The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Tanguy Altherr - One of the best experts on this subject based on the ideXlab platform.
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resummation of Perturbation Series in non equilibrium scalar field theory
Physics Letters B, 1995Co-Authors: Tanguy AltherrAbstract:Abstract The general behaviour of Perturbation Series in non-equilibrium scalar field theory is analysed in some detail, with a particular emphasis on the “pathological terms”, generated by multiple products of δ-functions. Using an intuitive regularization method, it is shown that these terms give large contributions at all orders, even when considering small deviations from equilibrium. Fortunately, these terms can also be resummed and I give the general expressions for the resummed propagators in non-equilibrium scalar field theory, regardless of the size of deviations from equilibrium.
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problems of Perturbation Series in non equilibrium quantum field theories
Physics Letters B, 1994Co-Authors: Tanguy Altherr, D SeibertAbstract:Abstract In the standard framework of non-equilibrium quantum field theories, the pinch singularities associated to multiple products of δ-finctions do not cancel in a perturbative expansion unless the particle distributions are those for a system in thermal and chemical equilibrium.
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resummation of Perturbation Series in non equilibrium scalar field theory
arXiv: High Energy Physics - Phenomenology, 1994Co-Authors: Tanguy AltherrAbstract:The general behaviour of Perturbation Series in non-equilibrium scalar field theory is analysed in some detail, with a particular emphasis on the ``pathological terms'', generated by multiple products of $\delta$-functions. Using an intuitive regularization method, it is shown that these terms give large contributions at all orders, even when considering small deviations from equilibrium. Fortunately, these terms can also be resummed and I give the general expressions for the resummed propagators in non-equilibrium scalar field theory, regardless of the size of deviations from equilibrium.
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problems of Perturbation Series in non equilibrium quantum field theories
arXiv: High Energy Physics - Phenomenology, 1994Co-Authors: Tanguy Altherr, D SeibertAbstract:In the standard framework of non-equilibrium quantum field theories, the pinch singularities associated to multiple products of $\delta$-functions do not cancel in a perturbative expansion unless the particle distributions are those for a system in thermal and chemical equilibrium.
Ulrich D Jentschura - One of the best experts on this subject based on the ideXlab platform.
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resummation of the divergent Perturbation Series for a hydrogen atom in an electric field
Physical Review A, 2001Co-Authors: Ulrich D JentschuraAbstract:We consider the resummation of the Perturbation Series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power Series in the electric-field strength. The Perturbation Series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented that appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pad\'e resummation method, with an additional improvement due to utilization of the leading renormalon poles, and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pad\'e approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.
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resummation of qed Perturbation Series by sequence transformations and the prediction of perturbative coefficients
Physical Review Letters, 2000Co-Authors: Ulrich D Jentschura, Jens Becher, Ernst Joachim Weniger, G SoffAbstract:We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values of a finite number of perturbative coefficients. The results obtained in this way are for alternating Series superior to those obtained using Pade approximants. The nonlinear sequence transformation fulfills an accuracy-through-order relation and can be used to predict perturbative coefficients. In many cases, these predictions are closer to available analytic results than predictions obtained using the Pade method.
Peter R Surjan - One of the best experts on this subject based on the ideXlab platform.
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application of the cauchy integral formula as a tool of analytic continuation for the resummation of divergent Perturbation Series
Journal of Chemical Physics, 2019Co-Authors: Zsuzsanna E Mihalka, Agnes Szabados, Peter R SurjanAbstract:Previous attempts to the resummation of divergent power Series by means of analytic continuation are improved applying the Cauchy integral formula for complex functions. The idea is tested on divergent Moller-Plesset Perturbation expansions of the electron correlation energy. In particular, the potential curve of the LiH molecule is computed from single reference MPn results which are divergent for bond distances larger than 3.6 A. Preliminary results for the Hartree-Fock molecule are also tabulated.
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the inverse boundary value problem application in many body Perturbation theory
Theoretical Chemistry Accounts, 2018Co-Authors: Peter R Surjan, Zsuzsanna E Mihalka, Agnes SzabadosAbstract:An algorithm is discussed to find boundary values to partial differential equations in the knowledge of the solution of that equation inside a part of the domain enclosed by the boundary. The method is used as a tool of analytic continuation to complement a method proposed recently (Mihalka and Surjan, in Phys Rev A 96:062106, 2017) for finding resummed values of divergent Perturbation Series.
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effect of partitioning on the convergence properties of the rayleigh schrodinger Perturbation Series
Journal of Chemical Physics, 2017Co-Authors: Zsuzsanna E Mihalka, Agnes Szabados, Peter R SurjanAbstract:Convergence features of the Rayleigh-Schrodinger Perturbation theory (PT) strongly depend on the partitioning applied. We investigate the large order behavior of the Moller-Plesset and Epstein Nesbet partitionings in comparison with a less known partitioning obtained by level shift parameters minimizing the norm of operator Q^W^, with W^ being the Perturbation operator while Q standing for the reduced resolvent of the zero order Hamiltonian H^0. Numerical results, presented for molecular systems for the first time, indicate that it is possible to find level shift parameters in this way which convert divergent Perturbation expansions to convergent ones in some cases. Besides numerical calculations of high-order PT terms, convergence radii of the corresponding Perturbation expansions are also estimated using quadratic Pade approximants.
Achim Schwenk - One of the best experts on this subject based on the ideXlab platform.
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from weak to strong constrained extrapolation of Perturbation Series with applications to dilute fermi systems
Physical Review Research, 2020Co-Authors: C Wellenhofer, Daniel R Phillips, Achim SchwenkAbstract:This work develops a method for extrapolating a Perturbation Series from weak to strong coupling using low-order constraints from the strong-coupling regime.
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from weak to strong constrained extrapolation of Perturbation Series with applications to dilute fermi systems
arXiv: Quantum Gases, 2020Co-Authors: C Wellenhofer, Daniel R Phillips, Achim SchwenkAbstract:We develop a method that uses truncation-order-dependent re-expansions constrained by generic strong-coupling information to extrapolate Perturbation Series to the nonperturbative regime. The method is first benchmarked against a zero-dimensional model field theory and then applied to the dilute Fermi gas in one and three dimensions. Overall, our method significantly outperforms Pade and Borel extrapolations in these examples. The results for the ground-state energy of the three-dimensional Fermi gas are robust with respect to changes of the form of the re-expansion and compare well with quantum Monte Carlo simulations throughout the BCS regime and beyond.
Agnes Szabados - One of the best experts on this subject based on the ideXlab platform.
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application of the cauchy integral formula as a tool of analytic continuation for the resummation of divergent Perturbation Series
Journal of Chemical Physics, 2019Co-Authors: Zsuzsanna E Mihalka, Agnes Szabados, Peter R SurjanAbstract:Previous attempts to the resummation of divergent power Series by means of analytic continuation are improved applying the Cauchy integral formula for complex functions. The idea is tested on divergent Moller-Plesset Perturbation expansions of the electron correlation energy. In particular, the potential curve of the LiH molecule is computed from single reference MPn results which are divergent for bond distances larger than 3.6 A. Preliminary results for the Hartree-Fock molecule are also tabulated.
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the inverse boundary value problem application in many body Perturbation theory
Theoretical Chemistry Accounts, 2018Co-Authors: Peter R Surjan, Zsuzsanna E Mihalka, Agnes SzabadosAbstract:An algorithm is discussed to find boundary values to partial differential equations in the knowledge of the solution of that equation inside a part of the domain enclosed by the boundary. The method is used as a tool of analytic continuation to complement a method proposed recently (Mihalka and Surjan, in Phys Rev A 96:062106, 2017) for finding resummed values of divergent Perturbation Series.
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effect of partitioning on the convergence properties of the rayleigh schrodinger Perturbation Series
Journal of Chemical Physics, 2017Co-Authors: Zsuzsanna E Mihalka, Agnes Szabados, Peter R SurjanAbstract:Convergence features of the Rayleigh-Schrodinger Perturbation theory (PT) strongly depend on the partitioning applied. We investigate the large order behavior of the Moller-Plesset and Epstein Nesbet partitionings in comparison with a less known partitioning obtained by level shift parameters minimizing the norm of operator Q^W^, with W^ being the Perturbation operator while Q standing for the reduced resolvent of the zero order Hamiltonian H^0. Numerical results, presented for molecular systems for the first time, indicate that it is possible to find level shift parameters in this way which convert divergent Perturbation expansions to convergent ones in some cases. Besides numerical calculations of high-order PT terms, convergence radii of the corresponding Perturbation expansions are also estimated using quadratic Pade approximants.