I am sorry to be so troublesome and possibly infringing some rules, but could I once more invoke the help of other participants in order to solve my query on the Caldeira-Legget model, namely the introduction of a phase shift, better detailed in Caldeira-Leggett Dissipation: frequency shift due to bath coupling?
Thank you very much. I am so keen to understand this point but got into a "loop" and cannot make sense of it any more...