Spectral Properties of Polyharmonic Operators with Limit-Periodic\n Potential in Dimension Two

2006/01/03 by Yulia Karpeshina, Karpeshina, Yulia, Young-Ran Lee +1
Computer Science · Mathematics · Physics and Astronomy · #81Q15 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math-ph/0601008

openalex publication_date 2006/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a polyharmonic operator H=(-\Δ)^l+V(x) in dimension two\nwith l\≥ 6 and a limit-periodic potential V(x). We prove that the\nspectrum of H contains a semiaxis and there is a family of generalized\neigenfunctions at every point of this semiaxis with the following properties.\nFirst, the eigenfunctions are close to plane waves e^{i< k, x>} at\nthe high energy region. Second, the isoenergetic curves in the space of momenta\n k corresponding to these eigenfunctions have a form of slightly\ndistorted circles with holes (Cantor type structure).\n

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