PHY 765: Graduate Advanced Physics, Fall 2016
SynopsisThis is a graduate course on the wonderful world of quantum many-body physics. It covers several essential phenomena that (almost) every physicist should have heard of and prepares for more specialized studies of quantum optics, quantum information, condensed matter, and quantum field theory.After warming up with generalizations of the postulates of quantum physics (density matrices, quantum channels, POVM), we will 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 atoms and molecules. Quantum many-body systems are efficiently described using the formalism of 2nd quantization. With this tool at hand, we will study the electron gas, Landau's Fermi liquid theory (describing the normal state of metals), the BCS theory and Ginzburg-Landau theory of superconductivity, and the quantum Hall effect. Switching from fermions to bosons, we will discuss the Bose gas, Bose-Einstein condensation, and the effects of interactions on the basis of the Bogoliubov theory and Gross-Pitaevskii equations (depletion, phonons, healing length, superfluidity). If time permits, we will also discuss the Bose-Hubbard model with its superfluid-Mott transition and aspects of quantum magnetism. We will end our tour with topics from quantum information theory and quantum computation such as no-cloning, teleportation, Bell inequalities, quantum algorithms, error correction, 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.F16.]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.) However, you are allowed to work in groups of two. In that case, both partners still need to hand in a handwritten copy of their solution and should additionally always specify the name of their partner.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. [Are provided on the Sakai site PHYSICS.765.01.F16.] Useful literatureQuantum mechanics (single-particle).
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