一维或二维吸引性费米气体的半经典极限
Semi-classical limit of an attractive Fermi gas in one or two dimensions
AI总结：
研究一维或二维短程吸引相互作用费米气体的基态，证明在大N极限下哈密顿量基态能量收敛到Thomas-Fermi能量，并证明基态的Husimi函数收敛。
摘要：
我们研究了一维或二维中具有短程吸引相互作用的费米气体的基态。N个费米子被置于一个约束势中，并通过一个负势相互作用，其范围大于粒子之间的典型距离。我们证明了在大N极限下哈密顿量的基态能量收敛到Thomas-Fermi能量。此外，我们证明了基态在其Husimi函数意义下的收敛性。这些结果扩展到具有正傅里叶变换的排斥相互作用的情况。
英文摘要：
We study the ground-state of a Fermi gas with short range attrative interactions in one or two dimensions. N fermions are placed in a confining potential, and interact with each other through a negative potential, whose range is larger than the typical distance between particles. We show the convergence of the ground state energy of the Hamiltonian to a Thomas-Fermi energy in the large N limit. Furthermore, we prove convergence of the ground states, in the sense of their Husimi functions. These results extend to the case of a repulsive interaction of positive Fourier transform.
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