Crystal structure prediction by combined optimization of experimental data and first-principles calculation

xrayCrystal structure prediction has been known as one of the most difficult problems, and various prediction methods have been developed so far. Recently, joint optimization of experimental data and the theoretical potential energy calculation has been proposed. In that method, a combined cost function, a sum of reproducibility of experimental data and the potential energy, are optimized. However, combined cost function loses the information of the local minima of each cost functions. We developed a new optimization algorithm, Combined Optimization Method (COM), to overcome this difficulty. For example, it is known that the determination of crystal structure for SiO2 systems is quite difficult due to the existence of a lot of local minimum arrangements. By using the COM, we confirmed that the success rate of crystal structure prediction increases significantly.

Non-ergodicity in Classical Harmonic Oscillator System

ergodicity.pngUnlike the normal Langevin equation, the generalized Langevin equation, which deals with the memory effects, shows  various type diffusions depending on the memory function. Recently, the anomalous diffusion and the non-ergodicity have been actively studied in the terms of the generalized Langevin equation. There are, however, some confusions in the definition of the ergodicity and there are few analysis using physical models. We propose a new non-ergodic  model, which consists of harmonic oscillators, and analyze the model by the molecular dynamics, the exact diagonalization, and the analytical solution. We also reconsider the definition of the ergodicity, and clarify that the non-ergodicity observed in our model is caused by the localized mode.

  • Fumihiro Ishikawa, Synge Todo, Localized Mode and Nonergodicity of a Harmonic Oscillator Chain, preprint: arXiv:1805.02923.