Quantum Landau-Lifshitz-Gilbert Dynamics of a Dimer

Sammanfattning: The classical Landau-Lifshitz-Gilbert (LLG) equations are of crucialimportance in micro-magnetism, but a true quantum-mechanical descriptionwas not found until 2013. However, very few realistic quantumsystems have been modeled using it. This project describes the quantum LLG dynamics of a dimer system,accounting for the Heisenberg exchange and Dzyaloshinskii-Moriyainteractions, as well as local dephasing as an open system effect.Equations of motion are derived using an appropriate Hamiltonian, Wieser’s non-linear master equation and a two-qubit parametrization,then solved numerically. The non-locality and entanglenment of thesystem were then investigated using the CHSH inequality and concurrence. The solutions for the dimer system show oscillations in the Blochvector components aligned with the external magnetic field, and inthe anti-ferromagnetic case, both CHSH inequality violation and entanglementwere initially found, but underwent ”sudden death” anddisentanglement as the evolution continued, due to dephasing. Analysisof the kT-Bz parameter space reveals combinations which produceentanglement without violation of the Clauser, Horne, Shimony, Holt (CHSH) inequality, and regions of Bz where increasing kT increasesentanglement. This set of solutions to Wieser’s quantum LLG equation suggests thatthe disentangling effect of dephasing and other open-system effects willbe obstacles for future practical efforts in quantum communication.