The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
Andrei Gabrielov - One of the best experts on this subject based on the ideXlab platform.
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Analytic Continuation of Eigenvalues of a Quartic Oscillator
Communications in Mathematical Physics, 2009Co-Authors: Alexandre Eremenko, Andrei GabrielovAbstract:We consider the Schrödinger operator on the real line with even quartic potential x ^4 + α x ^2 and study Analytic Continuation of eigenvalues, as functions of parameter α . We prove several properties of this Analytic Continuation conjectured by Bender, Wu, Loeffel and Martin. 1. All eigenvalues are given by branches of two multi-valued Analytic functions, one for even eigenfunctions and one for odd ones. 2. The only singularities of these multi-valued functions in the complex α -plane are algebraic ramification points, and there are only finitely many singularities over each compact subset of the α -plane.
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Analytic Continuation of eigenvalues of a quartic oscillator
Communications in Mathematical Physics, 2008Co-Authors: Alexandre Eremenko, Andrei GabrielovAbstract:We consider the Schrodinger operator on the real line with even quartic potential and study Analytic Continuation of eigenvalues, as functions of the coefficient of the potential. We prove several properties of this Analytic Continuation conjectured by Bender, Wu, Loeffel and Martin. 1. All eigenvalues are given by branches of two multi-valued Analytic functions, one for even eigenfunctions and one for odd ones. 2. The only singularities of these multi-valued functions in the complex plane are algebraic ramification points, and there are only finitely many singularities over each compact subset of the plane.
Oleg V Yazyev - One of the best experts on this subject based on the ideXlab platform.
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artificial neural network approach to the Analytic Continuation problem
Physical Review Letters, 2020Co-Authors: Romain Fournier, Lei Wang, Oleg V YazyevAbstract:Inverse problems are encountered in many domains of physics, with Analytic Continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the Analytic Continuation problem is ill defined and currently no Analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum Monte Carlo calculations and simulated Green's function data demonstrates its high accuracy. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data, while performing significantly better when the noise strength increases. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy method.
Alexandre Eremenko - One of the best experts on this subject based on the ideXlab platform.
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Analytic Continuation of Eigenvalues of a Quartic Oscillator
Communications in Mathematical Physics, 2009Co-Authors: Alexandre Eremenko, Andrei GabrielovAbstract:We consider the Schrödinger operator on the real line with even quartic potential x ^4 + α x ^2 and study Analytic Continuation of eigenvalues, as functions of parameter α . We prove several properties of this Analytic Continuation conjectured by Bender, Wu, Loeffel and Martin. 1. All eigenvalues are given by branches of two multi-valued Analytic functions, one for even eigenfunctions and one for odd ones. 2. The only singularities of these multi-valued functions in the complex α -plane are algebraic ramification points, and there are only finitely many singularities over each compact subset of the α -plane.
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Analytic Continuation of eigenvalues of a quartic oscillator
Communications in Mathematical Physics, 2008Co-Authors: Alexandre Eremenko, Andrei GabrielovAbstract:We consider the Schrodinger operator on the real line with even quartic potential and study Analytic Continuation of eigenvalues, as functions of the coefficient of the potential. We prove several properties of this Analytic Continuation conjectured by Bender, Wu, Loeffel and Martin. 1. All eigenvalues are given by branches of two multi-valued Analytic functions, one for even eigenfunctions and one for odd ones. 2. The only singularities of these multi-valued functions in the complex plane are algebraic ramification points, and there are only finitely many singularities over each compact subset of the plane.
Romain Fournier - One of the best experts on this subject based on the ideXlab platform.
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artificial neural network approach to the Analytic Continuation problem
Physical Review Letters, 2020Co-Authors: Romain Fournier, Lei Wang, Oleg V YazyevAbstract:Inverse problems are encountered in many domains of physics, with Analytic Continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the Analytic Continuation problem is ill defined and currently no Analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum Monte Carlo calculations and simulated Green's function data demonstrates its high accuracy. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data, while performing significantly better when the noise strength increases. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy method.
Xavier Blase - One of the best experts on this subject based on the ideXlab platform.
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Robust Analytic-Continuation Approach to Many-Body GW Calculations
Journal of Chemical Theory and Computation, 2020Co-Authors: Ivan Duchemin, Xavier BlaseAbstract:The Analytic Continuation of the GW self-energy from the imaginary to the real energy axis is a central difficulty for approaches exploiting the favourable properties of response functions at imaginary frequencies. Within a scheme merging contour-deformation and Analytic-Continuation techniques, we show on the basis of extensive calculations for large molecular sets that it is preferable to perform an Analytic Continuation of the dynamically screened Coulomb potential W rather than the much more structured self-energy operator. The case of states lying far away from the gap, including core states, is addressed by generalizing the Analytic Continuation scheme, accounting further for quasiparticle lifetimes.