Sharp asymptotics of the quasimomentum

2011/10/21 by Evgeny Korotyaev, Evgeny L. Korotyaev, Korotyaev, Evgeny L. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #30C20 #34L40 #47E05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:30C20 #msc:34L40 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1110.4716

16 pages, 3 figures, keywords: quasimomentum, integrated density of states, periodic potential

arxiv created 2011/10/21 · openalex publication_date 2011/10/21 · arxiv updated 2011/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Schrödinger operator with a periodic potential p on the real line. We assume that p belongs to the Sobolev space \mH_m on the circle for some m≥ -1, and we determine the asymptotics of the quasimomentum and the Titchmarsh-Weyl functions, the Bloch functions at high energy.

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