强laser场中电子动力学的最佳基组：分子离子H $^{+}_2$的情况
On the optimal basis set for electron dynamics in strong laser fields: The case of molecular ion H$^{+}_2$
摘要：
对强激光场中电子动力学的控制机制的理解仍然是一个挑战，需要用先进的理论来解释。因此，发展准确的理论和计算方法，能够提供一个精确的治疗产生的基本过程中的强场制度，是至关重要的。一个中心问题是波函数展开基的选择。在描述多光子过程的准确性是严格相关的基础上，如数值收敛，计算成本，和连续表示的内在属性。通过显式求解H $^{+}_{2}$在强电场作用下的一维和三维含时薛定谔方程，我们研究了使用实空间网格、B样条基和高斯基（由连续体的最佳高斯函数改进）的数值性能。我们分析了H $^{+}_{2}$的高次谐波产生和阈上电离的三种基的性能。特别是，对于高次谐波的产生，基础的能力，以再现双中心干涉和超拉曼现象进行了研究。
英文摘要：
A clear understanding of the mechanisms that control the electron dynamics in strong laser field is still a challenge that requires to be interpreted by advanced theory. Development of accurate theoretical and computational methods, able to provide a precise treatment of the fundamental processes generated in the strong field regime, is therefore crucial. A central aspect is the choice of the basis for the wave-function expansion. Accuracy in describing multiphoton processes is strictly related to the intrinsic properties of the basis, such as numerical convergence, computational cost, and representation of the continuum. By explicitly solving the 1D and 3D time-dependent Schrödinger equation for H$^{+}_{2}$ in presence of an intense electric field, we explore the numerical performance of using a real-space grid, a B-spline basis, and a Gaussian basis (improved by optimal Gaussian functions for the continuum). We analyze the performance of the three bases for high-harmonic generation and above-threshold ionization for H$^{+}_{2}$. In particular, for high-harmonic generation, the capability of the basis to reproduce the two-center interference and the hyper-Raman phenomena is investigated.
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