Quantum Vibrational Impurity Embedded in a One-dimensional Chain

TL;DR

This paper investigates quantum electron transport in a one-dimensional chain with a Holstein impurity, revealing significant differences from classical nonlinear models in the intermediate nonlinearity regime.

Contribution

It provides a fully quantum numerical analysis of electron-phonon interactions in a 1D chain with a single impurity, highlighting discrepancies with classical nonlinear models.

Findings

Quantum calculations show different probability distributions than classical models.

Intermediate nonlinearity leads to unique electron localization effects.

Results are relevant for understanding quantum impurity dynamics in low-dimensional systems.

Abstract

We perform a fully quantum mechanical numerical calculation for the problem of a single electron (or excitation) propagating in a N-site one-dimensional chain in the presence of a single Holstein impurity. We compute the long-time averaged probability for finding the electron on the impurity site as a function of the nonlinearity parameter, defined in terms of the electron-phonon coupling strength and the oscillator frequency. The results, in the intermediate nonlinearity parameter range, differ substantially from the ones obtained through the use of the discrete nonlinear Schroedinger equation, even in the high-frequency regime.