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Semiclassical analysis of quantum asymptotic fields in the Yukawa theory

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Semiclassical analysis of quantum asymptotic fields in the Yukawa theory. / Ammari, Zied; Falconi, Marco; Olivieri, Marco.
I: Journal of Differential Equations, Bind 357, 06.2023, s. 236-274.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Harvard

Ammari, Z, Falconi, M & Olivieri, M 2023, 'Semiclassical analysis of quantum asymptotic fields in the Yukawa theory', Journal of Differential Equations, bind 357, s. 236-274. https://doi.org/10.1016/j.jde.2023.01.037

APA

Ammari, Z., Falconi, M., & Olivieri, M. (2023). Semiclassical analysis of quantum asymptotic fields in the Yukawa theory. Journal of Differential Equations, 357, 236-274. https://doi.org/10.1016/j.jde.2023.01.037

CBE

Ammari Z, Falconi M, Olivieri M. 2023. Semiclassical analysis of quantum asymptotic fields in the Yukawa theory. Journal of Differential Equations. 357:236-274. https://doi.org/10.1016/j.jde.2023.01.037

MLA

Ammari, Zied, Marco Falconi, og Marco Olivieri. "Semiclassical analysis of quantum asymptotic fields in the Yukawa theory". Journal of Differential Equations. 2023, 357. 236-274. https://doi.org/10.1016/j.jde.2023.01.037

Vancouver

Ammari Z, Falconi M, Olivieri M. Semiclassical analysis of quantum asymptotic fields in the Yukawa theory. Journal of Differential Equations. 2023 jun.;357:236-274. doi: 10.1016/j.jde.2023.01.037

Author

Ammari, Zied ; Falconi, Marco ; Olivieri, Marco. / Semiclassical analysis of quantum asymptotic fields in the Yukawa theory. I: Journal of Differential Equations. 2023 ; Bind 357. s. 236-274.

Bibtex

@article{ee565a8bb9ac40ccbce6e2f5f1825144,
title = "Semiclassical analysis of quantum asymptotic fields in the Yukawa theory",
abstract = "In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics in the semiclassical regime ℏ→0, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes between final (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear Schr{\"o}dinger–Klein–Gordon (S-KG) equation. Thus, we rigorously link the scattering theory of the Yukawa model to that of the Schr{\"o}dinger–Klein–Gordon equation. Moreover, we prove that the asymptotic vacuum states of the Yukawa model have a phase space concentration property around classical radiationless solutions. Under further assumptions, we show that the S-KG energy admits a unique minimizer modulo symmetries and we identify exactly the semiclassical measure of Yukawa ground states. Some additional consequences of asymptotic completeness are also discussed, and some further open questions are raised.",
keywords = "Asymptotic fields, Scattering theory, Schr{\"o}dinger-Klein-Gordon equation, Semiclassical analysis, Yukawa interaction",
author = "Zied Ammari and Marco Falconi and Marco Olivieri",
note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",
year = "2023",
month = jun,
doi = "10.1016/j.jde.2023.01.037",
language = "English",
volume = "357",
pages = "236--274",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Semiclassical analysis of quantum asymptotic fields in the Yukawa theory

AU - Ammari, Zied

AU - Falconi, Marco

AU - Olivieri, Marco

N1 - Publisher Copyright: © 2023 Elsevier Inc.

PY - 2023/6

Y1 - 2023/6

N2 - In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics in the semiclassical regime ℏ→0, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes between final (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear Schrödinger–Klein–Gordon (S-KG) equation. Thus, we rigorously link the scattering theory of the Yukawa model to that of the Schrödinger–Klein–Gordon equation. Moreover, we prove that the asymptotic vacuum states of the Yukawa model have a phase space concentration property around classical radiationless solutions. Under further assumptions, we show that the S-KG energy admits a unique minimizer modulo symmetries and we identify exactly the semiclassical measure of Yukawa ground states. Some additional consequences of asymptotic completeness are also discussed, and some further open questions are raised.

AB - In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics in the semiclassical regime ℏ→0, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes between final (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear Schrödinger–Klein–Gordon (S-KG) equation. Thus, we rigorously link the scattering theory of the Yukawa model to that of the Schrödinger–Klein–Gordon equation. Moreover, we prove that the asymptotic vacuum states of the Yukawa model have a phase space concentration property around classical radiationless solutions. Under further assumptions, we show that the S-KG energy admits a unique minimizer modulo symmetries and we identify exactly the semiclassical measure of Yukawa ground states. Some additional consequences of asymptotic completeness are also discussed, and some further open questions are raised.

KW - Asymptotic fields

KW - Scattering theory

KW - Schrödinger-Klein-Gordon equation

KW - Semiclassical analysis

KW - Yukawa interaction

UR - http://www.scopus.com/inward/record.url?scp=85148005884&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2023.01.037

DO - 10.1016/j.jde.2023.01.037

M3 - Journal article

AN - SCOPUS:85148005884

VL - 357

SP - 236

EP - 274

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -