Table of contents:
- Quantum mechanics: first principles and effective theories
(Mathematical formulation of quantum mechanics, the Bose–Einstein condensation, mean-field approximation, linear vs. nonlinear Schrödinger equations) - The GP functional and its minimizers
(Existence, uniqueness, and regularity of minimizers) - Derivation of the GP functional from first principles
(Proof of the BEC for the many-body ground state in the mean-field limit) - The time-dependent GP equation
(Dispersion, regularity, Strichartz estimates, and scattering theory) - Derivation of the GP dynamics from first principles
(Proof of the BEC for the many-body dynamics in the mean-field limit) - Bogoliubov theory
(Fock space, quasi-free particles, excitation spectrum, Landau criterion for superfluidity) - Links to classical particles
(Landau damping, plasma echoes, plasma oscillations) - Open problems
Timetable:
Monday, 01/08/2022
|
08:00 – 09:30 |
Phan Thanh Nam (Quantum mechanics: first principles and effective theories) |
|
10:00 – 11:30 |
Nguyen Trong Toan (The GP functional and its minimizers) |
|
14:00 – 16:00 |
Duong Giao Ky (Exercise section) |
Tuesday, 02/08/2022
|
08:00 – 09:30 |
Phan Thanh Nam (Derivation of the GP functional from first principles) |
|
10:00 – 11:30 |
Nguyen Trong Toan (The time-dependent GP equation I) |
|
14:00 – 16:00 |
Duong Giao Ky (Exercise section) |
Wednesday, 03/08/2022
|
08:00 – 09:30 |
Nguyen Trong Toan (The time-dependent GP equation II) |
|
10:00 – 11:30 |
Phan Thanh Nam (Derivation of the GP dynamics from first principles) |
|
14:00 – 16:00 |
Duong Giao Ky (Exercise section) |
Thursday, 04/08/2022
|
08:00 – 09:30 |
Phan Thanh Nam (Bogoliubov theory I) |
|
10:00 – 11:30 |
Phan Thanh Nam (Bogoliubov theory II) |
|
14:00 – 16:00 |
Duong Giao Ky (Exercise section) |
Friday, 05/08/2022
|
08:00 – 09:30 |
Nguyen Trong Toan (Links to classical particles I) |
|
10:00 – 11:30 |
Nguyen Trong Toan (Links to classical particles II) |
|
14:00 – 15:00 |
Phan Thanh Nam and Nguyen Trong Toan (Open problems) |