COURSE UNIT TITLE

: QUANTUM THEORY OF MANY-PARTICLE SYSTEMS - II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5166 QUANTUM THEORY OF MANY-PARTICLE SYSTEMS - II ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR ISMAIL SÖKMEN

Offered to

PHYSICS
PHYSICS

Course Objective

In this lecture it's aimed to teach the techniques of many-body quantum theory with a
large number of applications to condensed matter physics to people who have knowledge
of quantum theory and condensed matter physics.

Learning Outcomes of the Course Unit

1   Being able to obtain Feynman diagrams for non-interacting particles in an
2   Being able to evaluate Feynman diagram technique for a system fermions with pair
3   Being able to determine the dielectric properties such as the static and
4   Being able to reanalyze the Coulomb interaction electron gas using Feynman
5   Being able to develop semi-classical Fermi liquid theory for interacting
6   Being able to search the statistical properties of conductance of disordered
7   Being able to develop and perform green s function technique for free phonons and
8   Being able to search superconductivity and the consequences of superconductivity
9   Being able to understand Luttinger liquid theory comprehensively.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Chapter-12 Feynman diagrams and external potentials Non-interacting particles in external potentials, Elastic scattering and Matsubara frequencies, Random impurities in disordered metals, Self energy for impurity scattered electrons
2 Chapter-13 Feynman diagrams and pair interactions, The perturbation series for G, The Feynman rules for pair interactions, Self-energy and Dyson s equation, The Feynman rules in Fourier space, Examples of how to evaluate Feynman diagrams
3 Chapter-13 Feynman diagrams and pair interactions, Cancellation of disconnected diagrams (general case), Feynman diagrams for Kondo model Chapter-14 The interacting electron gas, The selfenergy in the random phase approximation
4 Chapter-14 The interacting electron gas, The renormalized Coulomb interaction in RPA, The groundstate energy of the electron gas, The dielectric function and screening, Plasma oscillations and Landau damping
5 Chapter-15 Fermi liquid theory, Adiabatic continuity, semi-classical treatment of screening and plasmons, Semi-classical transport equation, Microscopic basis of the Fermi liquid theory
6 Chapter-16 Impurity scattering and conductivity, Vertex corrections and dressed Green s functions, The conductivity in terms of a general vertex function, The conductivity in the first Born approximation, The weak localization correction to the conductivity, Disordered mesoscopic systems
7 1st MIDTERM
8 Chapter-17 Green s functions and phonons, The Green s function for free phonons, Electron-phonon interaction and Feynman diagrams, Combining Coulomb and electron-phonon interactions
9 Chapter-17 Green's functions and phonons, Phonon renormalization by electron scattering in RPA, The Cooper instability and Feynman diagrams
10 Chapter-18 Superconductivity, The Cooper instability, The BCS groundstate, Microscopic BCS theory, BCS theory with Matsubara Green s functions, The Nambu formalism of the BCS theory, Gauge symmetry breaking and zero resistivity, The Josephson effect
11 2nd MIDTERM
12 Chapter-19 1D electron gases and Luttinger liquids, What is a Luttinger liquid , Experimental realizations of Luttinger liquid physics
13 Chapter-19 1D electron gases and Luttinger liquids, A first look at the theory of interacting electrons in 1D, The spinless Luttinger-Tomonaga model Hamiltonian
14 Chapter-19 1D electron gases and Luttinger liquids, Bosonization of the Tomonaga model Hamiltonian, Electron operators in bosonized form, Green s functions, Measuring local density of states by tunneling, Luttinger liquid with spin

Recomended or Required Reading

Textbook:
Many-body Quantum Theory in Condensed Matter Physics (Henrik Bruus, Karsten Flensberg)
Supplementary Books:
Quantum Many-Particle Systems (John W. Negele, Henri Orland)
Many-Particle Physics (Gerald D. Mahan)
Quantum Theory of Many-particle Systems (Alexander L. Fetter, John Dirk Walecka)
Molecular Electronic Structure Theory (Trygive Helgaker, Poul Jorgensen, Jeppe Olsen)
Introduction to Many Body Physics (Piers Coleman)
Electronic Transport in Mesoscopic Systems (Supriyo Datta)
Quantum Transport: Atom to Transistor (Supriyo Datta)

Planned Learning Activities and Teaching Methods

Lecturing
Question-Answer
Discussing
Home Work

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE 1 MIDTERM EXAM 1
2 MTE 2 MIDTERM EXAM 2
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + FCG * 0.5
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

1. The homeworks will be assessed by directly adding to the mid-term scores.
2. Final examination will be evaluated by essay or test typ examination technique.

Language of Instruction

Turkish

Course Policies and Rules

1. It is obligated to continue to at least 70% of lessons.
2. Every trial to copying will be finalized with disciplinary proceedings.
3. The instructor has right to make practical quizzes. The scores obtained from
quizzes will be directly added to exam scores.

Contact Details for the Lecturer(s)

ismail.sokmen@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 12 3 36
Preparations before/after weekly lectures 12 5 60
Preparation for midterm exam 2 8 16
Preparation for final exam 1 8 8
Preparing assignments 12 2 24
Preparing presentations 12 3 36
Final 1 3 3
Midterm 2 3 6
TOTAL WORKLOAD (hours) 189

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1555433
LO.2555433
LO.3555433
LO.4555433
LO.5555433
LO.6555433
LO.7555433
LO.8555433
LO.9555433

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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