A density matrix approach to the dynamical properties of a two-site Holstein model

TL;DR

This paper investigates the charge dynamics in a two-site Holstein model using a density matrix approach in the adiabatic limit, comparing exact results with semi-classical approximations to understand quantum effects.

Contribution

It introduces a density matrix method for the two-site Holstein model and compares exact solutions with semi-classical approximations in the adiabatic limit.

Findings

Quantum effects are significant in charge dynamics.

Semi-classical approximations show good agreement in certain regimes.

The density matrix approach provides a detailed understanding of quantum behavior.

Abstract

The two-site Holstein model represents a first non-trivial paradigm for the interaction between an itinerant charge with a quantum oscillator, a very common topic in different ambits. Exact results can be achieved both analytically and numerically, nevertheless it can be useful to compare them with approximate, semi-classical techniques in order to highlight the role of quantum effects. In this paper we consider the adiabatic limit in which the oscillator is very much slow than the electron. A density matrix approach is introduced for studying the charge dynamics and the exact results are compared with two different approximations: a Born-Oppenheimer-based Static Approximation for the oscillator (SA) and a Quantum-classical (QC) dynamics.