We demonstrate that the cooperative charge transfer among constructive molecules in organic crystals of tetrathiafulvalene-chloranil, i.e., the bidirectional transition between the neutral and ionic phases, can certainly be induced by irradiation of a laser pulse with an 80-fs width. We also report the dynamics of the photoinduced neutral-ionic phase transition by means of the time-resolved spectroscopic technique. Studies using various excitation intensities have shown that the photoconverted fraction (Φ) depends nonlinearly on the excitation intensity. In addition, it has been found that the growth dynamics of the macroscopic domain of the metastable phase strongly depends on the excitation intensity as well. The role of the cooperative charge-transfer interaction in the driving process of this unusual photoeffect is discussed from both the experimental and the theoretical viewpoints.

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This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used in deep learning. Within this framework, we also propose AMSGrad on embedded submanifolds of Euclidean space. Moreover, we give convergence analyses valid for both a constant and a diminishing step size. Our analyses also reveal the relationship between the convergence rate and mini-batch size.In numerical experiments, we applied the proposed algorithm to principal component analysis and the low-rank matrix completion problem, which can be considered to be Riemannian optimization problems. Python implementations of the methods used in the numerical experiments are available at https://github.com/iiduka-researches/202408-adaptive.