Measure concentration and the Schrödinger equation

Abstract

AbstractThis talk pursued the aim to represent the solutions of the electronic Schrödinger equation as traces of higher‐dimensional functions. This allows to decouple the electron‐electron interaction potential but comes at the price of a degenerate elliptic operator replacing the Laplace operator on the higher‐dimensional space. The surprising observation is that this operator can without much loss again be substituted by the Laplace operator, the more successful the larger the system under consideration is. This is due to a nontrivial concentration of measure phenomenon that has much to do with the random projection theorem known from probability theory and can, for example, serve as a building block for the construction of iterative methods that map sums of products of orbitals and geminals onto functions of the same type.