Publication Information

{'id': 'https://openalex.org/W1874309567', 'doi': 'https://doi.org/10.48550/arxiv.math-ph/0501024', 'title': 'On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators', 'display_name': 'On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators', 'publication_year': 2005, 'publication_date': '2005-01-01', 'ids': {'openalex': 'https://openalex.org/W1874309567', 'doi': 'https://doi.org/10.48550/arxiv.math-ph/0501024', 'mag': '1874309567'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math-ph/0501024', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/math-ph/0501024', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5109937068', 'display_name': 'Sergio Albeverio', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Sergio Albeverio', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5103094669', 'display_name': 'S. N. Lakaev', 'orcid': 'https://orcid.org/0000-0003-4951-9340'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Saidakhmat N. Lakaev', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5014515219', 'display_name': 'Ramiza Kh. Djumanova', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Ramiza Kh. Djumanova', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 61}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11022', 'display_name': 'Spectral Theory in Mathematical Physics', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11022', 'display_name': 'Spectral Theory in Mathematical Physics', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12589', 'display_name': 'Differential Equations and Boundary Problems', 'score': 0.9987, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11205', 'display_name': 'Numerical methods in inverse problems', 'score': 0.9985, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/essential-spectrum', 'display_name': 'Essential spectrum', 'score': 0.90795803}, {'id': 'https://openalex.org/keywords/operator', 'display_name': 'Operator (biology)', 'score': 0.69356555}, {'id': 'https://openalex.org/keywords/discrete-spectrum', 'display_name': 'Discrete spectrum', 'score': 0.6564946}, {'id': 'https://openalex.org/keywords/zero', 'display_name': 'Zero (linguistics)', 'score': 0.4949991}, {'id': 'https://openalex.org/keywords/lattice', 'display_name': 'Lattice (music)', 'score': 0.48998037}, {'id': 'https://openalex.org/keywords/schrödingers-cat', 'display_name': "Schrödinger's cat", 'score': 0.45474693}, {'id': 'https://openalex.org/keywords/energy-operator', 'display_name': 'Energy operator', 'score': 0.42167416}], 'concepts': [{'id': 'https://openalex.org/C2780297109', 'wikidata': 'https://www.wikidata.org/wiki/Q917390', 'display_name': 'Essential spectrum', 'level': 3, 'score': 0.90795803}, {'id': 'https://openalex.org/C158693339', 'wikidata': 'https://www.wikidata.org/wiki/Q190524', 'display_name': 'Eigenvalues and eigenvectors', 'level': 2, 'score': 0.8166498}, {'id': 'https://openalex.org/C17020691', 'wikidata': 'https://www.wikidata.org/wiki/Q139677', 'display_name': 'Operator (biology)', 'level': 5, 'score': 0.69356555}, {'id': 'https://openalex.org/C156778621', 'wikidata': 'https://www.wikidata.org/wiki/Q1365748', 'display_name': 'Spectrum (functional analysis)', 'level': 2, 'score': 0.6763122}, {'id': 'https://openalex.org/C13487092', 'wikidata': 'https://www.wikidata.org/wiki/Q5282061', 'display_name': 'Discrete spectrum', 'level': 3, 'score': 0.6564946}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.57577765}, {'id': 'https://openalex.org/C2780813799', 'wikidata': 'https://www.wikidata.org/wiki/Q3274237', 'display_name': 'Zero (linguistics)', 'level': 2, 'score': 0.4949991}, {'id': 'https://openalex.org/C2781204021', 'wikidata': 'https://www.wikidata.org/wiki/Q6497091', 'display_name': 'Lattice (music)', 'level': 2, 'score': 0.48998037}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.45790574}, {'id': 'https://openalex.org/C194800363', 'wikidata': 'https://www.wikidata.org/wiki/Q8588', 'display_name': "Schrödinger's cat", 'level': 2, 'score': 0.45474693}, {'id': 'https://openalex.org/C19579662', 'wikidata': 'https://www.wikidata.org/wiki/Q461145', 'display_name': 'Energy operator', 'level': 3, 'score': 0.42167416}, {'id': 'https://openalex.org/C134440745', 'wikidata': 'https://www.wikidata.org/wiki/Q1186765', 'display_name': 'Ladder operator', 'level': 4, 'score': 0.41965702}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.4075199}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.3856408}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.3189888}, {'id': 'https://openalex.org/C79013869', 'wikidata': 'https://www.wikidata.org/wiki/Q1780743', 'display_name': 'Compact operator', 'level': 3, 'score': 0.27027178}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.24428171}, {'id': 'https://openalex.org/C186370098', 'wikidata': 'https://www.wikidata.org/wiki/Q442787', 'display_name': 'Energy (signal processing)', 'level': 2, 'score': 0.23395887}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.072460085}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.06862566}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.05101928}, {'id': 'https://openalex.org/C158448853', 'wikidata': 'https://www.wikidata.org/wiki/Q425218', 'display_name': 'Repressor', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86339819', 'wikidata': 'https://www.wikidata.org/wiki/Q407384', 'display_name': 'Transcription factor', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C104317684', 'wikidata': 'https://www.wikidata.org/wiki/Q7187', 'display_name': 'Gene', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C41895202', 'wikidata': 'https://www.wikidata.org/wiki/Q8162', 'display_name': 'Linguistics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C24890656', 'wikidata': 'https://www.wikidata.org/wiki/Q82811', 'display_name': 'Acoustics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C2778029271', 'wikidata': 'https://www.wikidata.org/wiki/Q5421931', 'display_name': 'Extension (predicate logic)', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math-ph/0501024', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.math-ph/0501024', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math-ph/0501024', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'display_name': 'Affordable and clean energy', 'score': 0.48, 'id': 'https://metadata.un.org/sdg/7'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 16, 'referenced_works': ['https://openalex.org/W1518139628', 'https://openalex.org/W1529412658', 'https://openalex.org/W1592958377', 'https://openalex.org/W1901756235', 'https://openalex.org/W1972495272', 'https://openalex.org/W1991409076', 'https://openalex.org/W1996692332', 'https://openalex.org/W2013357038', 'https://openalex.org/W2039278766', 'https://openalex.org/W2042626637', 'https://openalex.org/W2055338151', 'https://openalex.org/W2059799714', 'https://openalex.org/W2249562544', 'https://openalex.org/W2465937085', 'https://openalex.org/W289664737', 'https://openalex.org/W588763588'], 'related_works': ['https://openalex.org/W4386309365', 'https://openalex.org/W4382054798', 'https://openalex.org/W4377234943', 'https://openalex.org/W4361795763', 'https://openalex.org/W4295314662', 'https://openalex.org/W332148229', 'https://openalex.org/W2090359632', 'https://openalex.org/W1965669842', 'https://openalex.org/W1874309567', 'https://openalex.org/W1152196991'], 'abstract_inverted_index': {'A': [0], 'model': [1], 'operator': [2, 10, 43, 85], '$H$': [3, 44, 86], 'corresponding': [4], 'to': [5], 'a': [6, 12, 46, 71, 80, 109], 'three-particle': [7], 'discrete': [8], 'Schrödinger': [9], 'on': [11], 'lattice': [13], '$\\Z^3$': [14], 'is': [15, 20], 'studied.': [16], 'The': [17, 36, 42, 84], 'essential': [18, 57, 102], 'spectrum': [19, 24, 58], 'described': [21], 'via': [22], 'the': [23, 53, 56, 62, 93, 98, 101], 'of': [25, 49, 55, 61, 100], 'two': [26], 'Friedrichs': [27], 'models': [28], 'with': [29], 'parameters': [30], '$h_α(p),$': [31], '$α=1,2,$': [32], '$p': [33], '\\in': [34], '\\T^3=(-π,π]^3.$': [35], 'following': [37, 63], 'results': [38], 'are': [39], 'proven:': [40], '1)': [41], 'has': [45, 79, 87], 'finite': [47], 'number': [48], 'eigenvalues': [50, 90], 'lying': [51, 91], 'below': [52, 92], 'bottom': [54, 94, 99], 'in': [59], 'any': [60], 'cases:': [64], '(i)': [65], 'both': [66, 105], 'operators': [67, 106], '$h_α(0),': [68], 'α=1,2,$': [69], 'have': [70, 108], 'zero': [72, 81, 110], 'eigenvalue;': [73], '(ii)': [74], 'either': [75], '$h_1(0)$': [76], 'or': [77], '$h_2(0)$': [78], 'eigenvalue.': [82], '2)': [83], 'infinitely': [88], 'many': [89], 'and': [95], 'accumulating': [96], 'at': [97], 'spectrum,': [103], 'if': [104], '$h_α(0),α=1,2,$': [107], 'energy': [111], 'resonance.': [112]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1874309567', 'counts_by_year': [], 'updated_date': '2025-01-20T01:22:47.785680', 'created_date': '2016-06-24'}