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Quantum devices based on the Josephson effect in superconductors are usually described by a Hamiltonian obtained by commonly used canonical quantization.
However, this recipe has not yet been rigorously and systematically justified. We show that this approach is indeed correct in a certain range of parameters. We find the condition of validity of such quantization and the systematic corrections to the Josephson energy EJ: namely, the capacitance
energy Ec = e^2/2C must be much smaller than the superconducting gap Δ. Moreover, we find an experimentally testable modification of Josephson energy at large capacitance energy also with nonlinear capacitance.
. K.Pomorski, A.Bednorz, "Justification of canonical quantization of Josephson effect and its modification due to large capacitance energy", J. Phys. A: Math. Theor. 49, 2016
. K.Pomorski, A.Bednorz, "Justification of canonical quantization of Josephson junction", 2015 (http://arxiv.org/abs/1502.00511)