3,837 research outputs found

    Drude Weight for the Lieb-Liniger Bose Gas

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    Based on the method of hydrodynamic projections we derive a concise formula for the Drude weight of the repulsive Lieb-Liniger δ\delta-Bose gas. Our formula contains only quantities which are obtainable from the thermodynamic Bethe ansatz. The Drude weight is an infinite-dimensional matrix, or bilinear functional: it is bilinear in the currents, and each current may refer to a general linear combination of the conserved charges of the model. As a by-product we obtain the dynamical two-point correlation functions involving charge and current densities at small wavelengths and long times, and in addition the scaled covariance matrix of charge transfer. We expect that our formulas extend to other integrable quantum models.Comment: 23 pages. v2: improved discussion, typos corrected, references added. v3: 26 pages, further improved discussion, references adde

    A geometric viewpoint on generalized hydrodynamics

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    Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles, in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.Comment: 14 pages, 1 figure. v2: 16 pages, 2 figures, improved derivation, discussion, and numerical analysis. v3: 17 pages, small adjustments, accepted versio

    Further studies of vapor-liquid equilibria of methanol-ethylene glycol-water

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    The freezing points of the ternary system methanol-glycol-water have been investigated by Conrad, Hill and Ballman. The vapor-liquid equilibria of the same system was studied by Sjoberg. These investigations were carried out to determine the properties of the system relative to its possible use as an antifreeze mixture. Since Sjoberg\u27s work in 1948, the improved Othmer equilibrium still has been introduced for vapor-liquid experimental determinations. It is therefore the purpose of the present investigation to evaluate the use of this still, compare results with those obtained by Sjoberg, and analyze ternary mixtures for the entire range of glycol concentrations. The system has been completely covered in the present work, and is presented graphically. The figures and tables are in Appendix A and Appendix B respectively --Introduction, page 1

    Z-Selective Homodimerization of Terminal Olefins with a Ruthenium Metathesis Catalyst

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    The cross-metathesis of terminal olefins using a novel ruthenium catalyst results in excellent selectivity for the Z-olefin homodimer. The reaction was found to tolerate a large number of functional groups, solvents, and temperatures while maintaining excellent Z-selectivity, even at high reaction conversions

    Generating Photon Number States on Demand via Cavity Quantum Electrodynamics

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    Z-Selectivity in Olefin Metathesis with Chelated Ru Catalysts: Computational Studies of Mechanism and Selectivity

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    The mechanism and origins of Z-selectivity in olefin metathesis with chelated Ru catalysts were explored using density functional theory. The olefin approaches from the “side” position of the chelated Ru catalysts, in contrast to reactions with previous unchelated Ru catalysts that favor the bottom-bound pathway. Steric repulsions between the substituents on the olefin and the N-substituent on the N-heterocyclic carbene ligand lead to highly selective formation of the Z product

    "So wirft Dirk Nowitzki!"

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