Dynamics of simple dissipative systems

The dynamics of a two-level system (TLS) coupled to an external heat bath has been studied. Correlation functions are obtained by combining analytical and numerical renormalization-group methods. It is shown that perturbation theory can be applied to obtain the low-energy, long-time behavior of the system. Analytical expressions are given for 〈σz(t)σz(0)〉T=0 valid in the long- and short-time limits (as compared with the renormalized frequency of the TLS). It is shown that other correlation functions, like 〈σₓ(t)σₓ(0)〉, depend sensitively on the nature of the high-energy cutoff of the environment. Thermodynamic functions, like the susceptibility to a bias potential and the correction to the specific heat of the environment, are also calculated. Finally, it is discussed how, in these systems, the experimental setup may influence the quantity being measured.