PHY 765: Graduate Advanced Physics, Fall 2019


Instructor:   Prof. Thomas Barthel
Lectures:   Tuesdays and Thurdays 10:05-11:20AM in Physics 047
Office hours:   Tuesdays 11:20-12:00AM and Fridays 10:45-11:45AM in Physics 287
Teaching assistant:   Yikang Zhang (Physics 294)
Tutorials:   upon request
Grading:   Problem Sets (40%), Midterm exam (20%), Final exam (40%)

Synopsis

This is a graduate course on the wonderful world of quantum many-body physics. We will cover aspects from five fields: quantum information theory, atomic physics, condensed matter physics, quantum optics, and relativistic quantum field theory, addressing phenomena and techniques that (almost) every physicist should be familiar with.

We will warm up with generalizations of the postulates of quantum physics (density matrices, quantum channels, POVM) which are essential in quantum information theory and capture interactions with environmental degrees of freedom. This also allows us to understand the effect of decoherence. We then start looking at systems of identical particles and, first, discuss entanglement in such systems. On the basis of the approximative Hartree-Fock equations, we will study the electronic structure of multi-electron atoms. Quantum many-body systems are efficiently described using the formalism of 2nd quantization. With this tool at hand, we will address electron band structures of solids, topological insulators, Landau's Fermi liquid theory (describing the normal state of metals), and the BCS theory of superconductivity. Technically, this exemplifies the derivation of effective low-energy Hamiltonians, mean-field approximations, spontaneous symmetry breaking, and off-diagonal long-range order, topological invariants, and symmetry-protected topological order. Finally, we will see how to construct Lorentz invariant quantum field theories (QFT) which are essential for high-energy physics. In particular, we will look into the Klein-Gordon QFT and the Dirac QFT which describe relativistic bosonic and fermionic systems.

If time permits, we will also cover a selection of the following topics: interacting Bose-Einstein condensates (superfluidity), the Bose-Hubbard model with its superfluid-Mott quantum phase transition, topological order, and further topics from quantum information theory and quantum computation such as no-cloning, teleportation, Bell inequalities, quantum algorithms, and entanglement.

Knowledge of single-particle quantum mechanics on the level of courses PHY 464 or PHY 764 is expected.

Lecture Notes

[Are provided on the Sakai site PHYSICS.765.01.F19.]

Homework

You are encouraged to discuss homework assignments with fellow students and to ask questions in the Sakai Forum or by email. But the written part of the homework must be done individually and cannot be a copy of another student's solution. (See the Duke Community Standard.)
Homework due dates are strict (for the good of all), i.e., late submissions are not accepted. If there are grave reasons, you can ask for an extension early enough before the due date.

[Problem sets are provided on the Sakai site PHYSICS.765.01.F19.]

Literature & References

In addition to the lecture notes, supplementary reading material for each part of the course will be provided on the Sakai site. For background reading, I recommend the following books.
  • Sakurai "Modern Quantum Mechanics", Addison Wesley (1993)
  • Nielsen, Chuang "Quantum Computation and Quantum Information", Cambridge University Press (2000)
  • Altland, Simons "Condensed Matter Field Theory" 2nd Edition, Cambridge University Press (2010)
  • Peskin, Schroeder "An Introduction to Quantum Field Theory", Addison-Wesley (1995)
Here, some further references for the course.

Quantum mechanics (basics).
  • Sakurai "Modern Quantum Mechanics", Addison Wesley (1993)
  • Shankar "Principles of Quantum Mechanics" 2nd Edition, Plenum Press (1994)
  • Le Bellac "Quantum Physics", Cambridge University Press (2006)
  • Schwabl "Quantum Mechanics" 4th Edition, Springer (2007)
  • Baym "Lectures on Quantum Mechanics", Westview Press (1974)
Quantum information and computation.
  • Nielsen, Chuang "Quantum Computation and Quantum Information", Cambridge University Press (2000)
  • Preskill "Quantum Computation", Lecture Notes (2015)
  • Wilde "Quantum Information Theory" 2nd Edition, arXiv:1106.1445 (2017)
  • Bruss, Leuchs "Lectures on Quantum Information", Wiley (2007)
Non-relativistic quantum many-body physics (varying topics).
  • Coleman "Introduction to Many-Body Physics", Cambridge University Press (2015)
  • Nazarov, Danon "Advanced Quantum Mechanics", Cambridge University Press (2013)
  • Altland, Simons "Condensed Matter Field Theory" 2nd Edition, Cambridge University Press (2010)
  • Negele, Orland "Quantum Many-Particle Systems", Westview Press (1988, 1998)
  • Bruus, Flensberg "Many-Body Quantum Theory in Condensed Matter Physics", Oxford University Press (2004)
  • Ashcroft, Mermin "Solid State Physics", Harcourt (1976)
  • Ibach, Lüth "Solid State Physics" 4th Edition, Springer (2009)
Topological insulators.
  • Asbóth, Oroszlány, Pályi "A Short Course on Topological Insulators", Springer (2016)
  • Bernevig, Hughes "Topological Insulators and Topological Superconductors", Princeton University Press (2013)
  • Xiao, Chang, Niu "Berry Phase Effects on Electronic Properties", Rev. Mod. Phys. 82, 1959 (2010)
Relativistic quantum many-body physics.
  • Schwabl "Advanced Quantum Mechanics" 3th Edition, Springer (2005)
  • Peskin, Schroeder "An Introduction to Quantum Field Theory", Addison-Wesley (1995)
  • Mandl, Shaw "Quantum field theory" 2nd Edition Wiley (2010)

have a nice day!