Variational approach to the Caldeira-Leggett model

We apply the displaced-oscillator variational ansatz to the Caldeira-Leggett model for a quantum particle in a one-dimensional box described by a tight-binding chain. We focus on the case of an Ohmic environment and study the phase diagram for different chain lengths. At zero temperature there is a phase transition to a localized phase when the number of sites is even. At finite temperature, a transition from a coherent to an incoherent regime is predicted for all the chain lengths considered. Finally, the results are compared to those obtained with numerical techniques.