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<p>In this paper we study the spectral gap of a discrete Schrödinger operator defined on the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external potential, it is shown that the spectral gap converges to zero strictly faster than it does for the discrete Laplacian. The underlying mechanism is a combination of the increase in volume and an effective degeneracy of the ground state in the limiting regime.</p>

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On the Spectral Gap of a Discrete Schrödinger Operator on the Path Graph in the Limit of Large Volume

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  • 发表日期：

    2025年6月24日

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  • Joachim Kerner,
  • Pavlo Yatsyna

摘要

In this paper we study the spectral gap of a discrete Schrödinger operator defined on the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external potential, it is shown that the spectral gap converges to zero strictly faster than it does for the discrete Laplacian. The underlying mechanism is a combination of the increase in volume and an effective degeneracy of the ground state in the limiting regime.