Submitted by admin_sps on 9 March, 2016 - 16:58

Course No:

P460

Credit:

8

Prerequisites:

P301 (Statistical Mechanics), P302 (Quantum Mechanics II) and P475 (Special topic in Quantum Mechanics)

Approval:

UG-Elective

Syllabus:

(42 Lectures + 14 Tutorial)

- Review of second quantisation, one and two body operators, mean field solutions of interacting systems.
- CanonicalTransformation: Jordan-Wigner, Bogoliubov-Valetin, SchriefferWolf,etc.
- Green's function formalism at zero & finite temperatures, observables and their relationship to one and two body Greens functions.
- Thermodynamic potential, spectral functions, analytic properties of Green’s function.
- Linear Response, correlation function, sum rules.
- Green’s functions equation of motion.
- Diagrammaticperturbationtheory for Greenfunction and the thermodynamic potential. Interacting fermions: Hartree-Fock, Random phase and ladder approximation, Goldstone theorem, Luttinger Ward identities. Interacting bosons: condensate depletion.
- Functional methods: Imaginary time and coherent state path integrals, many particle partition function and perturbation theory in path integral approach. Stationary phase approximation. Hubbard-Stratonovich transformationand auxiliary field representation of time evolution operator and the partition function. Saddle point approximation and small fluctuation corrections.

Reference Books:

- StatisticalPhysics part 2 by E.M.Lifshitz& L.P. Pitaevskii
- QuantumTheoryof Many body particle systems by FetterWalecka
- Introduction to Many-Body Physics by Piers Coleman
- Many particle physics by Ben Simon
- Green’s Function for SolidState Physics by S. Doniach & E.H. Sondheimer
- Quantum Mechanics R. Shankar
- Quantum many particle systems J. W. Negele and H. Orland
- Techniquesand Applicationof Path-integration by S.Schulman

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