Inverse Eigenvalue Difference Problems for Quantum Dots

A system of three tunnel-coupled quantum dots is considered in the presence of an applied electric field. Given the measurements of differences between ground state energy levels as the electric field is varied, we seek to recover the quantum Hamiltonian matrix that describes this system. We formulate this as an inverse Eigenvalue difference problem and develop algebraic and computational methods along with a warm starting strategy to solve it. The results demonstrate the efficacy of these approaches in the presence of measurement noise.