Course Topics
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| This is the third quantum mechanics course, following up on the sequence of two core courses (PHYS 811 + PHYS 812; they, or equivalents taken at some other institution, are prerequisite to enroll in this course). Unlike PHYS 811 and PHYS 812 which are focused on single particle quantum mechanics, PHYS 814 aims to introduce graduate students to quantum-mechanics of many-body interacting systems.The course is focused on practical introduction via carefully chosen examples and hands-on tutorials using computer algebra system such as Mathematica. The examples will be drawn from the applications in condensed matter (such as magnetism, superconductors and superfluids) and AMO physics (such as quantum optics, nonclassical light and light-matter interaction), as are the areas of relevance to research in DPA.
Main Course Topics:
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- Second quantization formalism for bosons and fermions.
- Applications of second quantization: Hartree-Fock method, magnons, superconductivity and superfluidity.
- Time-dependent perturbation theory: Dyson vs. Magnus expansions.
- Floquet theory of periodically driven time-dependent quantum systems.
- Quantization of the electromagnetic field.
- Nonclassical light.
- Light-matter interaction.
- Dissipative quantum mechanics with application to qubits.
- Relativistic quantum mechanics.
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News
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- Fall 2021 course starts on August 31 at 3:30PM in Sharp Lab 118.
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Lecture in Progress
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- LECTURE 1: Second quantization formalism for harmonic oscillator
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Quick Links
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The course utilizes hands-on Computer Labs based on:
- QuSpin Python package for numerical calculations (exact diagonalization and quantum dynamics) of arbitrary boson, fermion and spin many-body systems,
- QuTiP Python package for numerical calculations of time evolution of open quantum systems, such as qubits in dissipative environment,
- SNEG Mathematica package for analytical calculations in second quantization.
It also offers students Research-Project Based Learning track where a scientific paper can be completed by the end of the semester as exemplified by:
- U. Bajpai, A. Suresh, and B. K. Nikolić, Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons, Phys. Rev. B 104, 184425 (2021). [PDF]
- P. Mondal, A. Suresh, and B. K. Nikolić, When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states, Phys. Rev. B 104, 214401 (2021). [PDF]
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Course Motto
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- In teaching, writing, and research, there is no greater clarifier than a well-chosen example.
- Formalism should not be introduced for its own sake, but only when it is needed for some particular problem.
- Physics comes in two parts: the precise mathematical formulation of the laws, and the conceptual interpretation of the mathematics. However, if words of conceptual interpretation actually convey the wrong meaning of the mathematics, they must be replaced by more accurate words. (W. J. Mullin)
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