描述吸收边界条件导致粒子损失的多组态含时Hartree方法
Multiconfigurational time-dependent Hartree method for describing particle loss due to absorbing boundary conditions
AI总结：
针对吸收边界条件引起的粒子损失，提出了Lindblad主方程的多组态含时Hartree方法，推广了纯态传播的标准MCTDH，并通过数值实验验证。
摘要：
在薛定谔方程中，通常以复吸收势形式引入吸收边界条件，以限制计算域或使用多组态含时Hartree方法（MCTDH）研究反应散射事件。然而，已知纯波函数描述无法建模和传播系统被吸收边界移除部分后的残余。最近的研究[S. Selstø and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. {fseries 43} (2010), 065004]表明，Lindblad形式的主方程对于这种描述是必要的。我们针对该主方程提出了多组态含时Hartree方法，适用于任何由任意物种混合组成的量子系统。该公式是使用标准MCTDH进行纯态传播的严格推广。我们通过数值实验演示了该公式。
英文摘要：
Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schrödinger equation to limit the computational domain or to study reactive scattering events using the multi-configurational time-dependent Hartree method (MCTDH). However, it is known that a pure wave-function description does not allow the modeling and propagation of the remnants of a system of which some parts are removed by the absorbing boundary. It was recently shown [S. Selstø and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. {\bfseries 43} (2010), 065004] that a master equation of Lindblad form was necessary for such a description. We formulate a multiconfigurational time-dependent Hartree method for this master equation, usable for any quantum system composed of any mixture of species. The formulation is a strict generalization of pure-state propagation using standard MCTDH. We demonstrate the formulation with a numerical experiment.
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