The Experts below are selected from a list of 16521 Experts worldwide ranked by ideXlab platform
V M Shabaev - One of the best experts on this subject based on the ideXlab platform.
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qed corrections to the p 1 2 2 p 3 2 2 fine structure in fluorinelike ions model lamb Shift Operator approach
2020Co-Authors: V M Shabaev, I I Tupitsyn, M Y Kaygorodov, Y S Kozhedub, A V Malyshev, D V MironovaAbstract:In Li et al. [Phys. Rev. A 98, 020502(R) (2018)] it was claimed that the model-potential computations of the Lamb Shift on the $^{2}P_{1/2}\ensuremath{-}^{2}P_{3/2}$ fine structure in fluorinelike uranium lead to a discrepancy between theory and experiment. Later, it was reported by Volotka et al. [Phys. Rev. A 100, 010502(R) (2019)] that ab initio QED calculation, including the first-order one-electron QED contributions and the related effects of two-electron screening, yields the result which restores the agreement between theory and experiment and strongly disagrees with the model-potential Lamb-Shift values. In the present paper, the model Lamb-Shift Operator [Shabaev et al., Phys. Rev. A 88, 012513 (2013)] is used to evaluate the QED effects on the $^{2}P_{1/2}\ensuremath{-}^{2}P_{3/2}$ fine structure in F-like ions. The calculations are performed by incorporating this Operator into the Dirac-Coulomb-Breit equation employing different methods. It is demonstrated that the methods, based on including the Lamb-Shift Operator either into the Dirac-Fock equations or into the calculations by perturbation theory, lead to the theoretical results which are in good agreement with each other and with experiment. The restriction of these results to the first order in the QED effects leads to a value which agrees with the aforementioned ab initio QED result.
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qedmod fortran program for calculating the model lamb Shift Operator
2015Co-Authors: V M Shabaev, I I Tupitsyn, V A YerokhinAbstract:We present Fortran package QEDMOD for computing the model QED Operator hQED that can be used to account for the Lamb Shift in accurate atomic-structure calculations. The package routines calculate the matrix elements of hQED with the user-specified one-electron wave functions. The Operator can be used to calculate Lamb Shift in many-electron atomic systems with a typical accuracy of few percent, either by evaluating the matrix element of hQED with the many-electron wave function, or by adding hQED to the Dirac–Coulomb–Breit Hamiltonian.
Geert Leus - One of the best experts on this subject based on the ideXlab platform.
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the dual graph Shift Operator identifying the support of the frequency domain
2021Co-Authors: Geert Leus, Santiago Segarra, Alejandro Ribeiro, Antonio G. MarquesAbstract:Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The two most important tools in GSP are the graph Shift Operator (GSO), which is a sparse matrix accounting for the topology of the graph, and the graph Fourier transform (GFT), which maps graph signals into a frequency domain spanned by a number of graph-related Fourier-like basis vectors. This alternative representation of a graph signal is denominated the graph frequency signal. Several attempts have been undertaken in order to interpret the support of this graph frequency signal, but they all resulted in a one-dimensional interpretation. However, if the support of the original signal is captured by a graph, why would the graph frequency signal have a simple one-dimensional support? Departing from existing work, we propose an irregular support for the graph frequency signal, which we coin dual graph. A dual GSO leads to a better interpretation of the graph frequency signal and its domain, helps to understand how the different graph frequencies are related and clustered, enables the development of better graph filters and filter banks, and facilitates the generalization of classical SP results to the graph domain.
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Graphon Filters: Graph Signal Processing in the Limit
2020Co-Authors: Matthew W. Morency, Geert LeusAbstract:Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the graph Shift Operator. Our approach is to investigate the question of graph filtering on a graph about which we only know a model. To do this we leverage the theory of graphons proposed by L. Lovasz and B. Szegedy. We make three key contributions to the emerging field of graph signal processing. We show first that filters defined over the scaled adjacency matrix of a random graph drawn from a graphon converge to filters defined over the Fredholm integral Operator with the graphon as its kernel. Second, leveraging classical findings from the theory of the numerical solution of Fredholm integral equations, we define the Fourier-Galerkin Shift Operator. Lastly, using the Fourier-Galerkin Shift Operator, we derive a graph filter design algorithm which only depends on the graphon, and thus depends only on the probabilistic structure of the graph instead of the particular graph itself. The derived graphon filtering algorithm is verified through simulations on a variety of random graph models.
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The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain.
2017Co-Authors: Geert Leus, Santiago Segarra, Alejandro Ribeiro, Antonio G. MarquesAbstract:Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The two most important tools in GSP are the graph Shift Operator (GSO), which is a sparse matrix accounting for the topology of the graph, and the graph Fourier transform (GFT), which maps graph signals into a frequency domain spanned by a number of graph-related Fourier-like basis vectors. This alternative representation of a graph signal is denominated the graph frequency signal. Several attempts have been undertaken in order to interpret the support of this graph frequency signal, but they all resulted in a one-dimensional interpretation. However, if the support of the original signal is captured by a graph, why would the graph frequency signal have a simple one-dimensional support? That is why, for the first time, we propose an irregular support for the graph frequency signal, which we coin the dual graph. The dual GSO leads to a better interpretation of the graph frequency signal and its domain, helps to understand how the different graph frequencies are related and clustered, enables the development of better graph filters and filter banks, and facilitates the generalization of classical SP results to the graph domain.
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sampling of graph signals successive local aggregations at a single node
2015Co-Authors: Santiago Segarra, Geert Leus, Antonio G. Marques, Alejandro RibeiroAbstract:A new scheme to sample bandlimited graph signals is proposed. The signals are defined in the nodes of a graph and admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so- called graph-Shift Operator. Most of the existing works focused on using the value of the signal observed at a subset of nodes to recover the signal in the entire graph. Differently, the sampling scheme proposed here uses as input observations taken at a single node. The observations correspond to sequential applications of the graph-Shift Operator, which are linear combinations of the information gathered by the neighbors of the node. When the graph corresponds to a directed cycle, which is the support of time-varying signals, our method is equivalent to the classical sampling in the time domain. When the graph is more general, we show that the Vandermonde structure of the sampling matrix, which plays a critical role in guaranteeing recovery when sampling time-varying signals, is preserved.
I I Tupitsyn - One of the best experts on this subject based on the ideXlab platform.
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qed corrections to the p 1 2 2 p 3 2 2 fine structure in fluorinelike ions model lamb Shift Operator approach
2020Co-Authors: V M Shabaev, I I Tupitsyn, M Y Kaygorodov, Y S Kozhedub, A V Malyshev, D V MironovaAbstract:In Li et al. [Phys. Rev. A 98, 020502(R) (2018)] it was claimed that the model-potential computations of the Lamb Shift on the $^{2}P_{1/2}\ensuremath{-}^{2}P_{3/2}$ fine structure in fluorinelike uranium lead to a discrepancy between theory and experiment. Later, it was reported by Volotka et al. [Phys. Rev. A 100, 010502(R) (2019)] that ab initio QED calculation, including the first-order one-electron QED contributions and the related effects of two-electron screening, yields the result which restores the agreement between theory and experiment and strongly disagrees with the model-potential Lamb-Shift values. In the present paper, the model Lamb-Shift Operator [Shabaev et al., Phys. Rev. A 88, 012513 (2013)] is used to evaluate the QED effects on the $^{2}P_{1/2}\ensuremath{-}^{2}P_{3/2}$ fine structure in F-like ions. The calculations are performed by incorporating this Operator into the Dirac-Coulomb-Breit equation employing different methods. It is demonstrated that the methods, based on including the Lamb-Shift Operator either into the Dirac-Fock equations or into the calculations by perturbation theory, lead to the theoretical results which are in good agreement with each other and with experiment. The restriction of these results to the first order in the QED effects leads to a value which agrees with the aforementioned ab initio QED result.
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qedmod fortran program for calculating the model lamb Shift Operator
2015Co-Authors: V M Shabaev, I I Tupitsyn, V A YerokhinAbstract:We present Fortran package QEDMOD for computing the model QED Operator hQED that can be used to account for the Lamb Shift in accurate atomic-structure calculations. The package routines calculate the matrix elements of hQED with the user-specified one-electron wave functions. The Operator can be used to calculate Lamb Shift in many-electron atomic systems with a typical accuracy of few percent, either by evaluating the matrix element of hQED with the many-electron wave function, or by adding hQED to the Dirac–Coulomb–Breit Hamiltonian.
D V Mironova - One of the best experts on this subject based on the ideXlab platform.
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qed corrections to the p 1 2 2 p 3 2 2 fine structure in fluorinelike ions model lamb Shift Operator approach
2020Co-Authors: V M Shabaev, I I Tupitsyn, M Y Kaygorodov, Y S Kozhedub, A V Malyshev, D V MironovaAbstract:In Li et al. [Phys. Rev. A 98, 020502(R) (2018)] it was claimed that the model-potential computations of the Lamb Shift on the $^{2}P_{1/2}\ensuremath{-}^{2}P_{3/2}$ fine structure in fluorinelike uranium lead to a discrepancy between theory and experiment. Later, it was reported by Volotka et al. [Phys. Rev. A 100, 010502(R) (2019)] that ab initio QED calculation, including the first-order one-electron QED contributions and the related effects of two-electron screening, yields the result which restores the agreement between theory and experiment and strongly disagrees with the model-potential Lamb-Shift values. In the present paper, the model Lamb-Shift Operator [Shabaev et al., Phys. Rev. A 88, 012513 (2013)] is used to evaluate the QED effects on the $^{2}P_{1/2}\ensuremath{-}^{2}P_{3/2}$ fine structure in F-like ions. The calculations are performed by incorporating this Operator into the Dirac-Coulomb-Breit equation employing different methods. It is demonstrated that the methods, based on including the Lamb-Shift Operator either into the Dirac-Fock equations or into the calculations by perturbation theory, lead to the theoretical results which are in good agreement with each other and with experiment. The restriction of these results to the first order in the QED effects leads to a value which agrees with the aforementioned ab initio QED result.
V A Yerokhin - One of the best experts on this subject based on the ideXlab platform.
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qedmod fortran program for calculating the model lamb Shift Operator
2015Co-Authors: V M Shabaev, I I Tupitsyn, V A YerokhinAbstract:We present Fortran package QEDMOD for computing the model QED Operator hQED that can be used to account for the Lamb Shift in accurate atomic-structure calculations. The package routines calculate the matrix elements of hQED with the user-specified one-electron wave functions. The Operator can be used to calculate Lamb Shift in many-electron atomic systems with a typical accuracy of few percent, either by evaluating the matrix element of hQED with the many-electron wave function, or by adding hQED to the Dirac–Coulomb–Breit Hamiltonian.
