PHY 765: Graduate Advanced Physics, Fall 2017
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 derive the approximative Hartree-Fock equations. On the basis of these, we will discuss 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 study Fermi gases, electron band structures of solids, 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. Switching from fermions to bosonic systems as studied in experiments with trapped ultracold gases, we will discuss the Bose-Einstein condensation and the effects of interactions on the basis of the Bogoliubov theory (depletion, phonons, superfluidity). Finally, we will see how to come up with Lorentz invariant quantum field theories which are essential for high-energy physics. If time permits, we will cover a selection of the following topics: the Bose-Hubbard model with its superfluid-Mott quantum phase transition, quantum magnets, and 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.F17.]HomeworkYou are encouraged to discuss homework assignments with fellow students. 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.F17.] 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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