“…Note that the series inductance does not break the 2π periodicity of the Hamiltonian, despite the occurrence of ϕ 2 . This is in contrast to a shunt inductance, for which the flux ϕ and the charge n would need to be treated as non-compact operators with continuous spectrum R, see [85][86][87][88]. For a series inductance, though, due to the two symmetry properties of ϕ ∆ (ϕ), the two ϕ-dependent terms of Eq.…”