Many-Electron Approaches in Physics, Chemistry and Mathematics (eBook)

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.