期刊论文详细信息
Symmetry Integrability and Geometry-Methods and Applications
Breathing Modes, Quartic Nonlinearities and Effective Resonant Systems
article
Oleg Evnin1 
[1] Department of Physics, Faculty of Science, Chulalongkorn University
关键词: weak nonlinearity;    multiscale dynamics;    time-periodic energy transfer;   
DOI  :  10.3842/SIGMA.2020.034
来源: National Academy of Science of Ukraine
PDF
【 摘 要 】

A breathing mode in a Hamiltonian system is a function on the phase space whose evolution is exactly periodic for all solutions of the equations of motion. Such breathing modes are familiar from nonlinear dynamics in harmonic traps or anti-de Sitter spacetimes, with applications to the physics of cold atomic gases, general relativity and high-energy physics. We discuss the implications of breathing modes in weakly nonlinear regimes, assuming that both the Hamiltonian and the breathing mode are linear functions of a coupling parameter, taken to be small. For a linear system, breathing modes dictate resonant relations between the normal frequencies. These resonant relations imply that arbitrarily small nonlinearities may produce large effects over long times. The leading effects of the nonlinearities in this regime are captured by the corresponding effective resonant system. The breathing mode of the original system translates into an exactly conserved quantity of this effective resonant system under simple assumptions that we explicitly specify. If the nonlinearity in the Hamiltonian is quartic in the canonical variables, as is common in many physically motivated cases, further consequences result from the presence of the breathing modes, and some nontrivial explicit solutions of the effective resonant system can be constructed. This structure explains in a uniform fashion a series of results in the recent literature where this type of dynamics is realized in specific Hamiltonian systems, and predicts other situations of interest where it should emerge.

【 授权许可】

Unknown   

【 预 览 】
附件列表
Files Size Format View
RO202106300000692ZK.pdf 346KB PDF download
  文献评价指标  
  下载次数:2次 浏览次数:0次