7,024 research outputs found

    Variational Approach to Gaussian Approximate Coherent States: Quantum Mechanics and Minisuperspace Field Theory

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    This paper has a dual purpose. One aim is to study the evolution of coherent states in ordinary quantum mechanics. This is done by means of a Hamiltonian approach to the evolution of the parameters that define the state. The stability of the solutions is studied. The second aim is to apply these techniques to the study of the stability of minisuperspace solutions in field theory. For a λφ4\lambda \varphi^4 theory we show, both by means of perturbation theory and rigorously by means of theorems of the K.A.M. type, that the homogeneous minisuperspace sector is indeed stable for positive values of the parameters that define the field theory.Comment: 26 pages, Plain TeX, no figure

    Inference with interference between units in an fMRI experiment of motor inhibition

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    An experimental unit is an opportunity to randomly apply or withhold a treatment. There is interference between units if the application of the treatment to one unit may also affect other units. In cognitive neuroscience, a common form of experiment presents a sequence of stimuli or requests for cognitive activity at random to each experimental subject and measures biological aspects of brain activity that follow these requests. Each subject is then many experimental units, and interference between units within an experimental subject is likely, in part because the stimuli follow one another quickly and in part because human subjects learn or become experienced or primed or bored as the experiment proceeds. We use a recent fMRI experiment concerned with the inhibition of motor activity to illustrate and further develop recently proposed methodology for inference in the presence of interference. A simulation evaluates the power of competing procedures.Comment: Published by Journal of the American Statistical Association at http://www.tandfonline.com/doi/full/10.1080/01621459.2012.655954 . R package cin (Causal Inference for Neuroscience) implementing the proposed method is freely available on CRAN at https://CRAN.R-project.org/package=ci

    Quantum annealing of a disordered magnet

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    Traditional simulated annealing uses thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. Thermal and quantum annealing are compared in a model disordered magnet, where the effects of quantum mechanics can be tuned by varying an applied magnetic field. The results indicate that quantum annealing hastens convergence to the optimum state

    Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet

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    The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional square lattice, is simple and soluble, but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu2(BO3)2, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution x-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure.Comment: 16 pages, 4 figures. Accepted for publication in PNA

    Conductivity of Metallic Si:B near the Metal-Insulator Transition: Comparison between Unstressed and Uniaxially Stressed Samples

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    The low-temperature dc conductivities of barely metallic samples of p-type Si:B are compared for a series of samples with different dopant concentrations, n, in the absence of stress (cubic symmetry), and for a single sample driven from the metallic into the insulating phase by uniaxial compression, S. For all values of temperature and stress, the conductivity of the stressed sample collapses onto a single universal scaling curve. The scaling fit indicates that the conductivity of si:B is proportional to the square-root of T in the critical range. Our data yield a critical conductivity exponent of 1.6, considerably larger than the value reported in earlier experiments where the transition was crossed by varying the dopant concentration. The larger exponent is based on data in a narrow range of stress near the critical value within which scaling holds. We show explicitly that the temperature dependences of the conductivity of stressed and unstressed Si:B are different, suggesting that a direct comparison of the critical behavior and critical exponents for stress- tuned and concentration-tuned transitions may not be warranted

    A discontinuous melt sheet in the Manson impact structure

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    Petrologic studies of the core recovered from holes drilled in the Manson, Iowa, buried impact structure may unravel the thermal history of the crater-fill debris. We made a cursory examination of about 200 m of core recovered from the M-1 bore hole. The M-1 bore hole was the first of 12 holes drilled as part of a cooperative drilling program between the U.S. Geological Survey and the Iowa Geological Survey Bureau. The M-1 core hole is about 6 km northeast of the center of the impact structure, apparently on the flank of its central peak. We developed a working hypothesis that a 30-m-thick breccia unit within a 53-m-thick unit previously termed the 'crystalline clast breccia with glassy matrix' is part of a discontinuous melt sheet in the crater-fill impact debris. The 30-m-thick breccia unit reached temperatures sufficient to partially melt some small breccia clasts and convert the fine-grained breccia matrix into a silicate melt that cooled to a greenish-black, flinty, microcrystalline rock. The results of the investigation of this unit are presented
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