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  "authors": [
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          "country": "Japan", 
          "value": "Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan"
        }
      ], 
      "surname": "Ito", 
      "email": "ito@th.phys.titech.ac.jp", 
      "full_name": "Ito, Katsushi", 
      "given_names": "Katsushi"
    }, 
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan"
        }
      ], 
      "surname": "Yang", 
      "email": "j.yang@th.phys.titech.ac.jp", 
      "full_name": "Yang, Jingjing", 
      "given_names": "Jingjing"
    }
  ], 
  "titles": [
    {
      "source": "OUP", 
      "title": "Exact WKB Analysis and TBA Equations for the Stark Effect Quartic oscillator"
    }
  ], 
  "dois": [
    {
      "value": "10.1093/ptep/ptad154"
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  "publication_info": [
    {
      "journal_title": "Progress of Theoretical and Experimental Physics", 
      "material": "article", 
      "journal_volume": "2024", 
      "artid": "013A02", 
      "year": 2024, 
      "journal_issue": "1"
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    "submission_number": "4bf6f36cb5fd11eea49c8e4864f4776e"
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  "page_nr": [
    30
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      "url": "https://creativecommons.org/licenses/by/4.0/", 
      "license": "CC-BY-4.0"
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  ], 
  "copyright": [
    {
      "statement": "\u00a9 The Author(s) 2023. Published by Oxford University Press on behalf of the Physical Society of Japan.", 
      "year": "2023"
    }
  ], 
  "control_number": "82823", 
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      "primary": "Progress of Theoretical and Experimental Physics"
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  "arxiv_eprints": [
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      "categories": [
        "hep-th", 
        "math-ph", 
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        "physics.atom-ph"
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  "abstracts": [
    {
      "source": "OUP", 
      "value": "Abstract We apply the exact Wentzel\u2013Kramers\u2013Brillouin (WKB) analysis to a couple of 1D Schr\u00f6dinger-type equations reduced from the Stark effect of hydrogen in a uniform electric field. By introducing Langer\u2019s modification and incorporating the Stokes graphs, we prove the exactness of the Bohr\u2013Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods in the specific parameter regions of the electric field intensity and magnetic quantum number. It is also found these quantization conditions get modified with an additional suppressed contribution when the parameters vary beyond the specific regions. We also present thermodynamic Bethe ansatz (TBA) equations governing the quantum periods in the absence of Langer\u2019s modification and discuss its wall-crossing and analytic continuation. Numerical calculations are conducted to compare the complex resonant frequencies from our quantization conditions against ones from the Riccati\u2013Pad\u00e9 method; the TBA equations are also confirmed by comparing its expansions with all-order quantum periods."
    }
  ], 
  "imprints": [
    {
      "date": "2023-12-13", 
      "publisher": "OUP"
    }
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