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Abstract The Landau–Lifshitz (LL) equation has been proposed as the classical equation to describe the dynamics of a charged particle in a strong electromagnetic field when influenced by radiation reaction. Until recently, there has been no clear experimental verification. However, aligned crystals have remedied the situation: here, as in Nielsen et al CERN NA63 Collaboration (2020 Phys. Rev. D 102 052004), we report on a quantitative experimental test of the LL equation by measuring the emission spectra of electrons and positrons penetrating aligned single crystals. The recorded spectra are in remarkable agreement with simulations based on the LL equation of motion with moderate quantum corrections for recoil and, in the case of electrons in axially aligned crystals, spin and reduced radiation intensity.
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Nonlinear steepest descent on a torus: a case study of the Landau–Lifshitz equation
Abstract We obtain rigorous large time asymptotics for the Landau–Lifshitz (LL) equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The methods presented in this paper pave the way to a rigorous analysis of other integrable equations on the torus and enable asymptotic analysis on different regimes of the LL equation.
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- Award ID(s):
- 1955265
- PAR ID:
- 10579366
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 38
- Issue:
- 4
- ISSN:
- 0951-7715
- Format(s):
- Medium: X Size: Article No. 045023
- Size(s):
- Article No. 045023
- Sponsoring Org:
- National Science Foundation
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