Fuzzy Onion as a Matrix Model

TL;DR

This paper introduces a matrix model of a 3D quantum space with an onion-like structure of concentric fuzzy spheres, enabling simulations of quantum fields and atomic systems on this novel geometric framework.

Contribution

It presents a new matrix model realization of a 3D quantum space with concentric fuzzy spheres, combining analytical and numerical methods for quantum field and atomic physics.

Findings

Numerical simulation of scalar quantum field theory on the fuzzy onion space.

Analysis of classical heat transfer in the proposed model.

Study of the quantum mechanical hydrogen atom within this framework.

Abstract

We propose a matrix model realisation of a three-dimensional quantum space. It has an onion-like structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the fuzzy sphere. The radial part is constructed using operators that relate matrices of various sizes using the matrix harmonic expansion. As an example of this approach, we produce a numerical simulation of a scalar quantum field theory, the classical heat transfer, study the quantum mechanical hydrogen atom, and consider some analytical aspects of the scalar field theory on this space.