COURSE UNIT TITLE

: QUANTUM THEORY OF MANY-PARTICLE SYSTEMS - I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5087 QUANTUM THEORY OF MANY-PARTICLE SYSTEMS - I ELECTIVE 3 0 0 7

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 learn the basic concepts of first and second quantization.
2   . Being able to understand non-interacting electron gas, electron gases in 3,2,1 and 0 dimensions.
3   Being able to learn the basic concepts of mean field theory and its applications to ferromagnetic substances.
4   Being able to understand the basic concepts of linear response theory and apply linear response theory to electron systems under the influence of electric and magnetic fields.
5   Being able to understand the field of mesoscopic transport and calculate the transport properties of interacting mesoscopic systems using many-body formalism.
6   Being able to understand the concept of Green s functions in many body physics and calculate the single particle Green's functions and two particle correlation functions of various systems.
7   Being able to learn mathematical details of imaginary-time Green s functions and calculate the polarizability of free electrons.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Chapter-1 First and second quantization First quantization: single-particle systems, First quantization: many-particle systems, Basic concepts of second quantization
2 Chapter-1 First and second quantization Second quantization: specific operators, Second quantization and statistical mechanics Chapter-2 The electron gas The non-interacting electron gas
3 Chapter-2 The electron gas Electron interactions in perturbation theory, Electron gases in 3, 2, 1, and 0 dimensions Chapter-3 Phonons; coupling to electrons Jellium oscillations and Einstein phonons , Electron-phonon interaction and the sound velocity, Lattice vibrations and phonons in 1D
4 Chapter-3 Phonons; coupling to electrons The specific heat of solids in the Debye model , Electron-phonon interaction in the lattice model, Electron-phonon interaction in the jellium model Chapter-4 Mean Field Theory Basic concepts of mean field theory, The art of mean field theory
5 Chapter-5 Time Dependence in Quantum Theory The Schrödinger picture, The Heisenberg picture, The interaction Picture, Time-evolution in linear response, Time dependent creation and annihilation operators,Fermi's golden rule, the T-matrix and the generalized Fermi's golden rule
6 Chapter-6 Linear Response Theory The general Kubo formula, Kubo formula for conductivity, Kubo formula for conductance, Kubo formula for the dielectric function Chapter-7 Transport in Mesoscopic Systems The S-matrix and scattering states, Conductance and transmission coefficients
7 1st MIDTERM
8 Chapter-7 Transport in Mesoscopic Systems Electron wave guides Chapter-8 Green s functions Classical Green s functions, Green s function for the one-particle Schrödinger equation, Single-particle Green s functions of many-body systems
9 Chapter-8 Green's functions Measuring the single-particle spectral function, Two-particle correlation functions of many-body systems
10 Chapter-9 Equation of motion theory The single-particle Green's function, Single level coupled to continuum, Anderson's model for magnetic impurities, The two-particle correlation function
11 Chapter-10 Transport in Interacting Mesoscopic Systems Model Hamiltonians, Sequential tunelling: the Coulomb blockade regime, Coherent many-body transport phenomena, The conductance for Anderson- type models
12 2nd MIDTERM
13 Chapter-10 Transport in Interacting Mesoscopic Systems The Kondo effect in quantum dots Chapter-11 Imaginary Time Green s Functions Definitions of Matsubara Green s functions, Connection between Matsubara and retarded functions
14 Chapter-11 Imaginary Time Green's Functions Single-particle Matsubara Green's function, Evaluation of Matsubara sums, Equation of motion, Wick's theorem, Example: polarizability of free electrons

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
Preparation before/after weekly lectures 12 4 48
Preparation for Mid-term Exam 2 8 16
Preparation for Final Exam 1 8 8
Preparing Individual Assignments 12 2 24
Preparing Presentations 12 3 36
Final 1 2 2
Mid-term 2 2 4
TOTAL WORKLOAD (hours) 174

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

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

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