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arXiv 1811.06293quant-ph
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用耦合相干态方法模拟不可分辨玻色子的量子动力学

Simulation of the Quantum Dynamics of Indistinguishable Bosons with the Coupled Coherent States Method

James A. Green, Dmitrii V. Shalashilin

摘要:

计算机模拟不可分辨粒子的多体量子动力学是计算物理的一项具有挑战性的任务。在本文中,我们证明了耦合相干态(CCS)的方法以前开发的多维量子动力学的可区分的粒子可以用来研究不可区分玻色子的第二量子化形式主义。为了证明它的有效性,这里称为不可分辨玻色子耦合相干态(CCSB)的技术进行了测试两个模型的问题。第一个是一个系统浴问题组成的隧道模式耦合到一个谐波浴,以前研究CCS和其他方法在20维可区分的表示。谐波浴由相同的振荡器组成,并且可以被二次量子化以用于CCSB,使得该问题可以被认为是具有杂质的玻色子浴。系统动力学的交叉关联函数和傅立叶变换谱与基准计算相比非常好,这是研究该问题的现有方法都无法实现的。第二个模型的问题涉及100玻色子在一个移动的谐波陷阱。呼吸振荡的1体密度的计算和比较有利的多组态含时Hartree玻色子计算,证明了该方法的适用性作为一个新的正式的精确的方式来研究量子动力学的玻色-爱因斯坦凝聚体。

英文摘要:

Computer simulations of many-body quantum dynamics of indistinguishable particles is a challenging task for computational physics. In this paper we demonstrate that the method of coupled coherent states (CCS) developed previously for multidimensional quantum dynamics of distinguishable particles can be used to study indistinguishable bosons in the second quantisation formalism. To prove its validity, the technique termed here coupled coherent states for indistinguishable bosons (CCSB) is tested on two model problems. The first is a system-bath problem consisting of a tunnelling mode coupled to a harmonic bath, previously studied by CCS and other methods in distinguishable representation in 20 dimensions. The harmonic bath is comprised of identical oscillators, and may be second quantised for use with CCSB, so that this problem may be thought of as a bosonic bath with an impurity. The cross-correlation function for the dynamics of the system and Fourier transform spectrum compare extremely well with a benchmark calculation, which none of the prior methods of studying the problem achieved. The second model problem involves 100 bosons in a shifted harmonic trap. Breathing oscillations in the 1-body density are calculated and shown to compare favourably to a multiconfigurational time-dependent Hartree for bosons calculation, demonstrating the applicability of the method as a new formally exact way to study the quantum dynamics of Bose-Einstein condensates.

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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