This volume is based on lectures given during the program “Complex Quantum Systems” held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many-body methods originating from quantum information, and — the most complex — semirelativistic quantum electrodynamics.
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These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.Contents:
- Stability of Matter (Rafael D Benguria and Benjamín A Loewe)
- Mathematical Density and Density Matrix Functional Theory (DFT and DMFT) (Volker Bach)
- On the Dynamics of a Fermi Gas in a Random Medium with Dynamical Hartree–Fock Interactions (Thomas Chen)
- On the Minimization of Hamiltonians over Pure Gaussian States (Jan Dereziński, Marcin Napiórkowski and Jan Philip Solovej)
- Variational Approach to Electronic Structure Calculations on Second-Order Reduced Density Matrices and the N-Representability Problem (Maho Nakata, Mituhiro Fukuda, and Katsuki Fujisawa)
- Fermionic Quantum Many-Body Systems: A Quantum Information Approach (Christina V Kraus)
- Hydrogen-Like Atoms in Relativistic QED (Martin Könenberg, Oliver Matte, and Edgardo Stockmeyer)
Readership: Mathematicians and mathematical physicists, advanced graduate students and researchers in rigorous many body theory.