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Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\pi$ slips of the phase of the order parameter.
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E S j = 2 2 / π 8 E J j / E C j 4 8 E J j E C j exp [ − 8 E J j / E C j ] E_{S_{j}}=2\sqrt{2/\pi}\sqrt[4]{8E_{J_{j}}/E_{C_{j}}}\sqrt{8E_{J_{j}}E_{C_{j}}}\exp[-\sqrt{8E_{J_{j}}/E_{C_{j}}}] , in the limit of large N N and within the WKB approximation [ 6 ]
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