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Nanna Holmgaard List - One of the best experts on this subject based on the ideXlab platform.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from relativistic theory
Journal of Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:: We present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light-matter Interaction Operator and the two others on a truncated Interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated Interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4, when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter Interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter Interaction.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from relativistic theory
arXiv: Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:We present three schemes to go beyond the electric-dipole approximation in X-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light-matter Interaction Operator, and the two others on a truncated Interaction within Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion point are related by a gauge transformation, provided the expansion is not truncated. This suggests that the observed gauge-origin dependence in multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated Interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl$_4$, when calculated to second order in the wave vector, become negative, but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter Interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter Interaction.
Trond Saue - One of the best experts on this subject based on the ideXlab platform.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from relativistic theory
Journal of Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:: We present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light-matter Interaction Operator and the two others on a truncated Interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated Interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4, when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter Interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter Interaction.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from relativistic theory
arXiv: Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:We present three schemes to go beyond the electric-dipole approximation in X-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light-matter Interaction Operator, and the two others on a truncated Interaction within Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion point are related by a gauge transformation, provided the expansion is not truncated. This suggests that the observed gauge-origin dependence in multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated Interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl$_4$, when calculated to second order in the wave vector, become negative, but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter Interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter Interaction.
Robert Lilow - One of the best experts on this subject based on the ideXlab platform.
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cosmic structure formation with kinetic field theory
Annalen der Physik, 2019Co-Authors: Matthias Bartelmann, Elena Kozlikin, Robert Lilow, Carsten Littek, Felix Fabis, Ivan Kostyuk, Celia Viermann, Lavinia Heisenberg, Sara KonradAbstract:Kinetic field theory (KFT) is a statistical field theory for an ensemble of classical point particles in or out of equilibrium. Its application to cosmological structure formation is reviewed. Beginning with the construction of a generating functional, it is described in detail how the theory needs to be adapted to an expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, three approaches are developed to nonlinear cosmic structures, which rest either on expanding an Interaction Operator, averaging the Interaction term, or resumming perturbation terms. An analytic, parameter‐free equation for the nonlinear cosmic power spectrum is presented. It is explained how density profiles of bound structures and velocity power spectra can be derived from the theory. It is clarified how KFT relates to the BBGKY hierarchy. Kinetic field theory is then applied to fluids, reformulating KFT in terms of macroscopic quantities. The resulting resummation scheme is used to describe mixtures of gas and dark matter. Finally, it is discussed how KFT can be combined with modified theories of gravity. As an example for a noncosmological application, results are shown on the spatial correlation function of cold Rydberg atoms derived from KFT.
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cosmic structure formation with kinetic field theory
arXiv: Cosmology and Nongalactic Astrophysics, 2019Co-Authors: Matthias Bartelmann, Elena Kozlikin, Robert Lilow, Carsten Littek, Felix Fabis, Ivan Kostyuk, Celia Viermann, Lavinia HeisenbergAbstract:Kinetic Field Theory (KFT) is a statistical field theory for an ensemble of point-like classical particles in or out of equilibrium. We review its application to cosmological structure formation. Beginning with the construction of the generating functional of the theory, we describe in detail how the theory needs to be adapted to reflect the expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, we develop three main approaches to non-linear, late-time cosmic structures, which rest either on the Taylor expansion of an Interaction Operator, suitable averaging procedures for the Interaction term, or a resummation of perturbation terms. We show how an analytic, parameter-free equation for the non-linear cosmic power spectrum can be derived. We explain how the theory can be used to derive the density profile of gravitationally bound structures and use it to derive power spectra of cosmic velocity densities. We further clarify how KFT relates to the BBGKY hierarchy. We then proceed to apply kinetic field theory to fluids, introduce a reformulation of KFT in terms of macroscopic quantities which leads to a resummation scheme, and use this to describe mixtures of gas and dark matter. We discuss how KFT can be applied to study cosmic structure formation with modified theories of gravity. As an example for an application to a non-cosmological particle ensemble, we show results on the spatial correlation function of cold Rydberg atoms derived from KFT.
R N Faustov - One of the best experts on this subject based on the ideXlab platform.
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the contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen
Physics of Particles and Nuclei Letters, 2017Co-Authors: A E Dorokhov, Nikolai Kochelev, A P Martynenko, F A Martynenko, R N FaustovAbstract:In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the Interaction Operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into π,η mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.
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the contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen
arXiv: High Energy Physics - Phenomenology, 2017Co-Authors: A E Dorokhov, Nikolai Kochelev, A P Martynenko, F A Martynenko, R N FaustovAbstract:In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the Interaction Operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into $\pi$, $\eta$ mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.
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radiative nonrecoil nuclear finite size corrections of order α zα 5 to the hyperfine splitting of s states in muonic hydrogen
Physics Letters B, 2014Co-Authors: R N Faustov, A P Martynenko, G A Martynenko, V V SorokinAbstract:Abstract On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order α ( Z α ) 5 to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle Interaction Operator we employ the projection Operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried–Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used.
A P Martynenko - One of the best experts on this subject based on the ideXlab platform.
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the contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen
Physics of Particles and Nuclei Letters, 2017Co-Authors: A E Dorokhov, Nikolai Kochelev, A P Martynenko, F A Martynenko, R N FaustovAbstract:In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the Interaction Operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into π,η mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.
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the contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen
arXiv: High Energy Physics - Phenomenology, 2017Co-Authors: A E Dorokhov, Nikolai Kochelev, A P Martynenko, F A Martynenko, R N FaustovAbstract:In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the Interaction Operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into $\pi$, $\eta$ mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.
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radiative nonrecoil nuclear finite size corrections of order α zα 5 to the hyperfine splitting of s states in muonic hydrogen
Physics Letters B, 2014Co-Authors: R N Faustov, A P Martynenko, G A Martynenko, V V SorokinAbstract:Abstract On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order α ( Z α ) 5 to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle Interaction Operator we employ the projection Operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried–Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used.