The Mathematics of the Bose Gas and its Condensation

• Main Authors: Lieb, Elliott H. (Author), Solovej, Jan Philip (Author), Seiringer, Robert (Author), Yngvason, Jakob (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2005.
• Series: Oberwolfach Seminars ; 34
• Subjects: Physics.; Applied mathematics.; Engineering mathematics.; Condensed matter.; Statistical physics.; Dynamical systems.; Condensed Matter Physics.; Applications of Mathematics.; Mathematical Methods in Physics.; Statistical Physics, Dynamical Systems and Complexity.

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 anal...

Table of Contents:

• The Dilute Bose Gas in 3D
• The Dilute Bose Gas in 2D
• Generalized Poincaré Inequalities
• Bose-Einstein Condensation and Superfluidity for Homogeneous Gases
• Gross-Pitaevskii Equation for Trapped Bosons
• Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases
• One-Dimensional Behavior of Dilute Bose Gases in Traps
• Two-Dimensional Behavior in Disc-Shaped Traps
• The Charged Bose Gas, the One- and Two-Component Cases
• Bose-Einstein Quantum Phase Transition in an Optical Lattice Model.