Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View

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Volker Bach, Luigi Delle Site
Springer, Jul 1, 2014 - Science - 417 pages

This book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem.

 

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Contents

1 Relativistic Quantum Theory of ManyElectron Systems
3
2 Spurious Modes in Dirac Calculations and How to Avoid Them
30
3 Tensor Product Approximation DMRG and Coupled Cluster Method in Quantum Chemistry
53
4 Quantum Cluster Equilibrium
77
5 Linear Response Methods in Quantum Chemistry
97
Part IITopics in Density Functional Theoryand Related Approaches
111
OrbitalFree Density Functionals
113
7 TimeDependent Density Functional Theory
135
14 The Computational Complexity of Density Functional Theory
245
15 Computational Techniques for Density Functional Based Molecular Dynamics Calculations in PlaneWave and Localized Basis Sets
261
Part IVInformation Theoryin ManyElectron Descriptions
284
16 Towards the InformationTheoretic Construction of an OrbitalFree KineticEnergy Functional
287
17 LiebRobinson Bounds and the Simulation of TimeEvolution of Local Observables in Lattice Systems
301
Part VGreen FunctionBased Approaches
319
18 Electronic Structure Calculations with LDA+DMFT
320
19 The GW Approximation for the Electronic SelfEnergy
343

8 Density Functional Theory for StronglyInteracting Electrons
152
9 Towards the Computational Design of Compounds from First Principles
169
10 Application of KohnSham DensityFunctional Theory to Real Materials
191
11 The Quantum Energy Agrees with the Müller Energy up to Third Order
207
12 Mathematical Aspects of Density Functionals and Density Matrix Functionals in Quantum Chemistry
218
13 Some Important? Unsolved Mathematical Problems in Molecular Simulation
235
Part IIITopics in Computer Science
243
Part VITopics in Quantum Monte Carloand Related Approaches
358
20 LevyLieb Principle Meets Quantum Monte Carlo
361
21 The New Resonating Valence Bond Method for AbInitio Electronic Simulations
376
22 Mathematical Perspective on Quantum Monte Carlo Methods
393
Part VIIEpilogue
410
23 On Some Open Problems in ManyElectron Theory
411
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