Reduced Hierachal Equations of Motion for Exciton and electron transfer ssystems: Application to nonlinear response

2018 Fiscal Year Final Research Report

• Project/Area Number: 26248005
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Physical chemistry
• Research Institution: Kyoto University
• Principal Investigator: TANIMURA Yoshitaka 京都大学, 理学研究科, 教授 (20270465)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: 散逸系の量子力学 / 階層方程式（HEOM） / 非断熱遷移過程 / ２次元電子分光 / 励起子移動反応 / 多次元振動分光 / 量子熱力学 / 量子スピン系

Outline of Final Research Achievements

We have investigated the influence of non-Markovian and non-perturbative system-bath interaction on microscopic system by extending the reduced hierarchal equations of motion (HEOM) formalism. In order to calculate thermodynamics variables, we have derived HEOM in imaginary time, which represents an inverse temperature. To extend an applicability, we have deduced the HEOM for Holstein Hamiltonian. The Schroedinger HEOM has also been introduced to reduce the requirement of computational memory. As applications, we have studied the electron-transfer process by simulating two-dimensional electronic spectroscopy, an exciton coupled electron transfer process, quantum heat-transport and heat engines, multi-dimensional electronic-vibrational spectroscopy for various non-adiabatic transition processes, a quantum spin glass system, and a modeling of molecular liquids on the basis of multi-dimensional vibrational spectroscopy. Some of developed computer codes are provided on our WEB site.

Free Research Field

理論化学

Academic Significance and Societal Importance of the Research Achievements

散逸系の量子力学は光化学反応、光合成初期過程、量子デバイス、量子計算機などで重要な量子過程が、その周りにある溶媒やタンパク質、固体フォノンなどの環境との相互作用により生じた熱的散逸効果により、通常の量子力学で記述不可能な新奇な不可逆現象を記述する。研究代表者が導いた散逸系の量子階層方程式は、環境を特徴づけるゆらぎを非マルコフ・非摂動的に扱いながら厳密に解くことを可能とする運動方程式である。本研究ではこの方程式を非断熱遷移過程の多次元分光や量子熱機関のエントロピーの計算など、現代的な問題に適用することで、方程式の拡張を行い、計算プログラムを公開することで、分子科学のインフラの構築に寄与した。