In recent years there has been a growing activity on the problem of justification of mean field equations for many body quantum systems, with particular attention to the semiclassical limit. The methods used are often reminescent of averaging and normal form methods typically used in the theory of dynamical systems.
Furthermore, semiclassical methods have shown that there are deep connections between dynamical properties of a Hamiltonian system and the spectral properties of the corresponding quantum operator. The purpuse of this workshop is to discuss the relationships between normal form methods, spectral theory and effective equations in order to try to export the corresponding techniques from one field to the others.

People

Program

Location & Info

There will be two minicourses, by B. Schlein and S. Vũ Ngọc, and seven talks.

Abstracts: pdf file

Tuesday, 17th

14:45 - 16:15

"Bogoliubov theory for Bose-Einstein condensates (part I)"

B. Schlein

16:15 - 16:45

Coffee Break

16:45 - 17:45

"Concentration and non-concentration of modes and quasi-modes"

F. Macià

Wednesday, 18th

10:00 - 11:30

"Bogoliubov theory for Bose-Einstein condensates (part II)"

B. Schlein

11:30 - 12:00

Coffee Break

12:00 - 13:00

"Quantum Propagation of Wave Packets for codimension one crossings eigenvalues"

D. Robert

13:00 - 14:45

Lunch

14:45 - 16:15

"Quantum integrable systems and asymptotic lattices (part I)"

S. Vũ Ngọc

16:15 - 16:45

Coffee Break

16:45 - 17:45

"On the correlation energy of mean field Fermi gases"

M. Porta

Thursday, 19th

10:00 - 11:00

"KAM theorems quasimodes and applications"

G. Popov

11:00 - 11:30

Coffee Break

11:30 - 12:30

"Reducibility for a Schrodinger operator with almost-periodic potential"

M. Procesi

12:30 - 14:45

Lunch

14:45 - 16:15

"Quantum integrable systems and asymptotic lattices (part II)"

S. Vũ Ngọc

16:15 - 16:45

Coffee Break

Friday, 20th

10:30 - 11:30

"Contact interactions and Gamma convergence"

G. Dell'Antonio

11:30 - 12:00

Coffee Break

12:00 - 13:00

"Coherent dynamics in large size Bose-Hubbard models"

A. Ponno

We acknowledge:
PRIN 2017 PRIN201719VMAST_01 "Mathematical Quantum Matter”, MIUR
Dipartimento di Matematica, Università degli Studi di Milano
PSR Grant 2018 “Classical and quantum dynamical systems, statistical mechanics”, Università degli Studi di Milano,
PSR Grant 2018 “Analisi, Geometria e Fisica Matematica dei sistemi variazionali non-lineari”, Università degli Studi di Milano,
FFABR 2017, MIUR

            


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