Location- and observation time-dependent quantum tunneling

We investigate quantum tunneling in a translation invariant chain of particles. The particles interact harmonically with their nearest neighbors except for one bond, which is anharmonic. It is described by a symmetric double-well potential. In the first step, we show how the anharmonic coordinate can be separated from the normal modes. This yields a Lagrangian which has been used to study quantum dissipation. Elimination of the normal modes leads to a nonlocal action of Caldeira-Leggett type. If the anharmonic bond defect is in the bulk, one arrives at Ohmic damping, i.e., there is a transition of a delocalized bond state to a localized one if the elastic constant exceeds a critical value C(crit). The latter depends on the masses of the bond defect. Super-Ohmic damping occurs if the bond defect is in the site M at a finite distance from one of the chain ends. If the observation time T is smaller than a characteristic time tau(M) similar to M, depending on the location M of the defect, the behavior is similar to the bulk situation. However, for T >> tau(M) tunneling is never suppressed.