量子物理学

前半６回（平山　担当分） 1. Ab initio Calculation 1.1 Density functional theory 1.2 Band structure 1.3 Effective model 2. Topology in Crystals 2.1 topology in real spase 2.2 topology in k spase 2.3 Berry phase and Zak phase 3. Topological Materials (Insulator) 3.1 Quantum spin Hall effect 3.2 3D Topological insulator 3.3 Quantum anomalous insulator 4. Topological Materials (Semimetal) 4.1 Weyl semimetal 4.2 Dirac semimetal 4.3 Nodal-line semimetal 5. Strong Correlation 5.1 Correlation in ab initio calculation 5.2 Many body Hamiltonian 5.3 Strongly correlated systems 6. Exotic Materials 6.1 Correlation in topology 6.2 Topological superconductivity 6.3 Other materials 後半６回（江澤　担当分） 1 Topological soliton 　1.1 domain wall 　1.2 vortex 　1.3 skyrmion 2 Topological insulators 　2.1 Su-Schrieffer-Heeger model 　2.1.1 Bulk spectrum 　2.1.2 Edge states and bulk-edge correspondence 　2.1.3 Chiral symmetry 　2.1.4 Chiral index of the SSH model 　2.1.5 Dirac theory of the SSH model and Jackiw-Rebbi solution 3 Higher-order topological systems 　3.1 Corner and hinge states 　3.2 Breathing Kagome model 4 Non-Hermitian topological systems 　4.1 Nonreciprocity and Hatano-Nelson model 　4.1.1 Non-Hermitian Skin states 　4.2 Non-Hermitian SSH model with PT symmetry 5 Artifical topological systems 　5.1 Electric circuits 　5.2 Photonic systems 　5.3 Mechanical systems 6 Qubit 　6.1 Classical LC resonator 　6.2 Quantum LC resonator 　6.3 Superconducting qubit 　6.4 Circuit Quantum Electrodynamics 　6.5 Rabi model 　6.6 Campbell-Baker-Hausdorff formula 　6.7 Rotational-wave approximation 　6.8 Jaynes-Cummings model 　6.9 Schrieffer-Wolff transformation and quantum nondemolition measurement 　6.10 Rabi oscillation 7. Quantum gates and quantum computation 　7.1 Pauli X gate 　7.2 Pauli Y gate 　7.3 Pauli Z gate 　7.4 Phase-shift gate 　7.5 iSWAP gate 　7.6 CNOT gate 　7.7 Solovay-Kitaev theorem and universal quantum computation

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