【大学频道】西北大学物理学院呈献 | Boris A. Malomed of Tel Aviv University

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图 | Boris A. Malomed

题   目：Probing quasi-integrability of the Gross-Pitaevskii equation in a harmonic-oscillator potential

报告人：Boris A. Malomed

单   位：Tel Aviv University, Tel Aviv, Israel

时   间：2019-09-06

地   点：西北大学

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报告摘要

Previous simulations of the one-dimensional Gross-Pitaevskii equation (GPE) with repulsive nonlinearity and a harmonic-oscillator trapping potential hint towards the emergence of quasi-integrable dynamics - in the sense of quasi-periodic evolution of amoving dark soliton without any signs of ergodicity -- although this model doesnot belong to the list of integrable equations. To investigate this problem, we replace the full GPE by a suitably truncated expansion over harmonic-oscillator eigenmodes (the Galerkin approximation), which accurately reproduces the full dynamics, and then analyze the system's spectrum. The analysis enables us tointerpret the observed quasi-integrability as the fact that the Galerkin approximation's finite-mode dynamics always produces a quasi-discrete power spectrum, with no visible continuous component, the presence of the latterbeing a necessary manifestation of ergodicity. Undertaking, for the comparison's sake, the same analysis in an infinitely deep potential box, we conclude that it leads, instead, to a clearly continuous power spectrum, corresponding to effective non-integrability of the box model. 

个人简介

Boris A. Malomed教授是非线性光子学和简并量子气体（冷原子、冷分子）等领域享誉寰宇的理论科学家，也是最为活跃的科学家之一。 Malomed教授科研成绩硕果累累、辛勤耕耘成就斐然，著书立说《SolitonManagement in Periodic Systems》、《Guided-Wave Optics》、《Spontaneous symmetry breaking, self-trapping, and Josephson oscillations》和多篇章节（chapters）。已在Reviews of Modern Physics, Nature Reviews Physics, Nature Physics, Nature Photonics, Physical Review Letters等顶级学术期刊发表多篇学术论文，总计被引用四万余次，H指数为86。—— ——往期精彩回顾—— ——

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