Solving the Spectral Problem via the Periodic Boundary Approximation in \(\phi^6\) Theory

In \(\phi^6\) theory, the resonance scattering structure is triggered by the so-calls delocalized modes trapped between the \(\bar{K}K\) pair. The frequencies and configurations of such modes depend on the \(\bar{K}K\) half-separation 2\(a\), can be derived from the Schr\"{o}dinger-like equatio...

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Bibliographic Details
Published inarXiv.org
Main Authors Long, Lingxiao, Jiang, Yunguo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.04.2024
Subjects
Approximation
Boundary conditions
Configurations
Mathematical analysis
Resonance scattering
Separation
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Summary:In \(\phi^6\) theory, the resonance scattering structure is triggered by the so-calls delocalized modes trapped between the \(\bar{K}K\) pair. The frequencies and configurations of such modes depend on the \(\bar{K}K\) half-separation 2\(a\), can be derived from the Schr\"{o}dinger-like equation. We propose to use the periodic boundary conditions to connect the localized and delocalized modes, and use periodic boundary approximation (PBA) to solve the spectrum analytically. In detail, we derive the explicit form of frequencies, configurations and spectral wall locations of the delocalized modes. We test the analytical prediction with the numerical simulation of the Schr\"{o}dinger-like equation, and obtain astonishing agreement between them at the long separation regime.
ISSN:2331-8422
DOI:10.48550/arxiv.2404.13310