arXiv subjects

Yuji Nomura

Publications and source records attributed to Yuji Nomura.

2 recordsLinked to original sources

arXiv2019

Some properties of threshold eigenstates and resonant states of discrete Schrödinger operators

In this note, we study some properties of threshold resonant states or threshold eigenfunctions for discrete Schrödinger operators. We mainly prove two theorems. First, we prove that resonant states at the elliptic threshold have the same asymptotic expansion as the continuous Schrödinger operator. Second, we prove absence of resonant states at hyperbolic thresholds

math-ph↗

arXiv2017

Schrödinger operators with random $δ$ magnetic fields

We shall consider the Schrödinger operators on $\mathbf{R}^2$ with random $δ$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $δ$-fields, we prove the spectrum coincides with $[0,\infty)$ and the integrated density of states (IDS) decays exponentially at the bottom of the spectrum (Lifshitz tail), by using the Hardy type inequality by Laptev-Weidl. We also give a lower bound for IDS at the bottom of the spectrum.

math-ph↗