We investigate a chain of particles (bonds) with harmonic interbond and anharmonic intrabond interactions. In the classical limit we consider a breather solution that is strongly localized (essentially a single-site excitation). For the quantum case we study tunneling of this excitation to a neighboring site. In that case we neglect the anharmonicity except for the two sites between which the tunneling occurs. Within this model the breather tunneling reduces to the tunneling in a dimer coupled to two adjacent harmonic chains. Application of Feynman’s path instanton technique yields the tunneling splitting [Formula Presented]. For the isolated dimer we reproduce the exponential factor for the splitting [Formula Presented], obtained earlier by a perturbative approach. Assuming the frequency [Formula Presented] of the breather to be much larger than the inverse instanton width we use an adiabatic approximation to derive [Formula Presented] for the dimer coupled to the harmonic chains. We find that [Formula Presented] can be obtained from [Formula Presented] just by scaling the Planck constant. We argue that independent of the density of states of the harmonic chains tunneling can never be suppressed, if [Formula Presented] is large enough.
|Number of pages
|Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|Published - 1998