非局部Gros-Pitaevsky方程的准能谱级数和Aharonov-Anandan相位
Quasi-energy spectral series and the Aharonov-Anandan phase for the nonlocal Gross--Pitaevsky equation
摘要：
对于非局部的$T$ -周期Gross-Pitaevsky算子，构造了Floquet问题在小参数$\hbar$，$\hbar\to0$，直至$O(\hbar^{3/2})$上的渐近形式解.所得到的准能谱序列对应于线性近似下稳定的Hamilton-Eschlafest系统的闭相轨迹。该方程的单值算子被构造在概率集中函数类中的$\hat O(\hbar^{3/2})$内。计算了准能态的Aharonov-Anandan相。
英文摘要：
For the nonlocal $T$-periodic Gross-Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter $\hbar$, $\hbar\to0$, up to $O(\hbar^{3/2})$ have been constructed. The quasi-energy spectral series found correspond to the closed phase trajectories of the Hamilton-Ehrenfest system which are stable in the linear approximation. The monodromy operator of this equation has been constructed to within $\hat O(\hbar^{3/2})$ in the class of trajectory-concentrated functions. The Aharonov-Anandan phases have been calculated for the quasi-energy states.
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