Introduction to many-body physics of fermions and bosons - Département de Physique de l'Ecole Normale supérieure

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Introduction to many-body physics of fermions and bosons

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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Next student seminar :
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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

Faculty : Pascal Simon and Michele Casula

ECTS credits : 3

Language of instruction : English

Description :
Description
This course aims at introducing modern methods of many-body theory to M2 students. After some general motivations, we will lay the foundation of many-body physics by presenting fundamental tools such as Green functions and diagrammatic expansions formalisms. We will apply these tools to some concrete examples in condensed matter physics and cold atoms in order to connect the theoretical framework to standard observables. Finally, the course will give an overview on the latest numerical developments in the field.
Outlook of the course:
0) General introduction and some reminder.
Strong local interaction; role of dimensionality of particle statistics
I) Green function formalism
Green function at T=0. Application to free fermions.
The resonant level model and Friedel oscillations.
Spectral representations.
Finite temperature Matsubara Green functions
II) Introduction to Feynman diagrams
Interaction representation and Wick theorem
Perturbative expansion of Green functions and Feynman diagrams
Application to electron-phonon interaction
Application to electron-electron interaction
III) Introduction to quantum impurity models
Anderson model and various limiting cases
Feynman diagrams in the Anderson model.
Application to transport in quantum dots.
IV) Phenomenology of the Fermi liquid.
Notion of quasi-particle excitation
Self-energy and spectral consequences
V) Dynamical Mean Field Theory
Bethe lattice
Lattice Embedding to a Quantum impurity model
Hubbard model from a dynamical mean field perspective
Mott transition
Critical exponents
VI) Many-body theories for ab initio calculations
Hedin’s equations
GW approximation
Bosonic degrees of freedom: plasmons and phonons
Examination: oral exam

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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