Anomalous diffusion and ergodic property of random diffusivity models
Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a diffusing diffusivity. Based on a random diffusivity model, we here focus on the ergodic property and the scatter of the amplitude of time-averaged mean-squared displacement. Our results are valid for arbitrary random diffusivity.
Inverse spectral problems for radial Schrödinger operators
We study an inverse eigenvalue problem for the radial Schrödinger operators on the unit interval. We obtain a sufficient condition for the unique specification of the operator by a set of eigenvalues and a part of the potential function in terms of the cosine system closedness. The Borg-type and the Hochstadt-Lieberman type results are obtained as corollaries of our main result. Furthermore, under an additional hypothetical condition, we show that our condition is not only sufficient but also necessary for the uniqueness of the inverse problem solution.