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The trial free energy of the harmonic approximation, which has been widely used to study Josephson junctions, diverges to negative infinity in the normal state for any finite temperature because a nonperiodic, harmonic Hamiltonian is used to describe a periodic system. In this paper, I employ a periodic, scalloped potential to construct a well-defined free energy, which is then minimized to obtain self-consistent solutions that are close to the harmonic solutions when phase fluctuations are small.
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R. S. Fishman (1988) studied this question.
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