CAJ | 학술논문

利用变分法和数值计算方法研究了二维线性和非线性光晶格中二维玻色-爱因斯坦凝聚体系中物质波孤立子的存在及其稳定性.利用定态变分原理及Vakhitov-Kolokolov判据总结了线性和非线性结合光晶格中几种参数组合下定态定域解的稳定性.结果表明,当存在二维非线性光晶格时,在吸引和排斥相互作用的原子体系中均可以存在稳定的物质波孤立子.另外,利用含时变分法研究了线性和非线性光晶格中物质波孤立子随时间的传播特性,使波包参数对时间的一阶导数等于零,可以给出稳定状态对应的参数,结论和定态变分法给出的结果一致.最后用数值计算方法研究变分结果的正确性,把变分结果作为初始条件代入Gross-Pitaevskii方程研究其随时间传播特征,得到了稳定的传播过程,所得到的结果和变分分析结果一致.
이용변분법화수치계산방법연구료이유선성화비선성광정격중이유파색-애인사탄응취체계중물질파고립자적존재급기은정성.이용정태변분원리급Vakhitov-Kolokolov판거총결료선성화비선성결합광정격중궤충삼수조합하정태정역해적은정성.결과표명,당존재이유비선성광정격시,재흡인화배척상호작용적원자체계중균가이존재은정적물질파고립자.령외,이용함시변분법연구료선성화비선성광정격중물질파고립자수시간적전파특성,사파포삼수대시간적일계도수등우령,가이급출은정상태대응적삼수,결론화정태변분법급출적결과일치.최후용수치계산방법연구변분결과적정학성,파변분결과작위초시조건대입Gross-Pitaevskii방정연구기수시간전파특정,득도료은정적전파과정,소득도적결과화변분분석결과일치.
By means of variational solution and direct numerical simulation of the Gross-Pitaevskii equation (GPE), we have studied the stability of matter-wave solitons in two-dimensional (2D) Bose-Einstein condensations (BECs), with 2D linear and nonlinear optical lattices (OLs). Using the static variational approach and Vakhitov-Kolokolov criterion necessary for stability, we obtain the stability condition for solitons in different combinations of OL’s parameters. We show that the 2D linear and nonlinear optical lattices allow us to stabilize 2D solitons for both attractive and repulsive interactions. We also study the time-evolution problems of 2D BECs, using the time-dependent variational approach and numerical solution of GPE for 2D linear and nonlinear OLs. Very good agreement between the results corresponding to both treatments is observed.