Currents algebra for the two-sites Bose-Hubbard model

TL;DR

This paper develops a currents algebra framework for the two-sites Bose-Hubbard model, deriving quantum dynamics and oscillation periods based on Hamiltonian parameters, enhancing understanding of the model's temporal behavior.

Contribution

It introduces a currents algebra approach and generalizes the Heisenberg equations to analyze the quantum dynamics of the two-sites Bose-Hubbard model.

Findings

Derived the second time derivative of currents operators.

Determined oscillation periods as functions of Hamiltonian parameters.

Analyzed different parameter regimes for current dynamics.

Abstract

I present a currents algebra for the two-sites Bose-Hubbard model, generalize the Heisenberg equation of motion to write the second time derivative of the currents operators and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters I get different currents dynamics and determine the period of the oscillations in function of the parameters.