Tunneling of a quantum breather in a one-dimensional chain

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 ΔE. For the isolated dimer we reproduce the exponential factor for the splitting ΔE⁽⁰⁾, obtained earlier by a perturbative approach. Assuming the frequency ω of the breather to be much larger than the inverse instanton width we use an adiabatic approximation to derive ΔE for the dimer coupled to the harmonic chains. We find that ΔE can be obtained from ΔE⁽⁰⁾ 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 ω is large enough.