Phonon Casimir effect in polyatomic systems

TL;DR

This paper develops a general path-integral method to calculate phonon-mediated defect interactions in various condensed-matter systems, enabling analysis at any temperature and for different defect configurations.

Contribution

It introduces a versatile theoretical framework for computing the phonon Casimir effect in polyatomic systems of arbitrary dimensionality and composition.

Findings

Validated the method with numerical calculations on chains and molecules.

Demonstrated temperature-dependent defect interaction energies.

Provided a general approach applicable to complex systems.

Abstract

The phonon Casimir effect describes the phonon-mediated interaction between defects in condensed-matter systems. Using the path-integral formalism, we derive a general method for calculating the Helmholtz free energy due to vibrational modes in systems of arbitrary dimensionality and composition. Our results make it possible to extract the defect interaction energy at any temperature for various defect configurations. We demonstrate our approach in action by performing numerical calculations for mono- and diatomic chains, as well as a diatomic molecule, at zero and finite temperatures and validate our results using exact diagonalization.