非对易空间原子超流费米气体的能谱和相变
Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space
摘要：
本文在Bogoliubov非理想气体模型的基础上，讨论了正则非对易空间中具有弱吸引相互作用的原子超流费米气体的能谱和相变。由于BCS型超流费米气体的相互作用起源于一对动量和自旋相反的费米准粒子，因此费米气体在非对易空间上的哈密顿量可以用与对易空间有关的普通产生和湮灭算符来描述，而非对易效应只出现在相互作用哈密顿量的系数中.因此，我们可以严格地按照在对易空间中所采用的方法，而不需要使用微扰理论，求解非对易空间中费米气体的能谱。特别地，与以往对非对易简并电子气和超导体只导出基态能级和能隙的一阶修正的结果不同，我们得到了非对易超流费米气体的非微扰能谱，发现每个能级都包含一个非对易参数的余弦函数的修正因子.另外，与对易情况相比，能隙变窄，从超流态到普通流态的相变临界温度降低.
英文摘要：
Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the noncommutative space can be described in terms of the ordinary creation and annihilation operators related to the commutative space, while the noncommutative effect appears only in the coefficients of the interacting Hamiltonian. As a result, we can rigorously solve the energy spectrum of the Fermi gas on the noncommutative space exactly following the way adopted on the commutative space without the use of perturbation theory. In particular, different from the previous results on the noncommutative degenerate electron gas and superconductor where only the first order corrections of the ground state energy level and energy gap were derived, we obtain the nonperturbative energy spectrum for the noncommutative superfluid Fermi gas, and find that each energy level contains a corrected factor of cosine function of noncommutative parameters. In addition, our result shows that the energy gap becomes narrow and the critical temperature of phase transition from a superfluid state to an ordinary fluid state decreases when compared with that in the commutative case.
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