Noether symmetries and conservation laws of a reduced gauged bilayer graphene model

TL;DR

This paper derives a Hamiltonian for a simplified bilayer graphene model, identifies its symmetries and conserved quantities, and explores their algebraic structure and numerical solutions.

Contribution

It introduces a reduced Jackiw-Pi model for bilayer graphene and analyzes its Noether symmetries and conservation laws, revealing a connection to a fifth-dimensional symmetry group.

Findings

Identified the Hamiltonian for the reduced model.

Determined the Noether symmetries and conserved quantities.

Connected the symmetry group to a fifth-dimensional group.

Abstract

A canonical Hamiltonian is found for a reduced version of the Jackiw-Pi model for bilayer graphene. From the corresponding Lagrangian, the Noether point symmetries and conserved quantities are determined. The Noether symmetry group is the same as the fifth-dimensional group for the time-dependent harmonic oscillator. The realization of the algebra is achieved in terms of just one particular solution $g_1$ of the time-dependent harmonic oscillator equation underlying the reduced Jackiw-Pi model. Some numerical solutions are worked out.