Numbering Code	G-SCI41 57004 LJ60	Year/Term	2022 ・ Second semester
Number of Credits	2	Course Type	Lecture
Target Year	Master's students	Target Student
Language	Japanese	Day/Period
Instructor name	TANIMURA YOSHITAKA (Graduate School of Science Professor)
Outline and Purpose of the Course	In this course of lectures, I will teach the essence of nonlinear optical responses and quantum dissipative dynamics, which plays essential roles in electronic and vibrational optical spectroscopies in condensed phases, quantum information theory, exciton and electron transfer processes in photosynthesis systems, and quantum thermos dynamics using the PowerPoint lecture note available at the above WWW site.
Course Goals	散逸系の量子力学とは、注目する比較的小さな系とその周りの多自由度の熱浴と呼ばれる系から記述される系で、熱浴の自由度を縮約することにより、注目する系が熱平衡状態へと不可逆的に向かう過程を記述する理論体系である。この目的のためI first explain a basis of path integral formalism to derive Feynman-Vernon influence functional formalism. Then I introduce a system-bath model to explain how fluctuation and dissipation arises from the environment, and the concept will be illustrated with some examples from chemistry and biology. The quantum master, Redfield, and Fokker-Planck equations will be derived from a standard perturbative expansion approach with the use of the interaction picture. The quantum Fokker-Planck equations will be derived from this in hierarchy form based on the Feynman-Vernon influence functional formalism. The derived hierarchy equations can deal with strong system-bath coupling and non-Markovian noise. The reduced hierarchy equations of motion for systems with discrete energy levels will also be derived using a coherent state representation for the path integrals. Various applications of the hierarchy equation of motion approach, including linear and nonlinear spectroscopies, electron transfer, photodissociation, chemical reactions, quantum tunneling, and quantum information problems will also be discussed. The distributed source code, "nonMarkovian2009", will be demonstrated and examined.
Schedule and Contents	各章　２回ずつ CONTENTS 1. Introduction 2. Standard Reduced Equation of Motion Approach 3. Influence Functional 4. Quantum Fokker-Planck Equation in Hierarchy Form 5. Third-order Nonlinear Response 6. Low-Temperature Correction Terms 7. Hierarchy Equations of Motion for non-Ohmic Bath
Course Requirements	Students must know the basics of quantum mechanics and statistical physics
Study outside of Class (preparation and review)	None
Textbooks	Textbooks/References	パワーポイント講義ノート http://theochem.kuchem.kyoto-u.ac.jp/members/tanimura.htm
References, etc.	参考文献 https://journals.jps.jp/doi/10.1143/JPSJ.75.082001 https://aip.scitation.org/doi/10.1063/5.0011599
Related URL	https://journals.jps.jp/doi/10.1143/JPSJ.75.082001 https://aip.scitation.org/doi/10.1063/5.0011599 https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.1c08552