The energy-frequency diagram of the (1+1)-dimensional Φ4 oscillon

• Published in: The journal of high energy physics 2024-10, Vol.2024 (10), p.136-24, Article 136
• Main Authors: Alexeeva, N. V., Barashenkov, I. V., Dika, Alain, De Sousa, Raphael
• Format: Article
• Language: English
• Subjects: Applied mathematics; Approximation; Boundary value problems; Classical and Quantum Gravitation; Elementary Particles; Energy; Field Theories in Lower Dimensions; Mathematical analysis; Numerical analysis; Oscillons; Periodic functions; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Radiation; Regular Article - Theoretical Physics; Relativity Theory; Simulation; Solitons Monopoles and Instantons; Standing waves; String Theory; Symmetry; Two dimensional analysis
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2024)136

A bstract Two different methods are used to study the existence and stability of the (1+1)-dimensional Φ 4 oscillon. The variational technique approximates it by a periodic function with a set of adiabatically changing parameters. An alternative approach treats oscillons as standing waves in a finite-size box; these are sought as solutions of a boundary-value problem on a two-dimensional domain. The numerical analysis reveals that the standing wave’s energy-frequency diagram is fragmented into disjoint segments with ω n +1 < ω < ω n , where ω n = ω 0 /( n + 1), n = 0, 1, 2, . . ., and ω 0 is the endpoint of the continuous spectrum (mass threshold of the model). The variational approximation involving the first, zeroth and second harmonic components provides an accurate description of the oscillon with the frequency in ( ω 1 , ω 0 ), but breaks down as ω falls out of that interval.