量子物理学

前半６回（布能　担当分） 1. Dynamics of open quantum systems 1.1 Evolution of closed systems 1.2 Pure states, mixed states, and von Neumann equation 1.3 From closed system to open systems 1.4 Kraus representation and infinitesimal time-evolution 1.5 GKLS quantum master equation 2. Mathematical properties of KGLS equation 2.1 CPTP maps 2.2 Quantum dynamical semigroups 2.3 Spohn's representation 2.4 Information erasure: Landauer's bound 3. Derivation of weak-coupling and Born-Markov-Secular master equation 3.1 Nakajima-Zwanzig projection operator method 3.2 Redfield equation 3.3 Secular approximation 3.4 KMS condition and detailed balance 3.5 Pauli master equation 4. Quantum measurement 4.1 Discrete quantum measurement 4.2 Continous quantum measurement and stochastic Schrodinger equation 5. Advanced topics 5.1 Symmetry of Liouvillians 5.2 Reservior engineering 5.3 Exceptional points 後半６回（江澤　担当分） I. Introduction II. Quantum geometry A. Quantum distance and quantum geometric tensor B. Berry connection, Berry curvature and Chern number C. Wannier function and polarization D. Inequality E. Quantum Geometry for two-band systems F. Analogy of the theory of general relativity G. Non-Abelian quantum geometry III. Quantum geometry in condensed matter physics A. Thouless-Kohmoto-Nightingale-Nijs formula B. Dirac system C. Optical absorption and elliptic dichroism D. Sum rule E. Bulk photovoltaic effects F. Nonlinear conductivity IV. Zeeman Quantum geometry for momentum and spin A. Responses originated from the Zeeman geometry B. Zeeman Quantum Geometry for two-band systems C. Rashba system D. Non-Abelian Zeeman quantum geometry V. Quantum geometry for non-Hermitian systems A. Open quantum system and non-Hermitian Hamiltonian B. Non-Hermitian quantum geometry C. Two-band systems D. Dirac system with a complex mass VI. Quantum information geometry A. Uhlmann quantum geometry for density matrix B. Classical Fisher information C. Quantum Cramer-Rao inequality D. Quantum Fisher information for a pure state and quantum metric E. Fluctuation-dissipation theorem F. Quantum geometry at thermal equilibrium VII. X-wave magnets A. Fermi surface symmetry B. Model Hamiltonian C. Symmtery 1. Spin diagonal case 2. Spin nondiagonal case D. Quantum geometry of X-wave magnets E. Zeeman quantum geometry of X-wave magnets F. Zeeman quantum geometry induced cross response G. Materials 1. p-wave magnet 2. d-wave altermagnet 3. f-wave magnet 4. g-wave altermagnet 5. i-wave altermagnet VIII. Transport properties of X-wave magnets A. Without Rashba interaction 1. Spin current generation 2. Spin Nernst effects 3. Tunneling magnetoresistance B. With Rashba interaction 1. Anomalous Hall effects 2. Planar Hall effects IX. Quantum Hall effects A. Landau levels 1. p-wave magnets and coherent states 2. d-wave altermagnets and squeezed states 3. X-wave magnets B. Magneto-optical conductivity 1. p-wave magnets 2. d-wave altermagnets C. Magnetic circular dichroism X. Friedel oscillation A. Free electrons B. p-wave magnets C. d-wave altermagnets D. X-wave magnets

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布能担当分： 講義ノートをUTOLで公開するので、適宜予習・復習を行うこと 江澤担当分： 講義の内容は以下のレビュー論文を参考のこと M. Ezawa, Quantum geometry and X-wave magnets with X=p,d,f,g,i Appl. Phys. Express 19 030101 (2026) arXiv:2512.05477

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