Advanced Solid State I
Green's functions in condensed matter physics
Lectures: 10:45 am - 12:05 pm, Monday and Wednesday, JFB 210.Office hour: 10 - 11 am, Tuesday
Prof. Oleg Starykh, office: 304 JFB, email: starykh 'at' physics.utah.edu
This is a course about Green's functions, with focus on their numerous applications in condensed matter and statistical physics. Its outline follows G. Rickayzen's book "Green's functions and Condensed Matter" (Dover Publications; Reprint edition (May 15, 2013); ASIN: B00CWR4Z8W; here is the link to its Amazon page). In addition, detailed lecture notes will be provided by the lecturer.
Course work consists in lecture-taking (hand-written lecture notes are to be posted online) and in-class discussions, bi-weekly problem sets, and end-of-the-semester presentation (topics for these will be suggested later in the semester).
Historical introduction: an interesting and informative article in Physics Today 56(12), 41 (2003),
about George Green - the inventor of Green's functions.
Read it here online, or look here for a
Week 1: Green's functions in quantum mechanics Lectures 1 and 2
Homework 1, due Monday, February 2
Week 2: Linear response theory Lecture 3
Energy absorption rate and Im part of the retarted susceptibility Lecture 4
Electron spin resonance (ESR) in spin-rotation invariant system Lecture 5
Single-particle time-ordered (causal) GF for free Fermi gas Lecture 6
Formal properties of various GFs, and their spectral representation Lecture 7
Homework 2, due Monday, February 16
Practice: Friedel oscillations in 1d Fermi gas at finite T Lecture 8
Charge susceptibility of Fermi gas and 2-particle GF Lecture 9
Homework 3, due Monday, March 9
Using Matsubara technique to calculate density-density GF Lecture 10
Joule heating, conductivity and charge susceptibility Lecture 11
Required reading for the week of March 2 - 6: Chap.3 of the textbook, pp. 54-96, diagrammatic series, self-energy, random-phase approximation, etc.
Electrons in random potential - short-ranged (Lect. 12) and long-ranged and correlated (Lect.13) Lecture 12-13
Homework 4, due Monday, March 30
Chap.5 of Doniach-Sondheimer's book, required reading for homework 4
Dielectric function, random phase approximation Lecture 14
Chap.3 of Mahan's book, required reading for Lect. 14
Homework 5, due Monday, April 13
Screening, Friedel oscillations Lecture 15
RPA for charge and spin fluctuations (I) Lecture 16
Diagrammatic derivation of RPA for charge and (transverse) spin fluctuations (II) Lecture 17
Response of interacting system: particle-hole continuum and collective excitations. Zero sound. Ferromagnetic metal: Stoner continuum and spin waves (I) Lecture 18
Additional make-up lecture, Friday, April 10, 10 am, same room
Ferromagnetic metal: Stoner continuum and spin waves (II) Lecture 19
Pairing instability: linear response, ladder series for BCS reduced Hamiltonian. Electron-phonon mechanism. Lecture 20
Cooper problem for the pair with finite angular momentum. Lecture 21. Here is the classic solution of a 2+N electron problem by Leon Cooper (1956).
Leggett's 1975 review of He3, a must-read about p-wave superconductivity; and a brief summary about phases of Helium-3 from Chalmers Univ.
Superconductivity out of repulsion: Kohn-Luttinger mechanism for magnetized electron gas with contact interaction. Lecture 22
This lecture is based on a nice paper by S. Raghu and S. A. Kivelson. I find this detailed review of this topic from the author of several very important papers, Andrey Chubukov, to be very useful. Here are few of those papers, going back to 1988 (1, 2, 3).
Exam = collection day for your study projects: Tuesday, May 5, 10:30 am - 12:30 pm, JFB 210.