{"created":"2023-05-15T12:35:55.266203+00:00","id":12097,"links":{},"metadata":{"_buckets":{"deposit":"eb08f3df-8518-406a-b7df-9430de205e15"},"_deposit":{"created_by":4,"id":"12097","owners":[4],"pid":{"revision_id":0,"type":"depid","value":"12097"},"status":"published"},"_oai":{"id":"oai:kait.repo.nii.ac.jp:00012097","sets":["2:16:43:192"]},"author_link":[],"item_10002_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2020-03-01","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"22","bibliographicPageStart":"13","bibliographicVolumeNumber":"44","bibliographic_titles":[{"bibliographic_title":"神奈川工科大学研究報告.B,理工学編"}]}]},"item_10002_description_19":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_10002_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"The wavefunctions and band structures of the one-dimensional Schrödinger operators possessing periodic potentials, which are written as a sum of the  exactly-solvable finite-zone potential and the small integrability-breaking perturbation, are investigated using the renormalization-group/envelope (RG/E) method in the singular perturbation theory. Following the RG/E method, we obtain the fundamental equation which generates the solution free from power-law divergence caused by the secular terms. Using it, we provide the perturbative expansions of the eigenfunctions and the eigenvalues both for the non-resonant points, where the new gap does not open, and for the resonant points, where the wavelength of the square of the wavefunction is commensurate with that of the potential and hence the new gap opens. Furthermore, we propose a “patched” solution, which preserves the same analytic properties as the perturbative expansions for all points up to second order and is free from unphysical divergence for any parameter including a resonant wavenumber. These results are illustrated by several elementary examples.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_10002_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.34411/00032025","subitem_identifier_reg_type":"JaLC"}]},"item_10002_publisher_8":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"神奈川工科大学"}]},"item_10002_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA12669200","subitem_source_identifier_type":"NCID"}]},"item_10002_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"21882878","subitem_source_identifier_type":"PISSN"}]},"item_10002_version_type_20":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"高橋, 大介","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"Takahashi, Daisuke A.","creatorNameLang":"en"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2021-05-11"}],"displaytype":"detail","filename":"kkb-044-003.pdf","filesize":[{"value":"936.5 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"kkb-044-003.pdf","objectType":"fulltext","url":"https://kait.repo.nii.ac.jp/record/12097/files/kkb-044-003.pdf"},"version_id":"20e8a362-3167-4780-ad96-e078c92d6974"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"renormalization-group/envelope method","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Schrödinger operator","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"elliptic functions","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"周期的ポテンシャルを持つ一次元シュレーディンガー作用素の繰り込み群特異摂動論による解析","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"周期的ポテンシャルを持つ一次元シュレーディンガー作用素の繰り込み群特異摂動論による解析","subitem_title_language":"ja"},{"subitem_title":"Renormalization-group singular perturbation analysis for the one-dimensional Schrödinger operator with periodic potentials","subitem_title_language":"en"}]},"item_type_id":"10002","owner":"4","path":["192"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2021-05-11"},"publish_date":"2021-05-11","publish_status":"0","recid":"12097","relation_version_is_last":true,"title":["周期的ポテンシャルを持つ一次元シュレーディンガー作用素の繰り込み群特異摂動論による解析"],"weko_creator_id":"4","weko_shared_id":-1},"updated":"2023-08-04T09:32:06.967392+00:00"}