Atomic and Molecular Complex Resonances from Real Eigenvalues Using Standard (Hermitian) Electronic Structure Calculations

Landau, Arie; Haritan, Idan; Kaprálová-Žďánská, Petra Ruth; Moiseyev, Nimrod

doi:10.1021/acs.jpca.5b10685

Cited by 40 publications

(85 citation statements)

References 48 publications

(177 reference statements)

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“…Its k = 0 limit, which yields the grand potential, is numerically evolved via a flow equation from the classical action at a large scale Λ, thereby including quantum and thermal fluctuations. In a similar fashion the (inverse) single-particle propagators, which determine the spectral properties, can be obtained by solving flow equations for the second derivative of the effective action, Γ (2) k . The spectral function is then given as…”

Section: Identification Of Decay Thresholds From Numerical Calculatedmentioning

confidence: 99%

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Threshold energies and poles for hadron physical problems by a model-independent universal algorithm

et al. 2017

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In this work we show how by using a Padé type analytical continuation scheme, based on the Schlessinger point method, it is possible to find higher production thresholds in hadron physical problems. Recently, an extension of this numerical approach to the complex energy plane enabled the calculations of auto-ionization decay resonance poles in atomic and molecular systems. Here we use this so-called Resonances via Padé (RVP) method, to show its convergence beyond the singular point in hadron physical problems. In order to demonstrate the capabilities of the RVP method, two illustrations for the ability to identify singularities and branch points are given. In addition, two applications for hadron physical problems are given. In the first one, we identify the decay thresholds from a numerically calculated spectral function. In the second one, we use experimental data. First, we calculate the resonance pole of the f 0 (500) or σ meson using the S 0 partial wave amplitude for ππ scattering in very good agreement with the literature. Second, we use data on the cross section ratio R(s) for e + e − collisions and discuss the prediction of decay thresholds which proves to be difficult if the data is noisy.

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Section: Identification Of Decay Thresholds From Numerical Calculatedmentioning

confidence: 99%

“…In this letter we introduce a method that was originally developed for the calculation of auto-ionization resonances in quantum chemistry [2][3][4] to the field of hadron physics. This method is model-independent, easy to use and has a broad range of applicability.…”

Section: Introductionmentioning

confidence: 99%

Threshold energies and poles for hadron physical problems by a model-independent universal algorithm

et al. 2017

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“…While all three methods have been used and tested in the literature before, see e.g. [12] for MEM and the SPM in the context of estimating the optical conductivity in a condensed matter system, [13,14,15,16,17,18,19] for the SPM as a numerical analytic continuation technique in various situations, [20,21] for the MEM, and [22] for the BG method, the SP method has only rarely been used in a QCD setting and is applied for example to lattice QCD data for the first time in this work to our knowledge.…”

Section: Introductionmentioning

confidence: 99%

Numerical analytic continuation of Euclidean data

Tripolt

Gubler

Ulybyshev

et al. 2019

Computer Physics Communications

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In this work we present a direct comparison of three different numerical analytic continuation methods: the Maximum Entropy Method, the Backus-Gilbert method and the Schlessinger point or Resonances Via Padé method. First, we perform a benchmark test based on a model spectral function and study the regime of applicability of these methods depending on the number of input points and their statistical error. We then apply these methods to more realistic examples, namely to numerical data on Euclidean propagators obtained from a Functional Renormalization Group calculation, to data from a lattice Quantum Chromodynamics simulation and to data obtained from a tight-binding model for graphene in order to extract the electrical conductivity.

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“…This approach although very robust requires a large number of function evaluation. The branch point singularity is also exploited in [28,29] using multipoint Padé approximants. Here, the distribution of poles and zeros of the Padé approximated function lies along the branch cut where the function is multivalued [30,31] which allows to give a first estimate of the EP in the complex plane.…”

Section: Introductionmentioning

confidence: 99%

A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides

Nennig

Perrey‐Debain

2020

Journal of Computational Physics

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A numerical algorithm is proposed to explore in a systematic way the trajectories of the eigenvalues of non-Hermitian matrices in the parametric space and exploit this in order to find the locations of defective eigenvalues in the complex plane. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems.The method requires the computation of successive derivatives of two selected eigenvalues with respect to the parameter so that, after recombination, regular functions can be constructed. This algebraic manipulation permits the localization of exceptional points (EP), using standard root-finding algorithms and the computation of the associated Puiseux series up to an arbitrary order. This representation, which is associated with the topological structure of Riemann surfaces allows to efficiently approximate the selected pair in a certain neighbourhood of the EP.Practical applications dealing with guided acoustic waves propagating in straight ducts with absorbing walls and in periodic guiding structures are given to illustrate the versatility of the proposed method and its ability to handle large size matrices arising from finite element discretization techniques. The fact that EPs are associated with optimal dissipative treatments in the sense that they should provide best modal attenuation is also discussed.

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Atomic and Molecular Complex Resonances from Real Eigenvalues Using Standard (Hermitian) Electronic Structure Calculations

Cited by 40 publications

References 48 publications

Threshold energies and poles for hadron physical problems by a model-independent universal algorithm

Threshold energies and poles for hadron physical problems by a model-independent universal algorithm

Numerical analytic continuation of Euclidean data

A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides

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