The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Alessandro Roggero - One of the best experts on this subject based on the ideXlab platform.
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spectral density estimation with the Gaussian Integral transform
Physical Review A, 2020Co-Authors: Alessandro RoggeroAbstract:The spectral density operator $\hat{\rho}(\omega)=\delta(\omega-\hat{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross-sections. In this work, we describe a near optimal quantum algorithm providing an approximation to the spectral density with energy resolution $\Delta$ and error $\epsilon$ using $\mathcal{O}\left(\sqrt{\log\left(1/\epsilon\right)\left(\log\left(1/\Delta\right)+\log\left(1/\epsilon\right)\right)}/\Delta\right)$ operations. This is achieved without using expensive approximations to the time-evolution operator but exploiting instead qubitization to implement an approximate Gaussian Integral Transform (GIT) of the spectral density. We also describe appropriate error metrics to assess the quality of spectral function approximations more generally.
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Spectral-density estimation with the Gaussian Integral transform
Physical Review A, 2020Co-Authors: Alessandro RoggeroAbstract:The spectral-density operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}(\ensuremath{\omega})=\ensuremath{\delta}(\ensuremath{\omega}\ensuremath{-}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross sections. In this work, we describe a near optimal quantum algorithm providing an approximation to the spectral density with energy resolution $\mathrm{\ensuremath{\Delta}}$ and error $\ensuremath{\epsilon}$ using $O\left(\sqrt{{log}_{2}\left(1/\ensuremath{\epsilon}\right)\left[{log}_{2}\left(1/\mathrm{\ensuremath{\Delta}}\right)+{log}_{2}\left(1/\ensuremath{\epsilon}\right)\right]}/\mathrm{\ensuremath{\Delta}}\right)$ operations. This is achieved without using expensive approximations to the time-evolution operator, but instead exploiting qubitization to implement an approximate Gaussian Integral transform of the spectral density. We also describe appropriate error metrics to assess the quality of the spectral function approximations more generally.
Ambar N Sengupta - One of the best experts on this subject based on the ideXlab platform.
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Limiting Means for Spherical Slices
Communications on Stochastic Analysis, 2019Co-Authors: Amy Peterson, Ambar N SenguptaAbstract:We show that for a suitable class of functions of finitely-many variables, the limit of Integrals along slices of a high dimensional sphere is a Gaussian Integral on a corresponding finite-codimension affine subspace in infinite dimensions.
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The Gaussian limit for high-dimensional spherical means
Journal of Functional Analysis, 2019Co-Authors: Amy Peterson, Ambar N SenguptaAbstract:Abstract We show that the limit of Integrals along slices of a high dimensional sphere is a Gaussian Integral on a corresponding finite-codimension affine subspace in infinite dimensions.
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a Gaussian radon transform for banach spaces
arXiv: Probability, 2012Co-Authors: Irina Holmes, Ambar N SenguptaAbstract:We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian Integral over all hyperplanes outside a closed bounded convex set in the Hilbert space corresponding to the Gaussian measure then the function is zero outside this set.
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A support theorem for a Gaussian Radon transform in infinite dimensions
Transactions of the American Mathematical Society, 2012Co-Authors: Jeremy J. Becnel, Ambar N SenguptaAbstract:We prove that in infinite dimensions, if a bounded continuous function has zero Gaussian Integral over all hyperplanes outside a closed bounded convex set then the function is zero outside this set. This is an infinite-dimensional form of the well-known Helgason support theorem for Radon transforms in finite dimensions.
Ruiqiang Zhang - One of the best experts on this subject based on the ideXlab platform.
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Research on Transmission Line Voltage Measurement Method Based on Improved Gaussian Integral
IEEE Access, 2019Co-Authors: Jingang Wang, Ruiqiang ZhangAbstract:Currently, there are two non-contact measurement methods of the transmission line voltage based on field sensor: one is calculation with the inverse problem of electric field for the solution, and the other is to solve by the numerical integration algorithm. In general, the first one is confronted with data equation solving problems and difficulties in accurate calibration as well as low precision, while the second one is troubled by the complexity of algorithm equation and unsatisfactory integration node. In view of the above problems, this paper improves on the basis of the Gaussian Integral algorithm to seek better nodes, in order to reduce the difficulty of solving and improve the measurement accuracy of the Integral algorithm. First, starting from the Gaussian Integral algorithm and making research to improve the Gaussian Integral algorithm theory. Then, the finite element simulation of three-phase transmission line through Maxwell software is built, and the space electric field distribution data is acquired to calculate an Integral node as well as its corresponding weights. Finally, the three-phase transmission line voltage measurement test platform with D-dot sensor voltage measurement system is built to test verification. The text results show that the voltage measurement method based on the improved Gaussian Integral has characteristics of a simple solution, better Integral node, and higher precision, and all the measured voltage errors are less than 0.45%.
Jingang Wang - One of the best experts on this subject based on the ideXlab platform.
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Research on Transmission Line Voltage Measurement Method Based on Improved Gaussian Integral
IEEE Access, 2019Co-Authors: Jingang Wang, Ruiqiang ZhangAbstract:Currently, there are two non-contact measurement methods of the transmission line voltage based on field sensor: one is calculation with the inverse problem of electric field for the solution, and the other is to solve by the numerical integration algorithm. In general, the first one is confronted with data equation solving problems and difficulties in accurate calibration as well as low precision, while the second one is troubled by the complexity of algorithm equation and unsatisfactory integration node. In view of the above problems, this paper improves on the basis of the Gaussian Integral algorithm to seek better nodes, in order to reduce the difficulty of solving and improve the measurement accuracy of the Integral algorithm. First, starting from the Gaussian Integral algorithm and making research to improve the Gaussian Integral algorithm theory. Then, the finite element simulation of three-phase transmission line through Maxwell software is built, and the space electric field distribution data is acquired to calculate an Integral node as well as its corresponding weights. Finally, the three-phase transmission line voltage measurement test platform with D-dot sensor voltage measurement system is built to test verification. The text results show that the voltage measurement method based on the improved Gaussian Integral has characteristics of a simple solution, better Integral node, and higher precision, and all the measured voltage errors are less than 0.45%.
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Research on Transmission Line Voltage Measurement Method of D-Dot Sensor Based on Gaussian Integral.
Sensors (Basel Switzerland), 2018Co-Authors: Jingang Wang, Yanhang Zhao, Li Wenjiang, Zeng Xianglong, Tang Juan, Wang Yao, Xudong DengAbstract:D-dot sensors meet the development trend towards the downsizing, automation and digitalization of voltage sensors and is one of research hotspots for new voltage sensors at present. The traditional voltage measurement system of D-dot sensors makes possible the reverse solving of wire potentials according to the computational principles of the electric field inverse problem by measuring electric field values beneath the transmission line. Nevertheless, as it is limited by the solving method of the electric field inverse problem, the D-dot sensor voltage measurement system is struggling with solving difficulties and poor accuracy. To solve these problems, this paper suggests introducing a Gaussian Integral into the D-dot sensor voltage measurement system to accurately measure the voltage of transmission lines. Based on studies of D-dot sensors, a transmission line voltage measurement method based on Gaussian Integrals is proposed and used for the simulation of the electric field of a 220 kV and a 20 kV transmission line. The feasibility of the introduction of the Gaussian Integral to solve transmission line voltage was verified by the simulation results. Finally, the performance of the Gaussian Integral was verified by an experiment using the transmission line voltage measurement platform. The experimental results demonstrated that the D-dot sensor measurement system based on a Gaussian Integral achieves high accuracy and the relative error is lower than 0.5%.
W Schirmacher - One of the best experts on this subject based on the ideXlab platform.
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coherent potential approximation for diffusion and wave propagation in topologically disordered systems
Physical Review B, 2013Co-Authors: Stephan Kohler, G Ruocco, W SchirmacherAbstract:Using Gaussian Integral transform techniques borrowed from functional-Integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion of classical particles in a random environment and ($ii$) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown to correspond to the boson peak in the vibrational model. The anomalous regimes above the crossover are governed by a complex, frequency-dependent self energy. The boson peak is shown to be stronger for non-Gaussian disorder than for Gaussian disorder. We demonstrate that the low-frequency non-analyticity of the off-lattice version of the CPA leads to the correct long-time tails of the velocity autocorrelation function in the hopping problem and to low-frequency Rayleigh scattering in the wave problem. Furthermore we show that the present version of the CPA is capable to treat the percolative aspects of hopping transport adequately.