Majorana Representation and Mean Field Approach for Interacting-Boson System
Majorana Representation and Mean Field Approach for Interacting-Boson System
复制标题
相互作用玻色子系统的马约拉纳表示和平均场方法
DOI：
10.1088/0253-6102/68/4/439
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发表时间：
2017
影响因子：
3.1
通讯作者：
Zheng Tai-Yu
中科院分区：
文献类型：
--
作者：
Liu Hao-Di;Fang Jie;Zheng Tai-Yu
马约拉纳表示为研究高维希尔伯特空间中的量子演化提供了一种直观的工具，它代表了布洛赫球上恒星的量子态。在这项工作中，我们研究了在Majorana表示下相互作用玻色子系统的第二量子化模型和平均场模型。结果表明，在线性情况下，两种模型的状态运动是相同的。在第二量子化模型中，非线性相互作用对恒星运动的贡献可以用单个恒星部分来表示，该部分等于大玻色子数极限下平均场模型中恒星方程的非线性部分和由恒星之间的关联引起的额外部分。这些差异和关系不仅体现在两个模型中两个玻色子模式的居群差异上，还体现在具有非线性相互作用强度的第二次量子化演化的连续变化与与自俘获效应相关的平均场演化的临界行为之间的差异上。用有效哈密顿量讨论了两种模型差异的原因。
The Majorana representation, which represents a quantum state by stars on the Bloch sphere, provides us an intuitive tool to study the quantum evolution in high dimensional Hilbert space. In this work, we investigate the second quantized model and the mean-field model for the interacting-boson system in the Majorana representation. It is shown that the motions of states in the two models are same in the linear case. Furthermore, the contribution of the nonlinear interaction to the star motions in the second quantized model can be expressed by a single star part which is equal to the nonlinear part of the equation for the star in mean-field model under large boson number limit and an extra part caused by the correlation between stars. These differences and relations can not only be reflected by the population differences between the two boson modes in the two models, but also lie with the differences between the continuous changes of the second quantized evolution with the nonlinear interacting strength and the critical behavior of the mean-field evolution which related to the self-trapping effect. The reason of the difference between the two models is also discussed by an effective Hamiltonian.