Analysis of superlattice structure using spectral analysis of non-linear Schroedinger operator

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540208
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kanazawa University
• Principal Investigator: OGURISU Osamu 金沢大学, 数物科学系, 准教授 (80301191)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: スペクトル解析 / シュレーディンガー作用素 / 離散シュレーディンガー作用素 / 点相互作用 / 量子ウォーク

Outline of Final Research Achievements

We studied spectral structure of some mathematical models of superlattice semiconductor devices. We studied the relation between the ratio of in-coming and out-going waves and the energy level E for perfect transmission, and found a kind of singularity. We also found that the relation between E and the phase factor, which is mentioned by RT effect, is broken. In another aspect, we introduced and studied the pseudo manifold of potentials for sustainability of resonances or embedded eigenvalues of discrete Schroedinger operator. In addition, we constructed quantum walks on simplicial complex as an application.

Free Research Field

関数方程式論