Control Aspects of a Finite Length Hubbard Chain

F Assaad, G Dirr, F Goth, U Helmke
Solid state physics provides a rather new application area for quantum control. Yet, the high dimensional state spaces in this field require a thorough analysis of the underlying Lie algebraic structures for developing efficient control strategies. In this paper, we focus a one-dimensional chain of quantum dots described by the Hubbard model. The model plays an extremely important role in solid state physics since it is the simplest model which explicitly takes into account the interplay
more » ... he interplay between Coulomb repulsion of electrons and their kinetic energy. We begin with an comprehensive description to the mathemtical tools need for the appropriate state space construction. Based on these concepts, we introduce the general Hubbard Hamiltonian and discuss some aspects of is general Lie algebraic structure. Finally, we present a toy example for illustrating the afore established notions. The tutorial part of this work is supposed to enhance the collaboration between theoretical physicists and mathematicians in the area of quantum control.