On the Mathematical Theory of Superfluidity
Geoffrey L. Sewell, Walter F. Wreszinski
TL;DR
This paper develops a rigorous mathematical framework for superfluidity in Bose systems, linking it to off-diagonal long-range order, Goldstone excitations, and Landau's theory, with applications to specific models.
Contribution
It introduces an operator algebraic formulation of superfluidity, clarifies its relation to ODLRO and elementary excitations, and applies it to the Lieb-Liniger-Girardeau model.
Findings
ODLRO implies rotational superfluidity and Goldstone modes
The neo-Landau picture explains translational superfluidity in flow
Application to the Lieb-Liniger-Girardeau model
Abstract
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.
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