347 research outputs found

    An example of optimal field cut in lattice gauge perturbation theory

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    We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge theory. We show that the conventional perturbative series for the partition function has a zero radius of convergence and is asymptotic. The average plaquette is discontinuous at g^2=0. However, the fact that SU(2) is compact provides a perturbative sum that converges toward the correct answer for positive g^2. This alternate methods amounts to introducing a specific coupling dependent field cut, that turns the coefficients into g-dependent quantities. Generalizing to an arbitrary field cut, we obtain a regular power series with a finite radius of convergence. At any order in the modified perturbative procedure, and for a given coupling, it is possible to find at least one (and sometimes two) values of the field cut that provide the exact answer. This optimal field cut can be determined approximately using the strong coupling expansion. This allows us to interpolate accurately between the weak and strong coupling regions. We discuss the extension of the method to lattice gauge theory on a D-dimensional cubic lattice.Comment: 9 pages, 11 figs., uses revtex4, modified presentatio

    Imaging of Flaws in Solids by Velocity Inversion

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    We describe the application of a method for ultrasonic imaging of flaws in solids. These methods greatly extend earlier work along these lines at Rockwell and the Langenberg group in Germany, see [1,2,3,4,5,6,7,8,9,10]. The new inversion methods allow reflector imaging and parameter estimation in progressively more complex media with progressively more realistic source/receiver configurations. This research has been carried out in the context of seismic exploration. However, the problems are sufficiently similar that these more realistic models have direct counterparts in nondestructive testing [11,12,13,14,15,16,17]. In particular, both problems are high frequency inverse scattering problems. High frequency means that the wavelengths are much smaller (by a factor of three or more) than the other length scales of the problem.</p

    A New Phase Time Formula for Opaque Barrier Tunneling

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    After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase time is in excellent agreement with the numerical simulations and shows that for wave packets whose upper limit of the momentum distribution is very close to the barrier height, the transit time is proportional to the barrier width.Comment: 9 pages, 2 figure

    Molecular Feshbach dissociation as a source for motionally entangled atoms

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    We describe the dissociation of a diatomic Feshbach molecule due to a time-varying external magnetic field in a realistic trap and guide setting. An analytic expression for the asymptotic state of the two ultracold atoms is derived, which can serve as a basis for the analysis of dissociation protocols to generate motionally entangled states. For instance, the gradual dissociation by sequences of magnetic field pulses may delocalize the atoms into macroscopically distinct wave packets, whose motional entanglement can be addressed interferometrically. The established relation between the applied magnetic field pulse and the generated dissociation state reveals that square-shaped magnetic field pulses minimize the momentum spread of the atoms. This is required to control the detrimental influence of dispersion in a recently proposed experiment to perform a Bell test in the motion of the two atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].Comment: 12 pages, 3 figures; corresponds to published versio

    The effect of dressing on high-order harmonic generation in vibrating H2_2 molecules

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    We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths (≈2μ\approx 2 \mum), leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.Comment: 23 pages, 11 figures, submitted to PR

    Applications of a New Inverse Method to Nondestructive Evaluation

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    When a wave impinges upon an irregularity in an otherwise homogeneous medium, the wave is deformed in a manner which is characteristic of the irregularity. This is the basis of a method of nondestructive evaluation of materials. Problems in which one seeks information about material properties from scattered waves are known as inverse problems. Traditionally, such problems are analyzed either by cataloging many solutions of direct problems and comparing the results of a given experiment with catalogs, or by attempting to solve the relevant equation of wave properties backwards in time. In contrast, we formulate the inverse problem as an equation or system of equations in which one of the unknowns is a function which directly characterizes the irregularity to be determined. Under the assumption of small sized anomalies or small changes in media properties, our system reduces to a single linear integral equation for this characteristic function. In many cases of practical interest, this equation admits closed form solutions. Even under the constraints of practical limitations on the data, information about the irregularity can be deduced. As an example, we consider the case of a void in a solid probed by acoustic waves. We show how high frequency data can be directly processed to yield the actual shape of the anomaly in a region of the surface covered by specular reflect ion of the probe. In the low frequency case, we show how to directly process the data to yield the volume, centroid, and products of inertia of the void

    Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on the Hawking radiation

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    We consider dynamics of fluctuations in transonically accelerating Bose-Einstein condensates and luminous liquids (coherent light propagating in a Kerr nonlinear medium) using the hydrodynamic approach. It is known that neglecting the quantum potential (QP) leads to a singular behavior of quantum and classical fluctuations in the vicinity of the Mach (sonic) horizon, which in turn gives rise to the Hawking radiation. The neglect of QP is well founded at not too small distances ∣x∣≫lh|x| \gg l_h from the horizon, where lhl_h is the healing length. Taking the QP into account we show that a second characteristic length lr>lhl_r > l_h exists, such that the linear fluctuation modes become regularized for ∣x∣≪lr|x| \ll l_r. At ∣x∣≫lr|x| \gg l_r the modes keep their singular behavior, which however is influenced by the QP. As a result we find a deviation of the high frequency tail of the spectrum of Hawking radiation from Planck's black body radiation distribution. Similar results hold for the wave propagation in Kerr nonlinear media where the length lhl_h and lrl_r exist due to the nonlinearity.Comment: 23 pages, 2 figure

    Aperture Integral Ultrasonic Pulse Transmission Model

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    This paper discusses a numerical algorithm and supporting formulation for evaluating ultrasonic pulse transmission through non-planar component geometries. The algorithm is engineered to model experimental configurations where irregularities in surface geometry preclude the use of less rigorous approaches, such as a field expansion about a single entry point. The algorithm formulation represents the transmitted pulse as a surface integral coinciding with a pulse origin aperture, employing the Green function for the water-component system. The model explicitly considers the component surface geometry over the footprint of the incident pulse, thus allowing consideration of smooth yet non-expandable (i.e. in power series about a single point) geometries, such as adjoining flat and fillet surfaces. A computationally efficient algorithm results from use of asymptotic Green function approximations. Approaches are also discussed under conditions where the asymptotic Green function expressions are singular or invalid, due to focusing by surface concavity or transmission near critical angles. Consideration of pulse time dependence represents an extension of previous work [1], as also does treatment of surface concavity and critical angle transmission. The following sections summarize theoretical formulation and algorithmic implementation, followed by the presentation of illustrative computations

    Probing Quantized Einstein-Rosen Waves with Massless Scalar Matter

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    The purpose of this paper is to discuss in detail the use of scalar matter coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum gravity in the restricted setting provided by this symmetry reduction of general relativity. We will obtain the relevant Hamiltonian and quantize it with the techniques already used for the purely gravitational case. Finally we will discuss the use of particle-like modes of the quantized fields to operationally explore some of the features of quantum gravity within this framework. Specifically we will study two-point functions, the Newton-Wigner propagator, and radial wave functions for one-particle states.Comment: Accepted for publication in Physical Review

    Echolocation by Quasiparticles

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    It is shown that the local density of states (LDOS), measured in an Scanning Tunneling Microscopy (STM) experiment, at a single tip position contains oscillations as a function of Energy, due to quasiparticle interference, which is related to the positions of nearby scatterers. We propose a method of STM data analysis based on this idea, which can be used to locate the scatterers. In the case of a superconductor, the method can potentially distinguish the nature of the scattering by a particular impurity.Comment: 4+ page
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