The response field and the saddle points of quantum mechanical path integrals

Gozzi, E.; Pagani, Carlo; Reuter, Martin

doi:10.1016/j.aop.2021.168457

Cited by 3 publications

(1 citation statement)

References 42 publications

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“…In this setting, the diffractive limit corresponds to the application of perturbative methods resulting in the Feynman rules, whereas the refractive limit corresponds to nonperturbative methods such as the use of instantons and the study of (complex) classical trajectories. The tools of Picard-Lefschetz theory, which we use here to evaluate the Kirchoff-Fresnel integral, have been recently used to evaluate the Feynman path integral to reinterpret phenomena in quantum mechanics (Turok 2014;Cherman & Unsal 2014;Tanizaki & Koike 2014;Gozzi et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

Jow¹,

Pen²,

Feldbrugge³

2022

Preprint

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Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Diffractive optics is characterized by a perturbative expansion of the Kirchhoff-Fresnel diffraction integral, while refractive optics is characterized by the stationary phase approximation. Previously, it has been assumed that the Fresnel scale, 𝑅 𝐹 , is the relevant physical scale that separates these two regimes. With the recent introduction of Picard-Lefschetz theory to the field of lensing, it has become possible to generalize the refractive description of discrete images to all wave parameters, and, in particular, exactly evaluate the diffraction integral at all frequencies. In this work, we assess the regimes of validity of refractive and diffractive approximations for a simple one-dimensional lens model through comparison with this exact evaluation. We find that, contrary to previous assumptions, the true separation scale between these regimes is given by 𝑅 𝐹 / √ 𝜅, where 𝜅 is the convergence of the lens. Thus, when the lens is strong, refractive optics can hold for arbitrarily small scales. We also argue that intensity variations in diffractive optics are generically small, which has implications for the study of strong diffractive scintillation (DISS).

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Section: Introductionmentioning

confidence: 99%

Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

Jow¹,

Pen²,

Feldbrugge³

2022

Preprint

View full text Add to dashboard Cite

show abstract

Time evolution of density matrices as a theory of random surfaces

Pagani

Reuter

2023

Annals of Physics

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Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

Jow,

Pen,

Feldbrugge

2023

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Previously, it has been assumed that the Fresnel scale, RF, is the relevant physical scale that separates these two regimes. With the recent introduction of Picard-Lefschetz theory to the field of lensing, it has become possible to generalize the refractive description of discrete images to all wave parameters, and, in particular, exactly evaluate the diffraction integral at all frequencies. In this work, we assess the regimes of validity of refractive and diffractive approximations for a simple one-dimensional lens model through comparison with this exact evaluation. We find that, contrary to previous assumptions, the true separation scale between these regimes is given by $R_F/\sqrt{\kappa }$, where κ is the convergence of the lens. Thus, when the lens is strong, refractive optics can hold for arbitrarily small scales. We also argue that intensity variations in diffractive optics are generically small, which has implications for the study of strong diffractive scintillation (DISS).

show abstract

The response field and the saddle points of quantum mechanical path integrals

Cited by 3 publications

References 42 publications

Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

Time evolution of density matrices as a theory of random surfaces

Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

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