Vector coherent states for nanoparticle Hamiltonians

TL;DR

This paper develops a formalism for vector coherent states in complex quantum systems, specifically applied to nanoparticle Hamiltonians, revealing new mechanisms for electronic energy relaxation in nanocrystals.

Contribution

It introduces a novel vector coherent states framework for nanoparticle Hamiltonians, extending existing methods to systems with degeneracies and translational motion.

Findings

Vector coherent states satisfy key mathematical properties.

New mechanism for electronic energy relaxation in nanocrystals.

Analysis of finite degeneracies in Hamiltonian systems.

Abstract

The first part of this work deals with a formalism of vector coherent states construction for a system of $M$ Fermi-type modes associated with $N$ bosonic modes. Then follows a generalization to a Hamiltonian describing the translational motion of the center of mass of a nanoparticle. The latter gives rise to a new mechanism for the electronic energy relaxation in nanocrystals, intensively studied today in condensed matter physics. Finite degeneracies of the involved Hamiltonian systems are also investigated. The defined vector coherent states satisfy relevant mathematical properties of continuity, resolution of identity, temporal stability and action identity.