Scholarlink

<p>The trans-series completion of perturbative series of a wide class of quantum mechanical systems can be determined by combining the resurgence program with extra input coming from exact WKB analysis. In this paper, we reexamine the Harper-Hofstadter model and its spectrum, Hofstadter’s butterfly in light of recent developments. We demonstrate the connection between the perturbative energy series of the Harper-Hofstadter model and the vev of 1/2-BPS Wilson loop of 5d SYM and clarify the differences between their non-perturbative corrections. Taking insights from the cosine potential model, we construct the full energy trans-series for flux <i>ϕ</i> = 2<i>π</i>/<i>Q</i> and provide numerical evidence with remarkably high precision. Finally, we revisit the problem of self-similarity of the butterfly and discuss the possibility of a completed version of the Rammal-Wilkinson formula.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Towards full instanton trans-series in Hofstadter’s butterfly

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月18日

查看全文
  • Jie Gu,
  • Zhaojie Xu

摘要

The trans-series completion of perturbative series of a wide class of quantum mechanical systems can be determined by combining the resurgence program with extra input coming from exact WKB analysis. In this paper, we reexamine the Harper-Hofstadter model and its spectrum, Hofstadter’s butterfly in light of recent developments. We demonstrate the connection between the perturbative energy series of the Harper-Hofstadter model and the vev of 1/2-BPS Wilson loop of 5d SYM and clarify the differences between their non-perturbative corrections. Taking insights from the cosine potential model, we construct the full energy trans-series for flux ϕ = 2π/Q and provide numerical evidence with remarkably high precision. Finally, we revisit the problem of self-similarity of the butterfly and discuss the possibility of a completed version of the Rammal-Wilkinson formula.