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Deploying a recently developed semiclassical theory of quasiparticles in thesuperconducting state we study the de Haas-van Alphen effect. We find that theoscillations have the same frequency as in the normal state but their amplitudeis reduced. We find an analytic formulae for this damping which is due totunnelling between semiclassical quasiparticle orbits comprising bothparticle-like and hole-like segments. The quantitative predictions of thetheory are consistent with the available data.Comment: 7 pages, 5 figure

A damping of the de Haas van Alphen oscillations in the superconducting state