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arXiv 0904.2086quant-phmath-phmath.MPphysics.comp-ph
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动力学多体量子系统的吸收边界条件

Absorbing boundary conditions for dynamical many-body quantum systems

Sølve Selstø, Simen Kvaal

摘要:

在非束缚量子力学系统动力学的数值研究中,经常会用到吸收边界条件。虽然这确实提供了一个有用的工具,以促进系统的描述,其应用程序的系统组成的一个以上的粒子是有问题的。这是因为当一个粒子被吸收时,系统的所有信息都丢失了;仅仅基于Scrh{<$}dinger方程的形式主义无法描述系统的其余部分,因为粒子丢失了。在这里,我们演示了如何与一个给定数量的相同的费米子的量子系统的动力学可以描述的方式,允许粒子损失。通过林德布拉德方程构造了一个一致的形式主义,其中包括子系统的演变与减少的粒子数。具体地说,从$N$ -粒子系统的过渡到$(N-1)$ -粒子系统由于复杂的吸收势是通过关联的Lindblad运营商的湮灭运营商。该方法允许直接解释有多少组成粒子在相互作用后离开系统。我们说明了使用一维两粒子模型问题的形式主义。

英文摘要:

In numerical studies of the dynamics of unbound quantum mechanical systems, absorbing boundary conditions are frequently applied. Although this certainly provides a useful tool in facilitating the description of the system, its applications to systems consisting of more than one particle is problematic. This is due to the fact that all information about the system is lost upon absorption of one particle; a formalism based solely on the Scrh{ö}dinger equation is not able to describe the remainder of the system as particles are lost. Here we demonstrate how the dynamics of a quantum system with a given number of identical fermions may be described in a manner which allows for particle loss. A consistent formalism which incorporates the evolution of sub-systems with a reduced number of particles is constructed through the Lindblad equation. Specifically, the transition from an $N$-particle system to an $(N-1)$-particle system due to a complex absorbing potential is achieved by relating the Lindblad operators to annihilation operators. The method allows for a straight forward interpretation of how many constituent particles have left the system after interaction. We illustrate the formalism using one-dimensional two-particle model problems.

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