Many-Electron Approaches in Physics, Chemistry and Mathematics

"This book presents 23 papers that delve into various areas of research. The intent is to present a multidisciplinary perspective across the fields of computer science, physics, chemistry, and mathematics. ... This book should be of primary interest to those involved in ongoing research in physics and physical chemistry." (G. R. Mayforth, Computing Reviews, April, 2015)

• Topics in Quantum Chemistry.- Relativistic Quantum Theory of Many-Electron Systems.- Spurious Modes in Dirac Calculations and how to avoid them.- Tensor product approximation (DMRG) and Coupled Cluster Method in Quantum Chemistry.- Quantum Cluster Equilibrium.- Linear Response Methods in Quantum Chemistry.- Topics in Density Functional Theory and Related Approaches.- Progress on New Approaches to Old Ideas: Orbital-free Density Functionals.- Time-dependent Density Functional Theory.- Density Functional Theory for Strongly-Interacting Electrons.- Towards the Computational Design of Compounds from First Principles.- Application of (Kohn-Sham) Density Functional Theory to Real Materials.- The Quantum Energy agrees with the Muller Energy up to the Third Order.- Mathematical Aspects of Density Functionals and Density Matrix Functionals in Quantum Chemistry.- Some (important?) unsolved Mathematical Problems in Molecular Simulation.- Topics in Computer Science.- The Computational Complexity of Density Functional Theory.- Computational Techniques for Density Functional-based Molecular Dynamics Calculations in Plane-Wave and Localized Basis Sets.- Information Theory in Many-Electron Descriptions.- Towards the Information-Theoretic Construction of an Orbital-free Kinetic Energy Functional.- Lieb-Robinson Bounds and Simulation of Time Evolution of Local Observables in Lattice Systems.- Green Function-based Approaches.- Electronic Structure Calculations with LDA+DMFT.- The GW Approximation for the Electronic Self-Energy.- Topics in Quantum Monte Carlo and Related Approaches.- Levy-Lieb Principle meets Quantum Monte Carlo.- The new Resonating Valence Bond Method for ab-initio Electronic Simulations. Mathematical Perspective on Quantum Monte Carlo Methods.- Open Problems: A wish list of Mel Levy and Elliot Lieb.