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arXiv 1607.07211quant-phmath-phmath.MP
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一类相互作用玻色粒子的约化动力学

On the reduced dynamics of a subset of interacting bosonic particles

Manuel Gessner, Andreas Buchleitner

摘要:

用对称化多粒子态描述了固定粒子数子空间中相互作用玻色子子集的量子动力学。对$N$ -粒子系统的冯·诺伊曼方程进行适当的部分迹运算,可得到$M\leq N$粒子的子动力学的分级展开。用一个纯的乘积态模截断这个层次,得到一般的非线性相干平均场运动运动方程。在接触相互作用势的特殊情况下,这再现了Gross-Pitaevskii方程。为了解释平均场演化上的非相干效应,我们讨论了可能的扩展对一个二阶微扰理论,占相互作用引起的退相干的形式的非线性Lindblad型主方程。

英文摘要:

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle system produces a hierarchical expansion for the subdynamics of $M\leq N$ particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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