We describe the dynamics of a rf-SQUID, in presence of dissipation, by exploiting generalized non-Hermitian Hamiltonians. We discuss, by such an approach, the time evolution of the density matrix for an ohmic rf-SQUID in a MQC experiment. Our formalism allows us to recover the results by Caldeira and Leggett on the decay rate of the oscillations of the tunneling probability.
Chiatti, L., Mignani, R. (1997). Non-hermitian dynamics of a dissipative squid in a MQC experiment. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 11(8), 1051-1066 [10.1142/S021797929700054X].