The development of high-energy-density Na-ion batteries (SIBs) is hindered by the lack of high-capacity anode with fast Na-ion reaction kinetics due to the large Na+ radius and slow Na+ diffusion...

Recent experiments have suggested that the electron-phonon coupling may play an important role in the γ → α volume collapse transition in Cerium. A minimal model for the description of such transition is the periodic Anderson model. In order to better understand the effect of the electron-phonon interaction on the volume collapse transition, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling enhances the volume collapse, which is consistent with experiments in Cerium. While we start with the Kondo Volume Collapse scenario in mind, our results capture some interesting features of the Mott scenario, such as a gap in the conduction electron spectra which grows with the effective electron-phonon coupling. arXiv:1704.08684v6 [cond-mat.str-el]

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Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has independent increments, here I derive two integral equations to capture the time evolution of any such process. In order to solve these two integral equations explicitly, I need to introduce one more restriction condition. For sake of simplicity, I have imposed the Poisson condition on the two equations and successfully reproduced the renown Poisson results. The methods proposed here may also be applicable for investigating other stationary processes with independent increments.