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arXiv:cond-mat/0306376 · Physical Review Letters

Comment on “Off-Diagonal Long-Range Order in Bose Liquids: Irrotational Flow and Quantization of Circulation”

Yu Shi

Published Apr 8, 2003• 2 citations
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Abstract

In the context of an application to superfluidity, it is elaborated how to do quantum mechanics of a system with a rotational velocity. Especially, in both the laboratory frame and the non-inertial co-rotating frame, the canonical momentum, which corresponds to the quantum mechanical momentum operator, contains a part due to the rotational velocity.

DOI
10.1103/physrevlett.90.148901

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In the context of an application to superfluidity, it is elaborated how to do quantum mechanics of a system with a rotational velocity. Especially, in both the laboratory frame and the non-inertial co-rotating frame, the canonical momentum, which corresponds to the quantum mechanical momentum operator, contains a part due to the rotational velocity.
On the basis of gauge invariance, it is proven in an elementary and straightforward manner, but without invoking any ad hoc assumption, that the existence of off-diagonal long-range order in one-particle reduced density matrix in Bose liquids implies both the irrotational flow in a simply connected region and the quantization of circulation in a multiply connected region, the two fundamental properties of a Bose superfluid. The origin for both is the phase coherence of condensate wave functions. Some relevant issues are also addressed.
We provide a general operator algebraic formulation of superfluidity in Bose systems, with the aim of investigating the relationships of this phenomenon both to off-diagonal long range order (ODLRO) and to a mathematically precise version of Landau's picture of elementary excitations. Our principal results are that ODLRO leads both to rotational superfluidity and to Goldstone excitations, while the neo-Landau picture accounts for the translational superfluidity of flow along a pipe. The latter picture is realised by the Lieb-Liniger-Girardeau model. Open problems are briefly discussed.
Rotating supersolids challenge the conventional notion of superfluid flow: quantized vortices coexist with crystalline order arising from the system's intrinsic density modulation. Drawing on concepts developed in the context of superfluid helium, this seemingly paradoxical state is often described phenomenologically in terms of a dual response, combining superfluid flow with rigid-body-like motion. Here we show that these apparently distinct behaviors emerge from a single microscopic velocity field, globally constrained by irrotationality. By applying a Helmholtz decomposition, we disentangle a divergence-free incompressible component, which carries vortex circulation, from a curl-free compressible component generated by the intrinsic density modulation. In absence of vortices, the response is entirely encoded in the compressible field: the droplets co-rotate with the external drive, while the interstitial fluid develops an oppositely directed counterflow that preserves vanishing circulation. Above the vortex nucleation threshold, the incompressible component carries the usual quantized circulation, whereas the compressible field counteracts the vortex-induced angular momentum, reducing the total jump with respect to an unmodulated condensate. Our results recast supersolid rotation in terms of a flow-counterflow response, providing a microscopic interpretation of the phenomenological rigid/superfluid partitioning.
A quantum liquid of an almost ideal Bose gas brought into rotation is investigated from a physical and mechanical point of view on the basis of the Gross–Pitaevskii (GP) equation by applying a quantum-mechanical scenario, i.e. the London scenario. This scenario allows a superfluid to have rotational states. Considering that the equation governs an interacting Bose gas, it is proposed that the GP equation admits rotational flows of a superfluid. This is carried out without incurring essential change of the equation. By this reformulation, a superfluid placed in a rotating vessel is able to have a solid body rotation with the same angular velocity as its container and also to have a meniscus approximated by a parabolic profile. The solid body rotation is accompanied by a density increase proportional to the square of its angular velocity. These are consistent with experimental observations. In addition, this formulation allows a vortex of quantized circulation with coaxial rotational core whose density does not necessarily vanish at its center.