PHY 765: Graduate Advanced Physics, Fall 2018
SynopsisThis 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. One 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, the renormalization group and scale invariance for critical systems, 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.F18.]HomeworkYou 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.F18.] Useful literatureBesides the lecture notes, supplementary reading material for each part of the course will be provided on the Sakai site. Here, some references for the course topics.Quantum mechanics (basics).
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