2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228929We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures $T$ the decoherence rate $Γ$ is linear in $T$ while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high $T$. In contrast to the classical picture, impurity states spread in a wide interval of energies ($\gg T$) may essentially contribute to $Γ$.Both figures are changed to illustrate a more generic case of impurity states spread in wide interval of energies. Some changes have been made to the abstract and the introductionMesoscale and Nanoscale PhysicsSuperconductivitytext