Quantum versus Semiclassical Description of Selftrapping: Anharmonic Effects

TL;DR

This paper compares quantum and semiclassical models of selftrapping in anharmonic systems, showing that anharmonicity does not significantly alter long-term selftrapping behavior and that semiclassical approximations remain valid under certain conditions.

Contribution

It provides a fully quantum mechanical analysis of anharmonic selftrapping, extending previous harmonic models and validating semiclassical approximations in the anharmonic regime.

Findings

Selftrapping persists in highly anharmonic polarons for long times.

Polaron tunneling time scales exponentially with binding energy.

Semiclassical approximation agrees with quantum results in certain limits.

Abstract

Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum mechanical analysis of a two-site system, where the oscillator is described by a tunably anharmonic potential, with a square well with infinite walls and the harmonic potential as its extreme limits, and wherein the interaction is nonlinear in the oscillator displacement. We find that even highly anharmonic polarons behave similar to their harmonic counterparts in that selftrapping is preserved for long times in the limit of strong coupling, and that the polaronic tunneling time scale depends exponentially on the polaron binding energy. Further, in agreement, with earlier results related to harmonic polarons, the semiclassical approximation agrees with the full quantum result in the massive oscillator limit of small oscillator frequency and strong quasiparticle-oscillator coupling.