Integer partition manifolds and phonon damping in one dimension

TL;DR

This paper introduces a quantum model linking integer partitions to energy distribution among harmonic oscillators, enabling analysis of quantum typicality and non-exponential relaxation with confirmed theoretical and numerical agreement.

Contribution

It presents a novel quantum model based on integer partitions to study phonon damping and relaxation phenomena in one-dimensional systems.

Findings

Quantitative agreement between field-theoretical calculations and exact diagonalization.

Demonstration of quantum typicality within the model.

Observation of non-exponential relaxation behavior.

Abstract

We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states allows us to examine both the quantum typicality and the non-exponential relaxation in the same system. A quantitative agreement between the field-theoretical calculations and the exact diagonalization of the Hamiltonian is demonstrated.