相互作用玻色子的截断多体动力学：误差监控的变分原理
Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring
摘要：
我们开发了一种方法来描述玻色子的相互作用系统的时间演化，其中的场算子展开截断后，有限数量的$M$的模式，在严格控制的方式。利用麦克拉克伦的最小误差原理，我们找到了一个自洽的多体状态方程组。作为一个特别的好处，并在以前提出的方法的区别，目前介绍的方法有利于动态增加的轨道数量在时间演化过程中，由于这样的事实，我们可以严格监控的错误，通过增加截断维数$M$。由截断演化相对于精确演化的最小误差条件确定的附加轨道，通过最陡$constrained$下降从初始试验状态获得。
英文摘要：
We develop a method to describe the temporal evolution of an interacting system of bosons, for which the field operator expansion is truncated after a finite number $M$ of modes, in a rigorously controlled manner. Using McLachlan's principle of least error, we find a self-consistent set of equations for the many-body state. As a particular benefit, and in distinction to previously proposed approaches, the presently introduced method facilitates the dynamical increase of the number of orbitals during the temporal evolution, due to the fact that we can rigorously monitor the error made by increasing the truncation dimension $M$. The additional orbitals, determined by the condition of least error of the truncated evolution relative to the exact one, are obtained from an initial trial state by steepest $constrained$ descent.
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