通过磁通附着实现量子统计嬗变
Quantum statistics transmutation via magnetic flux attachment
AI总结：
针对垂直磁场中两类二维量子粒子模型，论文通过构造并严格估计自然试探态能量，证明示踪粒子与费米浴强耦合时会发生玻色—费米统计嬗变。
摘要：
我们考虑一个包含两类二维量子粒子（浴粒子和示踪粒子）且处于垂直磁场中的模型。相互作用是短程的且发生在不同种类之间，我们假设浴粒子是费米子，并全部处于磁场的最低 Landau 能级。启发式论证进而表明，如果示踪粒子与浴粒子强耦合，它们实际上会改变自身的量子统计，从玻色子变为费米子，或从费米子变为玻色子。我们严格计算了一个自然试探态的能量，确实展示了这种统计嬗变现象。证明涉及对随机矩阵 Ginibre 系综特征多项式的估计。
英文摘要：
We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular magnetic field. Interactions are short range and inter-species, and we assume that the bath particles are fermions, all lying in the lowest Landau level of the magnetic field. Heuristic arguments then indicate that, if the tracers are strongly coupled to the bath, they effectively change their quantum statistics, from bosonic to fermionic or vice-versa. We rigorously compute the energy of a natural trial state, indeed exhibiting this phenomenon of statistics transmutation. The proof involves estimates for the characteristic polynomial of the Ginibre ensemble of random matrices.
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