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arXiv 1707.09934cond-mat.quant-gas
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环上的两种玻色子混合:低能激发量子动力学的群论方法

Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations

Vittorio Penna, Andrea Richaud

摘要:

本文研究了由两个被囚禁在玻色-哈伯德环中的凝聚体通过种间排斥相互作用耦合而成的系统的弱激发。我们的方法,基于Bogoliubov近似方案,表明可以减少问题的哈密顿量的总和的子哈密顿量$\hat{H}_k$,每一个相关的动量模式$\pm k$。每个$\hat{H}_k$被认为是一个动力学代数的元素。这种不寻常的和显着的属性使我们能够提出一个简单的对角化方案,找到运动常数,突出显着的微观过程,并计算它们的时间演化。所提出的解决方案适用于一个简单的,但仍然非常有趣的闭合电路,三聚体。考虑到不同的初始条件的选择,低能量激发的动力学,对应于弱人口的漩涡,研究和证明了两个凝聚体之间的角动量转移。最后,解析地导出了观测到谱塌缩和动力学不稳定性的条件。

英文摘要:

We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians $\hat{H}_k$, each one associated to momentum modes $\pm k$. Each $\hat{H}_k$ is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but still very interesting closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly-populated vortices, is investigated considering different choices of the initial conditions, and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.

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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