Location- and observation time-dependent quantum-tunneling

TL;DR

This paper studies quantum tunneling in a chain with an anharmonic bond, revealing location- and time-dependent damping effects that influence the transition between delocalized and localized states.

Contribution

It introduces a model for quantum tunneling with a defect in a chain, analyzing how damping and tunneling behavior depend on the defect's position and observation time.

Findings

Ohmic damping causes a transition at a critical elastic constant.

Superohmic damping occurs when the defect is near the chain end.

Tunneling is unaffected by damping for long observation times when the defect is near the end.

Abstract

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. Superohmic 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 $\tau_M \sim M$, depending on the location M of the defect, the behavior is similar to the bulk situation. However, for $T \gg \tau_M$ tunneling is never suppressed.