Galilean Invariance in Confined Quantum Systems: Implications for Spectral Gaps, Superfluid Flow, and Periodic Order

Sütő, András (2014) Galilean Invariance in Confined Quantum Systems: Implications for Spectral Gaps, Superfluid Flow, and Periodic Order. PHYSICAL REVIEW LETTERS, 112 (9). ISSN 0031-9007

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Abstract

Galilean invariance leaves its imprint on the energy spectrum and eigenstates of N quantum parti- cles, 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 n2h2s⊥ρ/(2mL) 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 Hamil- tonian 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, the center of mass has a periodic distribution, while superfluidity persists at low flow velocities. This conclusion holds for the Lieb-Liniger model.

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