Elliott H. Lieb, Jan Philip Solovej, Robert Seiringer, Jakob Yngvason (auth.)3764373369, 9783764373368
This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.
Table of contents :
Introduction….Pages 1-8
The Dilute Bose Gas in 3D….Pages 9-25
The Dilute Bose Gas in 2D….Pages 27-32
Generalized Poincaré Inequalities….Pages 33-37
Bose-Einstein Condensation and Superfluidity for Homogeneous Gases….Pages 39-46
Gross-Pitaevskii Equation for Trapped Bosons….Pages 47-62
Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases….Pages 63-70
One-Dimensional Behavior of Dilute Bose Gases in Traps….Pages 71-86
Two-Dimensional Behavior in Disc-Shaped Traps….Pages 87-107
The Charged Bose Gas, the One- and Two-Component Cases….Pages 109-129
Bose-Einstein Quantum Phase Transition in an Optical Lattice Model….Pages 131-148
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