Statistical Physics of Non Equilibrium Quantum Phenomena

✍ Scribed by Yves Pomeau, Minh-Binh Tran

• Publisher: Springer
• Year: 2019
• Tongue: English
• Leaves: 232
• Category: Library

✦ Synopsis

This book provides an introduction to topics in non-equilibrium quantum statistical physics for both mathematicians and theoretical physicists. The first part introduces a kinetic equation, of Kolmogorov type, which is needed to describe an isolated atom (actually, in experiments, an ion) under the effect of a classical pumping electromagnetic field which keeps the atom in its excited state(s) together with the random emission of fluorescence photons which put it back into its ground state. The quantum kinetic theory developed in the second part is an extension of Boltzmann's classical (non-quantum) kinetic theory of a dilute gas of quantum bosons. This is the source of many interesting fundamental questions, particularly because, if the temperature is low enough, such a gas is known to have at equilibrium a transition, the Bose–Einstein transition, where a finite portion of the particles stay in the quantum ground state. An important question considered is how a Bose gas condensate develops in time if its energy is initially low enough.

✦ Table of Contents

Front Matter ....Pages i-xv
Front Matter ....Pages 1-1
Introduction (Yves Pomeau, Minh-Binh Tran)....Pages 3-6
The Kolmogorov Equation for a Two-Level System (Yves Pomeau, Minh-Binh Tran)....Pages 7-33
The Statistical Theory of Shelving (Yves Pomeau, Minh-Binh Tran)....Pages 35-39
Summary, Conclusion and Appendix of Part 1 (Yves Pomeau, Minh-Binh Tran)....Pages 41-55
Front Matter ....Pages 57-57
Introduction (Yves Pomeau, Minh-Binh Tran)....Pages 59-68
Quantum Boltzmann Equations (Yves Pomeau, Minh-Binh Tran)....Pages 69-104
Formation of Singularities (Yves Pomeau, Minh-Binh Tran)....Pages 105-117
Hydrodynamic Approximations (Yves Pomeau, Minh-Binh Tran)....Pages 119-147
Equilibrium Properties of a Dilute Bose Gas with Small Coupling at First Order (Yves Pomeau, Minh-Binh Tran)....Pages 149-162
Mathematical Analysis of the Coupling Condensate - Thermal Cloud Systems (Yves Pomeau, Minh-Binh Tran)....Pages 163-215
Back Matter ....Pages 217-227