Polarons in the harmonic lattice. I. Standing polaron

TL;DR

This paper derives analytical formulas for large- and small-radius polarons in a one-dimensional lattice using a mixed classical-quantum approach, and compares them with numerical simulations to study polaron formation and dynamics.

Contribution

It provides new analytical expressions for polarons in a 1D lattice within the TBA approximation, combining classical and quantum treatments of the system.

Findings

Analytical formulas agree well with numerical simulations.

Polaron formation dynamics depend on initial conditions.

Finite lattice effects influence wave function evolution.

Abstract

We obtain analytical expressions for the large- and small-radius polarons on the one-dimensional lattice in the TBA approximation. The equations of motion for this model are treated classically for the oscillator subsystem, while a quantum description is used for the electron. The electron-phonon interaction is considered in the linear Su--Schrieffer--Heeger approximation. Good agreement between analytical formulae and accurate numerical simulation is obtained. The dynamics of polaron formation from different initial conditions is considered. Some features of the wave function evolution, governed by the finite lattice length, are elucidated.