Dynamics of Holstein polaron in a chain with thermal fluctuations

TL;DR

This paper uses numerical modeling to study how polarons in a chain behave under thermal fluctuations and electric fields, revealing temperature and chain length effects on polaron mobility and dynamics.

Contribution

It introduces a detailed numerical analysis of polaron dynamics in a chain with thermal noise, highlighting the dependence on temperature, chain length, and polaron size.

Findings

Polaron existence depends on temperature and chain length.

Large radius polarons exhibit similar displacement behavior across chain lengths.

Small radius polarons can switch between immobile and delocalized states.

Abstract

Numerical modeling is used to investigate the dynamics of a polaron in a chain with small random Langevin-like perturbations which imitate the environmental temperature $T$ and under the influence of a constant electric field. In the semiclassical Holstein model the region of existence of polarons in the thermodynamic equilibrium state depends not only on temperature but also on the chain length. Therefore when we compute dynamics from initial polaron data, the mean displacement of the charge mass center differs for different-length chains at the same temperature. For a large radius polaron, it is shown numerically that the ``mean polaron displacement'' (which takes account only of the polaron peak and its position) behaves similarly for different-length chains during the time when the polaron persists. A similar slope of the polaron displacement enables one to find the polaron mean velocity and, by analogy with the charge mobility, assess the ``polaron mobility''. The calculated values of the polaron mobility for $T \approx 0$ are close to the value at $T=0$, which is small but not zero. For the parameters corresponding to the small radius polaron, simulations of dynamics demonstrate switching mode between immobile polaron and delocalized state. The position of the new polaron is not related to the position of the previous one; charge transfer occurs in the delocalized state.