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The effective junction length (Formula presented) for the steplike pair potential deviates somewhat from the "real" junction length 2a for a more realistic pair potential. For a discussion of this issue see, e.g., H. Plehn, U. Gunsenheimer and R. Kümmel, J. Low. Temp. Phys. 83, 71 (1991).
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it turns out that they may be neglected for short junctions
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A more general expression for arbitrary transmission probability and (Formula presented)=(Formula presented) is presented in P.F. Bagwell, Phys. Rev. B 46, 12 573 (1992) for the single-channel case, and the corresponding "classical limit" is found in W. Haberkorn, H. Knauer and J. Richter, Phys. Status Solidi A 47, K161 (1978).
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they derived the current-phase relation in the "classical limit" with a junction diameter large enough so that (Formula presented)/N≪(Formula presented) (see also, Ref. 47)
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I.O. Kulik and A.N. Omel'yanchuk, Fiz. Nizk. Temp. 3, 945 (1977) [Sov. J. Low Temp. Phys. 3, 459 (1977)]; they derived the current-phase relation in the "classical limit" with a junction diameter large enough so that (Formula presented)/N≪(Formula presented) (see also, Ref. 47).
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mechanically controllable break junctions, which are indeed atomic-size quantum point contacts, were developed first by C.J. Muller, J.M. van Ruitenbeek and L.J. de Jongh, Physica C 191, 485 (1992).
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Already Kulik and Omel'yanchuk presented current-phase relations for dirty and clean superconducting point contacts which are nonsinusoidal and yield π/2<(Formula presented)<π, see Ref. 42 and Pis'ma Zh. Eksp. Teor. Fiz. 21, 216 (1975) [JETP Lett. 21, 96 (1975)].
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