transition between fluid and shear-molten glass, simple and generalized Herschel-Bulkley laws are derived with power law exponents that can be computed for different particle interactions from the equilibrium structure factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted

    Near-field coupling of gold plasmonic antennas for sub-100 nm magneto-thermal microscopy

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    The development of spintronic technology with increasingly dense, high-speed, and complex devices will be accelerated by accessible microscopy techniques capable of probing magnetic phenomena on picosecond time scales and at deeply sub-micron length scales. A recently developed time-resolved magneto-thermal microscope provides a path towards this goal if it is augmented with a picosecond, nanoscale heat source. We theoretically study adiabatic nanofocusing and near-field heat induction using conical gold plasmonic antennas to generate sub-100 nm thermal gradients for time-resolved magneto-thermal imaging. Finite element calculations of antenna-sample interactions reveal focused electromagnetic loss profiles that are either peaked directly under the antenna or are annular, depending on the sample's conductivity, the antenna's apex radius, and the tip-sample separation. We find that the thermal gradient is confined to 40 nm to 60 nm full width at half maximum for realistic ranges of sample conductivity and apex radius. To mitigate this variation, which is undesirable for microscopy, we investigate the use of a platinum capping layer on top of the sample as a thermal transduction layer to produce heat uniformly across different sample materials. After determining the optimal capping layer thickness, we simulate the evolution of the thermal gradient in the underlying sample layer, and find that the temporal width is below 10 ps. These results lay a theoretical foundation for nanoscale, time-resolved magneto-thermal imaging.Comment: 24 pages including Supporting Information, 6 figures in the main text, 4 supporting figure
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