Multi Matrix Vector Coherent States

TL;DR

This paper introduces a new class of vector coherent states constructed with multiple matrices in a tensor product Hilbert space, including examples with quaternions and octonions, and explores their algebraic properties and applications to tensorized Hamiltonian systems.

Contribution

It presents a novel construction of vector coherent states using multiple matrices, extending the framework to quaternionic and octonionic cases, and applies it to tensorized Hamiltonian models.

Findings

Derived vector coherent states with quaternion and octonion matrices.

Connected the states to generalized oscillator algebras.

Applied the states to tensorized Jaynes-Cummings models.

Abstract

A class of vector coherent states is derived with multiple of matrices as vectors in a Hilbert space, where the Hilbert space is taken to be the tensor product of several other Hilbert spaces. As examples vector coherent states with multiple of quaternions and octonions are given. The resulting generalized oscillator algebra is briefly discussed. Further, vector coherent states for a tensored Hamiltonian system are obtained by the same method. As particular cases, coherent states are obtained for tensored Jaynes-Cummings type Hamiltonians and for a two-level two-mode generalization of the Jaynes-Cummings model.