Formulas of Szegő type for the periodic Schrödinger operator

2016/12/06 by Bernhard Pfirsch, Alexander V. Sobolev, Pfirsch, Bernhard +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1612.01747

openalex publication_date 2016/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator H=-(d²)/(dx²)+V in dimension one. Admitting fairly general functions h with h(0)=0, we study the trace of the operator h(χ_(-α,α)χ_(-∞,μ)(H)χ_(-α,α)) and link its subleading behaviour as α→∞ to the position of the spectral parameter μ relative to the spectrum of H.

Citations

• Entanglement in many-body systems

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