Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
Phys Rev Lett. 2014 Mar 7;112(9):095301. doi: 10.1103/PhysRevLett.112.095301. Epub 2014 Mar 3.
Galilean invariance leaves its imprint on the energy spectrum and eigenstates of N quantum particles, bosons, or fermions, confined in a bounded domain. It endows the spectrum with a recurrent structure, which in capillaries or elongated traps of length L and cross-section area s(⊥) leads to spectral gaps n(2)h(2)s(⊥)ρ/(2 mL) at wave numbers 2nπs(⊥)ρ, where ρ is the number density and m is the particle mass. In zero temperature superfluids, in toroidal geometries, it causes the quantization of the flow velocity with the quantum h/(mL) or that of the circulation along the toroid with the known quantum h/m. Adding a "friction" potential, which breaks Galilean invariance, the Hamiltonian can have a superfluid ground state at low flow velocities but not above a critical velocity, which may be different from the velocity of sound. In the limit of infinite N and L, if N/L = s(⊥)ρ is kept fixed, translation invariance is broken, and the center of mass has a periodic distribution, while superfluidity persists at low flow velocities. This conclusion holds for the Lieb-Liniger model.
伽利略不变性在能量谱和本征态上留下了印记，这些本征态涉及到在有界区域内被束缚的 N 个量子粒子（玻色子或费米子）。它赋予了能谱一个周期性的结构，在毛细管或长度为 L 和截面积为 s(⊥)的长形陷阱中，在波数 2nπs(⊥)ρ处会产生谱隙 n(2)h(2)s(⊥)ρ/(2 mL)，其中 ρ 是数密度，m 是粒子质量。在零温度超流体中，在环面几何形状中，它导致了流速的量子化，其量子为 h/(mL)，或者沿着环面的循环的量子化，其量子为已知的 h/m。加入一个打破伽利略不变性的“摩擦”势，哈密顿量可以在低流速下具有超流基态，但在临界速度以上没有，这个临界速度可能与声速不同。在 N 和 L 趋于无穷大的极限下，如果 N/L = s(⊥)ρ 保持固定，那么平移不变性被打破，质心具有周期性分布，而超流性在低流速下仍然存在。这个结论适用于 Lieb-Liniger 模型。
