辛算法是保持哈密顿系统辛结构的差分方法，已广泛地应用于许多学科领域。本项目我们研究量子系统的辛算法及其在强场多电子原子的非次序双电离和Bose-Einstein凝聚理论研究中的应用，具体内容包括：构造适用于量子系统的高精度及保持轨道稳定性的辛格式，并应用经典理论方法或耦合干涉态（CCS）方法，研究不同波长下多电子原子的非次序双电离以及椭圆偏振激光作用下Mg原子的非次序双电离机制；构造求解二维双势阱中耦合的二维Gross-Pitaevskii方程组的高阶保酉积守恒的分裂算符傅立叶变换方法，研究玻色-费米混合气体的自发对称破缺及其动力学过程；构造求解非线性哈密顿正则方程组的高阶辛Runge-Kutta格式，研究双模近似下双势阱中的玻色-费米和费米-费米混合气体的隧穿动力学；应用辛算法计算，建立合适的相空间，研究非线性Schr?dinger方程的动力学性质和时空混沌。

The symplectic algorithm, which has been widely used in many fields of science, is a kind of difference method that can preserve the symplectic structure of the Hamiltonian system. In this project, we will investigate the symplectic algorithm of quantum system and its applications in the study of the nonsequential double ionization and the Bose-Einstein condensate. The details are as follows: We will construct the trajectory-stability-preserving and high-accuracy symplectic scheme tailored to the quantum system, and investigate the nonsequential double ionization of polyelectron atom with different wavelength and nonsequential double ionization mechanism of magnesium atom with elliptically polarized laser pulse by using classical ensemble method or coupled coherent-state (CCS) approach. We will construct the unitary-product-preserving and the high-order splitting-operator-FFT method for solving the coupled two-dimensional Gross-Pitaevskii equation in a double-well potential, and investigate the spontaneous symmetry breaking and the dynamic properties of Bose-Fermi mixtures. We will investigate the tunneling dynamics of Bose-Fermi and Fermi-Fermi mixtures in a double-well potential by using high-order symplectic Runge-Kutta method under the two-mode model. We will investigate the dynamic properties and chaos of nonlinear Schr?dinger equation by using symplectic algorithm based on the appropriate phase space.