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arXiv 0811.3853quant-phcond-mat.other
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粒子转换系统的多体理论：多组态含时Hartree方法的扩展

Many-body theory for systems with particle conversion: Extending the multiconfigurational time-dependent Hartree method

Ofir E. Alon, Alexej I. Streltsov, Lorenz S. Cederbaum

备注：
46 pages
发表信息：
Phys. Rev. A 79, 022503 (2009)
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摘要：

我们推导了粒子转换系统的多组态含时Hartree理论。在这样的系统中，一种粒子可以转化为另一种粒子，粒子的总数随时间而变化。因此，该理论扩展了现有的和成功的多构型时间依赖哈特里方法的范围-这是唯一制定和应用于系统与固定数量的粒子-新的物理系统和问题。作为一个指导性的例子，我们明确地对待一个系统，玻色子原子可以结合形成玻色子分子，反之亦然。在粒子转换理论中，依赖于时间的多粒子波函数被写成由不同数量的粒子组成的配置的总和，并由原子和分子轨道集合组装而成。膨胀系数和形成组态的轨道都是依赖于时间的量，其完全根据Dirac-Frenkel依赖于时间的变分原理来确定。特别注意的是，减少密度矩阵的多粒子波函数出现在理论中，并进入运动方程。约化密度矩阵有两种：粒子守恒约化密度矩阵，它只直接耦合具有相同原子数和分子数的组态;粒子非守恒约化密度矩阵，它耦合具有不同原子数和分子数的组态。推导了接触和一般两体相互作用的封闭形式和紧凑的运动方程，并分析和讨论了它们的性质。

英文摘要：

We derive a multiconfigurational time-dependent Hartree theory for systems with particle conversion. In such systems particles of one kind can convert to another kind and the total number of particles varies in time. The theory thus extends the scope of the available and successful multiconfigurational time-dependent Hartree methods -- which were solely formulated for and applied to systems with a fixed number of particles -- to new physical systems and problems. As a guiding example we treat explicitly a system where bosonic atoms can combine to form bosonic molecules and vise versa. In the theory for particle conversion, the time-dependent many-particle wavefunction is written as a sum of configurations made of a different number of particles, and assembled from sets of atomic and molecular orbitals. Both the expansion coefficients and the orbitals forming the configurations are time-dependent quantities that are fully determined according to the Dirac-Frenkel time-dependent variational principle. Particular attention is paid to the reduced density matrices of the many-particle wavefunction that appear in the theory and enter the equations of motion. There are two kinds of reduced density matrices: particle-conserving reduced density matrices which directly only couple configurations with the same number of atoms and molecules, and particle non-conserving reduced density matrices which couple configurations with a different number of atoms and molecules. Closed-form and compact equations of motion are derived for contact as well as general two-body interactions, and their properties are analyzed and discussed.

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