PARALLEL COMPUTATION FOR ELECTRONIC WAVES IN QUANTUM CORRALS

Recent scanning tunneling microscopy (STM) studies on the (111) faces of noble metals have directly imaged electronic surface-confined state s and dramatic standing-wave patterns have been observed [1,2]. We sol ve for the local density of electronic states in these ''leaky'' quant um corral confinement structures using a coherent elastic scattering t heory. We seek solutions of the two-dimensional Schrodinger equation c ompatible with non-reflecting boundary conditions which asymptotically satisfy the Sommerfeld radiation condition [11,14]. The large matrice s generated by the discretization of realistic quantum corral structur es require the use of sparse matrix methods. In addition, a parallel f inite element solution was undertaken using the message passing interf ace standard (MPI) and the Portable, Extensible, Toolkit for Scientifi c Computation (PETSc) [5] for an efficient computational solution on b oth distributed and shared memory architectures. Our calculations reve al excellent agreement with the reported experimental dI/dV STM data.