Stark effect in low-dimensional hydrogen

Pedersen, Thomas Garm; Mera, H.; Nikolić, Branislav K.

doi:10.1103/physreva.93.013409

Cited by 45 publications

(90 citation statements)

References 25 publications

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“…Recently we have introduced hypergeometric resummation-a technique that enables summation on the cut using only a small number of expansion coefficients [5][6][7]46,47]. Various flavors of this technique were applied to a variety of problems with good results: in particular, it was shown how one could use low order data to derive accurate approximations to the decay rate in Stark-type problems [5][6][7].…”

Section: B Hypergeometric Resummationmentioning

confidence: 99%

“…Various flavors of this technique were applied to a variety of problems with good results: in particular, it was shown how one could use low order data to derive accurate approximations to the decay rate in Stark-type problems [5][6][7]. Typically the idea is to use hypergeometric functions to analytically continue divergent series.…”

Section: B Hypergeometric Resummationmentioning

confidence: 99%

“…We will then briefly review alternatives to Padé and Borel-Padé that make use of analytic continuation functions with a built-in branch cut, in particular the hypergeometric resummation method we introduced in Refs. [5][6][7]. After reviewing these other approaches we finally introduce the algorithm to calculate Meijer-G approximants and highlight various properties that make this method well suited to yield inexpensive-and yet accurate-low order approximations to the sum of a divergent series.…”

Section: Meijer-g Approximantsmentioning

confidence: 99%

“…The hypergeometric approximants we introduced in Refs. [5][6][7]46] have a number of clear limitations, which we overcome in this work and which we enumerate below:…”

Section: B Hypergeometric Resummationmentioning

confidence: 99%

“…This is exemplified by the asymptotic series for the LoSurdo-Stark effect of atoms and molecules where first-and second-order terms match measurements well, but only for very weak electric fields [3], or by high precision calculations of multiloop Feynman diagrams in quantum electrodynamics [4]where the fine-structure constant is small. On the other hand, extracting physically relevant information from the asymptotic series at larger coupling constants calls, almost invariably, for resummation techniques as exemplified by the LoSurdo-Stark effect [5,6] and field assisted excitonic ionization in layered materials [7], anharmonic oscillators in quantum mechanics [8,9], ϕ 4 theory in QFT [10], quantum chromodynamics [11], string perturbation theory [12,13], and diagrammatic Monte Carlo techniques in condensed matter physics [14]. Given the ubiquity of divergent series in physics, research on summation techniques remains an active research area [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Fast summation of divergent series and resurgent transseries from Meijer- G approximants

2018

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We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015)]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ 4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N-vector model; ϕ 4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one-and two-instanton contributions in the quantum-mechanical double-well problem.

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Section: B Hypergeometric Resummationmentioning

confidence: 99%

Section: B Hypergeometric Resummationmentioning

confidence: 99%

Section: Meijer-g Approximantsmentioning

confidence: 99%

“…The hypergeometric approximants we introduced in Refs. [5][6][7]46] have a number of clear limitations, which we overcome in this work and which we enumerate below:…”

Section: B Hypergeometric Resummationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast summation of divergent series and resurgent transseries from Meijer- G approximants

2018

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Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

Kamban

Christensen

Søndergaard

et al. 2020

Physica Status Solidi (b)

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A finite-difference time-domain (FDTD) scheme with perfectly matched layers (PMLs) is considered for solving the time-dependent Schrödinger equation and simulating the laser-induced ionization of two systems: 1) an electron initially bound to a 1D δ potential and 2) excitons in carbon nanotubes (CNTs). The performance of PMLs based on different absorption functions is compared, where slowly growing functions are found to be preferable. PMLs are shown to be able to reduce the computational domain, and thus the required numerical resources, by several orders of magnitude. This is demonstrated by testing the proposed method against an FDTD approach without PMLs and a very large computational domain. It is shown that PMLs outperform the well-known exterior complex scaling (ECS) technique for short-range potentials when implemented in FDTD. For long-range potentials such as in CNTs, however, ECS performs better than PMLs when propagating over many periods.

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Theoretical Methods for Excitonic Physics in 2D Materials

Quintela

Henriques

Tenório

et al. 2022

Physica Status Solidi (b)

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In this Perspective article, the reader is introduced to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semianalytical, or numeric. All the details associated with the different methods are made explicit, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The Perspective starts with a variational method and ends with a simple semianalytical approach to solve the Bethe–Salpeter equation (BSE) in gapped 2D materials. For the first methods addressed in this Perspective, the authors focus on a single layer of hexagonal boron nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe–Salpeter method, the biased bilayer graphene, which presents a tunable bandgap is chosen. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution in a context that can be easily generalized to more complex systems or to apply it to simpler models.

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Stark effect in low-dimensional hydrogen

Cited by 45 publications

References 25 publications

Fast summation of divergent series and resurgent transseries from Meijer- G approximants

Fast summation of divergent series and resurgent transseries from Meijer- G approximants

Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

Theoretical Methods for Excitonic Physics in 2D Materials

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