Quantum Theory of Superfluid Vortices. II. Type-II Superconductors

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Abstract
The London model of bulk type-II superconductors is used to derive the dynamical equations of quantized flux lines. These equations are rewritten in a Hamiltonian form, and the system is quantized by interpreting the conjugate variables as quantum-mechanical operators that obey the canonical commutation relations. Diagonalization of the Hamiltonian yields the exact dispersion relation for small-amplitude waves propagating with arbitrary wave vector in the vortex lattice. This formalism allows a straightforward calculation of the specific heat associated with thermally excited lattice vibrations and of the mean-square displacement of the vortex cores. Similar features are shown to occur in the mixed state of a thin superconducting film in a perpendicular magnetic field.