Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases
Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases
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DOI：
10.1007/s10955-013-0766-0
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发表时间：
2013-01
影响因子：
1.6
通讯作者：
N. Rougerie;S. Serfaty;J. Yngvason
中科院分区：
文献类型：
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作者：
N. Rougerie;S. Serfaty;J. Yngvason
分数量子霍尔效应的玻色子类似物发生在快速旋转的俘获玻色气体中：存在从不相关的哈特里态到强相关态（例如劳克林波函数）的转变。这种物理现象可以通过有效哈密顿量来描述，该哈密顿量具有作用于解析函数的玻色N体巴格曼空间的δ相互作用。在之前的一篇论文中（Rougerie 等人，发表于 Phys. Rev. A 87:023618, 2013），我们研究了二次加四次俘获势的情况，并导出了模型参数的条件，使其基态渐近强相关。这基本上依赖于使用量子霍尔试验状态的能量上限，除了固定在原点的多重量子化涡旋之外，还结合了玻色-劳克林状态的相关性。在本文中，我们更详细地研究了这些试验态的密度，从而进一步证实了（Rougerie 等人，在 Phys. Rev. A 87:023618, 2013）中描述的物理图片，改进了我们的能量估计，并允许考虑更一般的捕获势。我们的分析基于对量子霍尔试验态密度的解释作为经典二维库仑气体的吉布斯测量（等离子体类比）。提出了对此类系统的平均场极限的新估计。
A bosonic analogue of the fractional quantum Hall effect occurs in rapidly rotating trapped Bose gases: There is a transition from uncorrelated Hartree states to strongly correlated states such as the Laughlin wave function. This physics may be described by effective Hamiltonians with delta interactions acting on a bosonicN-body Bargmann space of analytic functions. In a previous paper (Rougerie et al. in Phys. Rev. A 87:023618, 2013) we studied the case of a quadratic plus quartic trapping potential and derived conditions on the parameters of the model for its ground state to be asymptotically strongly correlated. This relied essentially on energy upper bounds using quantum Hall trial states, incorporating the correlations of the Bose-Laughlin state in addition to a multiply quantized vortex pinned at the origin. In this paper we investigate in more details the density of these trial states, thereby substantiating further the physical picture described in (Rougerie et al. in Phys. Rev. A 87:023618, 2013), improving our energy estimates and allowing to consider more general trapping potentials. Our analysis is based on the interpretation of the densities of quantum Hall trial states as Gibbs measures of classical 2D Coulomb gases (plasma analogy). New estimates on the mean-field limit of such systems are presented.