The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars (34))

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.

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 is a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but it is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. It is an active subject of ongoing research, and this book provides a pedagogical entry into the field for 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.

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 "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."--Jacket Schrödinger's equation of 1926 defined a new mechanics whose Hamiltonian is based on classical mechanics.