Thin spectrum states in bulk superconductors and superconducting grains

We show how a local pairing model for superconductivity can be used to describe the symmetry breaking mechanism in exact analogy to the case of quantum crystal and antiferromagnets. We find that there are low energy states associated with the symmetry breaking process which are not influenced by the Anderson-Higgs mechanism. The presence of these ’thin spectrum’ states in qubits based on superconducting material leads to a maximum time for which such qubits can remain quantum coherent. We also show how the charging energy of superconducting quantum dots may give the thin spectrum states a finite energy gap, impeding the spontaneous breaking of phase symmetry.