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arXiv 0906.0741cond-mat.quant-gasmath-phmath.MP
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快速旋转玻色气体中的强关联相

Strongly correlated phases in rapidly rotating Bose gases

Mathieu Lewin, Robert Seiringer

摘要:

本文考虑一个被囚禁的无自旋玻色子与排斥势相互作用的系统。在快速转动和小散射长度的限制下,我们严格地证明了基态能量收敛于投影到最低朗道能级上的具有接触相互作用的简化模型哈密顿量.这种有效的哈密顿量模拟了分数量子霍尔效应(Fractional Quantum Hall Effect,简称FQHE)的玻色子模拟。对于一个固定数量的粒子,我们也证明了收敛的状态,特别是,在一定的制度,我们表现出收敛的玻色子Laughlin波函数。这是第一个严格的理由的有效哈密顿量的快速旋转玻色气体。我们回顾以前的结果,这个有效的哈密顿和大纲开放的问题。

英文摘要:

We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.

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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