利用拉格朗日方程推导出在水平面上受不稳定约束弹簧振子运动的动力学方程,运用Matlab软件对动力学方程进行数值求解,并通过Matlab图形用户界面(Graphical User Interface,GUI)对不同条件下弹簧振子运动进行仿真,绘制了弹簧振子坐标随...利用拉格朗日方程推导出在水平面上受不稳定约束弹簧振子运动的动力学方程,运用Matlab软件对动力学方程进行数值求解,并通过Matlab图形用户界面(Graphical User Interface,GUI)对不同条件下弹簧振子运动进行仿真,绘制了弹簧振子坐标随时间变化的演化曲线、相图以及运动轨迹,得到了更为直观的弹簧振子运动规律。结果表明,弹簧振子运动与弹簧一端的运动速度大小和初始角度有关;在一定条件下,弹簧振子作准周期运动。展开更多
We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping,based on driven dissipative Gross–Pitaevskii equations coupled to the rate equation.The equation of motio...We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping,based on driven dissipative Gross–Pitaevskii equations coupled to the rate equation.The equation of motion of the relative center position of two-dark soliton is obtained analytically by using the Lagrangian approach.In particular,the analytical expression of the effective potential between two dark solitons is given.The resulting equation of motion captures how the open-dissipative character of a polariton Bose–Einstein condensate affects properties of dynamics of two-dark soliton,i.e.,two-dark soliton relax by blending with the background at a finite time.We further simulate the relative motion of two dark solitons numerically with the emphasis on how two-soliton motion is manipulated by the initial velocity,in excellent agreement with the analytical results.The prediction of this work is sufficient for the experimental observations within current facilities.展开更多
文摘利用拉格朗日方程推导出在水平面上受不稳定约束弹簧振子运动的动力学方程,运用Matlab软件对动力学方程进行数值求解,并通过Matlab图形用户界面(Graphical User Interface,GUI)对不同条件下弹簧振子运动进行仿真,绘制了弹簧振子坐标随时间变化的演化曲线、相图以及运动轨迹,得到了更为直观的弹簧振子运动规律。结果表明,弹簧振子运动与弹簧一端的运动速度大小和初始角度有关;在一定条件下,弹簧振子作准周期运动。
基金supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ21A040001)the National Natural Science Foundation of China(Grant Nos.12074344 and 11975208)the Key Projects of the Natural Science Foundation of China(Grant No.11835011)。
文摘We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping,based on driven dissipative Gross–Pitaevskii equations coupled to the rate equation.The equation of motion of the relative center position of two-dark soliton is obtained analytically by using the Lagrangian approach.In particular,the analytical expression of the effective potential between two dark solitons is given.The resulting equation of motion captures how the open-dissipative character of a polariton Bose–Einstein condensate affects properties of dynamics of two-dark soliton,i.e.,two-dark soliton relax by blending with the background at a finite time.We further simulate the relative motion of two dark solitons numerically with the emphasis on how two-soliton motion is manipulated by the initial velocity,in excellent agreement with the analytical results.The prediction of this work is sufficient for the experimental observations within current facilities.
