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2022-2023 Timetable and calendar
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Program, courses and calendar Master ICFP 1st year (2023-2024)
2023-2024 Calendar and timetable
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Program, courses and calendar Master ICFP 1st year (2022-2023)
2022-2023 Calendar and timetable
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"Physics Now" Seminars 2019/2020
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Program, courses and calendar Master ICFP 2nd year 2022-2023
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"Physics Now" Seminars 2019/2020
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Erreur ( A supprimer)
Program, courses and calendar Master ICFP 1st year (2021-2022)
Program, courses and calendar Master ICFP 1st year (2021-2022)
Program, courses and calendar Master ICFP 2nd year 2021-2022
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Archives 2015-2016
Archives 2016-2017
Archives 2017-2018
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Program, courses and calendar 2022 - 2023
2022-2023 Timetable and calendar
Courses
Internships
Program, courses and calendar 2023 - 2024
2022-2023 Timetable and calendar
Courses
Internships
Program, courses and calendar 2021 - 2022
2021-2022 Timetable and calendar
Courses
Internships
Admissions
Recrutement sur concours
Recrutement sur dossier : Concours normalien étudiant
Contacts
Seminars
Seminars
2023-2024 FIP/ICFP seminar Program
Undergraduate program Intranet
Archives
Archives 2015-2016
Archives 2016-2017
Archives 2017-2018
Archives 2018-2019
Archives 2019-2020
Archives 2020-2021
Why choose this program?
Program, courses and calendar Master ICFP 1st year (2023-2024)
2023-2024 Calendar and timetable
Courses
Internships
Program, courses and calendar Master ICFP 1st year (2022-2023)
2022-2023 Calendar and timetable
Courses
Internships
Program, courses and calendar Master ICFP 2nd year 2023-2024
First Semester
Second Semester
"Physics Now" Seminars 2019/2020
"Physics Now" Seminars 2020/2021
"Physics Now" Seminars 2021/2022
"Physics Now" Seminars 2023/2024
"Physics Now" Seminars 2022/2023
Internships
2023 2024 calendar
Program, courses and calendar Master ICFP 2nd year 2022-2023
First Semester
Second Semester
"Physics Now" Seminars 2019/2020
"Physics Now" Seminars 2020/2021
"Physics Now" Seminars 2021/2022
"Physics Now" Seminars 2022/2023
Internships
2022 2023 calendar
Admission and Language Requirements
How to apply
Information for students
Information for International Students
Fees and Scholarships
Careers
Master Intranet
Archives
Erreur ( A supprimer)
Program, courses and calendar Master ICFP 1st year (2021-2022)
Program, courses and calendar Master ICFP 1st year (2021-2022)
Program, courses and calendar Master ICFP 2nd year 2021-2022
Program, courses and calendar Master ICFP 2nd year 2020-2021
Program, courses and calendar Master ICFP 2nd year 2019-2020
Archives 2015-2016
Archives 2016-2017
Archives 2017-2018
Archives 2018-2019
Archives 2019-2020
Archives 2020-2021
Next student seminar :
Access to the program
Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship
News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program
Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr
Next student seminar :
Access to the program
Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship
News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program
Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr
Enseignant : Vladimir Kazakov - LPENS - SORBONNE UNIVERSITE
ECTS : 3
Langue d’enseignement : Anglais
Modalités d’examen : Rédiger des projets individuels puis présentation orale à distance.
Mots clés : chaînes des spins, intégrabilité, théories des champs, PDE
Plan of lecture
1. Examples of integrable classical and quantum systems (degeneracy of spectrum of hydrogen atom, Kepler orbits, KAM theory, Hopf-Burgers equation, Calogero system)
2. Classical integrability: Lax pair, integrals of motion, construction of soliton solutions on the example of Korteweg-deVries (KdV) integrable hierarchy of PDE’s; Other examples of integrable many-body systems and field theories (KdV, Toda, non-linear Schrodinger, sigma-models)
3. Quantum integrability. Bosons in one dimension with delta interaction: equivalence to non-linear Schrödinger equation; Lieb-Liniger theory; Thermodynamical Bethe ansatz (TBA)
4. Quantum Heisenberg spin chain: solution by Bethe ansatz, Baxter equation, energy spectrum
5. Alternative methods for quantum spin chains: R-matrix, algebraic Bethe ansatz
6. Advanced subjects (if time permits): Spin chains with gl(N) symmetry; Integrable QFTs in 2d (sigma models); S matrix bootstrap, Integrability and AdS/CFT correspondence
10 cours de 3h 9h00, salle L361 (3ème étage du département de Physique de l’ENS)
Mercredis: 13,20,27/01; 3,10,17/02; 3,10,17/03; exam: 31/03, 2021
Next student seminar :
Access to the program
Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship
News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program
Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr
RECRUITMENT DIRECT ACCESS
The Department of Physics