where P αk and Q αk represent the mass-weighted momentum and coordinate of the kth oscillator with the frequency ω αk in bath α (∈ {ph,pt}). Every oscillator in the bath is displaced by c αk s α (x m ,x c )/ω 2 αk due to its coupling to the system, where c αk denotes the coupling strength and s α (x m ,x c ) the coupling operator.