On sharp lower bound of the spectral gap for a Schrödinger operator and some related results

2014/07/02 by Yue He, He, Yue
Computer Science · Mathematics · #35B50 #35J05 #35P15 (Primary) #58C40 #58J05 #65N25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1407.0526

openalex publication_date 2014/07/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we give an easy proof of the main results of Andrews and Clutterbuck's paper [J. Amer. Math. Soc. 24 (2011), no. 3, 899--916], which gives both a sharp lower bound for the spectral gap of a Schröinger operator and a sharp modulus of concavity for the logarithm of the corresponding first eigenfunction. We arrive directly at same estimates by the `double coordinate' approach and asymptotic behavior of parabolic flows. Although using the techniques appeared in the above paper, we partly simplify the method and argument. This maybe help to provide an easy way for estimating spectral gap. Besides, we also get a new lower bound of spectral gap for a class of Schödinger operator.

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