Abstract
In this paper, two developments, the theory of hierarchical equations of motion (HEOM) for open quantum dynamics systems and the theory of ultrafast nonlinear two-dimensional (2D) spectroscopies, are described, following the history of their founder. The HEOM was discovered by attempting to derive an equation similar to Kuob's stochastic Liouville equation based on the system-bath Hamiltonian. The theory of 2D spectroscopy was developed in the process of investigating the effect of quantum coherence on nonlinear vibrational spectra based on the Feynman-Vernon influence functional. The paper also describes the development of these two theories for problems such as electron and exciton transfer in photosynthetic systems, quantum statistical thermodynamics, and solid-state physics.
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