This chapter covers some of the basics of superfluidity. It discusses Bose–Einstein condensation in an ideal gas; the Bogoliubov transformation; superfluid helium II; microscopic interpretation of the Bose order parameter; phenomenological theories of superconductivity; the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity; the first unusual superfluid, 3He; and recent developments in superfluidity.

Oxford University Press eBooksFeb 28, 20132 citations

Physical Review

Theory of Superfluidity

F.W. Cummings, James R. Johnston

Published Dec 5, 1967• 1 citation

Publisher

DOI: 10.1103/physrev.164.270

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^4

He give the

λ

-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.

T

) and provide detailed derivations of all results announced in [1]. Using Popov's hydrodynamic action, we show that the theory of low-temperature depletion in a

d

-dimensional quantum superfluid maps onto the problem of finite-size (

L

) corrections in a

(d+1)

-dimensional anisotropic (pseudo-)classical-field system with U(1)-symmetric complex-valued action. In addition to generalizing Landau's (canonical) formula, we develop the grand canonical theory, which in a broader context reveals a universal scaling,

T^{d+1}

and

1/L^{d+1}

, for finite-

T

and finite-

L

effects of many thermodynamic quantities. We validate our theory with numeric simulations of interacting lattice bosons and the J-current model.