A Direct Derivation of the Dark Soliton Excitation Energy
Li-Chen Zhao1,2 , Yan-Hong Qin1,2 , Wen-Long Wang3** , Zhan-Ying Yang1,2
1 School of Physics, Northwest University, Xi'an 7101272 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 7101273 College of Physics, Sichuan University, Chengdu 610065
Abstract ：Dark solitons are common topological excitations in a wide array of nonlinear waves. The dark soliton excitation energy is crucial for exploring dark soliton dynamics and is necessarily calculated in a renormalized form due to its existence on a finite background. Despite its tremendous importance and success, the renormalized energy form was at first only suggested with no detailed derivation, and was then "derived" in the grand canonical ensemble. We revisit this fundamental problem and provide an alternative and intuitive derivation of the energy form from the fundamental field energy by utilizing a limiting procedure that conserves number of particles. Our derivation yields the same result, thus putting the dark soliton energy form on a solid basis.
收稿日期: 2020-01-03
出版日期: 2020-04-25
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2020, Vol. 37 
