Mathematical Consistency of Time Dependent Density Functional Theory with Kohn-Sham Potentials

Monday, November 14, 2016 - 15:00
Thackeray Hall 703
Speaker Information
Joseph Jerome
Northwestern University

Abstract or Additional Information

Abstract:  The talk analyzes a general version of time dependent quantum
           mechanics, introduced in 1984 by E. Runge and E.K.U. Gross.
           The nonlinear system is analyzed by the evolution operators,
           introduced by T. Kato in the 1970s. The talk discusses closed
           quantum systems, corresponding to homogeneous Dirichlet boundary
           conditions on a bounded domain. The existence of a unique weak
           solution on a given finite time interval is demonstrated. This
           part of the talk is based upon a 2015 publication. We also
           discuss some unpublished work relating to the convergence of
           operator Newton iteration. This is based upon the fixed point
           map, used to establish existence/uniqueness.