The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2017-08-31

AUTHORS

A. M. Khalkhuzhaev

ABSTRACT

We consider a family of three-particle discrete Shrödinger operators Hμ(K). These operators are associated with the Hamiltonian for a system of three identical particles (fermions) with pairwise two-particle interactions on neighboring junctions of the d-dimensional lattice Zd. We describe the location and the structure of the essential spectrum of the operator Hμ(K) for all values of the three-particle quasi-momentum K ∈ Td and the interaction energy μ > 0. More... »

PAGES

67-78

References to SciGraph publications

  • 1989. The problem of a few quasi-particles in solid-state physics in APPLICATIONS OF SELF-ADJOINT EXTENSIONS IN QUANTUM PHYSICS
  • 1986-06. Clustering operators in JOURNAL OF MATHEMATICAL SCIENCES
  • 2009-02. The number of eigenvalues of the two-particle discrete Schrödinger operator in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2008-05. Spectrum of the two-particle Schrödinger operator on a lattice in THEORETICAL AND MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.3103/s1066369x17090080

    DOI

    http://dx.doi.org/10.3103/s1066369x17090080

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091393549


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Samarkand State University, Universiteskii bulv. 15, 140101, Samarkand, Republic of Uzbekistan", 
              "id": "http://www.grid.ac/institutes/grid.77443.33", 
              "name": [
                "Samarkand State University, Universiteskii bulv. 15, 140101, Samarkand, Republic of Uzbekistan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Khalkhuzhaev", 
            "givenName": "A. M.", 
            "id": "sg:person.015116440573.52", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015116440573.52"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s11232-009-0018-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011019006", 
              "https://doi.org/10.1007/s11232-009-0018-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11232-008-0064-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009581998", 
              "https://doi.org/10.1007/s11232-008-0064-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0022946", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016631416", 
              "https://doi.org/10.1007/bfb0022946"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01086541", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021202704", 
              "https://doi.org/10.1007/bf01086541"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2017-08-31", 
        "datePublishedReg": "2017-08-31", 
        "description": "We consider a family of three-particle discrete Shr\u00f6dinger operators H\u03bc(K). These operators are associated with the Hamiltonian for a system of three identical particles (fermions) with pairwise two-particle interactions on neighboring junctions of the d-dimensional lattice Zd. We describe the location and the structure of the essential spectrum of the operator H\u03bc(K) for all values of the three-particle quasi-momentum K \u2208 Td and the interaction energy \u03bc > 0.", 
        "genre": "article", 
        "id": "sg:pub.10.3103/s1066369x17090080", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1295492", 
            "issn": [
              "0021-3446", 
              "1934-810X"
            ], 
            "name": "Russian Mathematics", 
            "publisher": "Allerton Press", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "9", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "61"
          }
        ], 
        "keywords": [
          "neighboring junctions", 
          "particles", 
          "discrete operators", 
          "operators", 
          "system", 
          "two-particle interactions", 
          "structure", 
          "spectra", 
          "identical particles", 
          "junction", 
          "location", 
          "values", 
          "TD", 
          "lattice", 
          "interaction", 
          "three-particle", 
          "ZD", 
          "Hamiltonian", 
          "fermions", 
          "pairwise", 
          "lattice Zd", 
          "essential spectrum", 
          "family", 
          "three-particle discrete Shr\u00f6dinger operators", 
          "discrete Shr\u00f6dinger operators", 
          "Shr\u00f6dinger operators", 
          "dimensional lattice Zd", 
          "interaction energy \u03bc", 
          "energy \u03bc", 
          "three-particle discrete operator"
        ], 
        "name": "The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice", 
        "pagination": "67-78", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1091393549"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.3103/s1066369x17090080"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.3103/s1066369x17090080", 
          "https://app.dimensions.ai/details/publication/pub.1091393549"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:41", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_728.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.3103/s1066369x17090080"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.3103/s1066369x17090080'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.3103/s1066369x17090080'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.3103/s1066369x17090080'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.3103/s1066369x17090080'


     

    This table displays all metadata directly associated to this object as RDF triples.

    104 TRIPLES      22 PREDICATES      59 URIs      47 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.3103/s1066369x17090080 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N8fd981c374b0406cb7054368b0393967
    4 schema:citation sg:pub.10.1007/bf01086541
    5 sg:pub.10.1007/bfb0022946
    6 sg:pub.10.1007/s11232-008-0064-1
    7 sg:pub.10.1007/s11232-009-0018-2
    8 schema:datePublished 2017-08-31
    9 schema:datePublishedReg 2017-08-31
    10 schema:description We consider a family of three-particle discrete Shrödinger operators Hμ(K). These operators are associated with the Hamiltonian for a system of three identical particles (fermions) with pairwise two-particle interactions on neighboring junctions of the d-dimensional lattice Zd. We describe the location and the structure of the essential spectrum of the operator Hμ(K) for all values of the three-particle quasi-momentum K ∈ Td and the interaction energy μ > 0.
    11 schema:genre article
    12 schema:inLanguage en
    13 schema:isAccessibleForFree false
    14 schema:isPartOf N0710ee02b47444eea7cf86a76d0c510c
    15 N438131a3ff6a49e08e916ec96a3fabb2
    16 sg:journal.1295492
    17 schema:keywords Hamiltonian
    18 Shrödinger operators
    19 TD
    20 ZD
    21 dimensional lattice Zd
    22 discrete Shrödinger operators
    23 discrete operators
    24 energy μ
    25 essential spectrum
    26 family
    27 fermions
    28 identical particles
    29 interaction
    30 interaction energy μ
    31 junction
    32 lattice
    33 lattice Zd
    34 location
    35 neighboring junctions
    36 operators
    37 pairwise
    38 particles
    39 spectra
    40 structure
    41 system
    42 three-particle
    43 three-particle discrete Shrödinger operators
    44 three-particle discrete operator
    45 two-particle interactions
    46 values
    47 schema:name The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice
    48 schema:pagination 67-78
    49 schema:productId N2c743051c8e94a42a2d45b9a67ef7e86
    50 Ne2d420332d47485ea49d1c4c2746e908
    51 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091393549
    52 https://doi.org/10.3103/s1066369x17090080
    53 schema:sdDatePublished 2022-01-01T18:41
    54 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    55 schema:sdPublisher N936386b8408e4251b21b4bea8b9fb6ae
    56 schema:url https://doi.org/10.3103/s1066369x17090080
    57 sgo:license sg:explorer/license/
    58 sgo:sdDataset articles
    59 rdf:type schema:ScholarlyArticle
    60 N0710ee02b47444eea7cf86a76d0c510c schema:issueNumber 9
    61 rdf:type schema:PublicationIssue
    62 N2c743051c8e94a42a2d45b9a67ef7e86 schema:name dimensions_id
    63 schema:value pub.1091393549
    64 rdf:type schema:PropertyValue
    65 N438131a3ff6a49e08e916ec96a3fabb2 schema:volumeNumber 61
    66 rdf:type schema:PublicationVolume
    67 N8fd981c374b0406cb7054368b0393967 rdf:first sg:person.015116440573.52
    68 rdf:rest rdf:nil
    69 N936386b8408e4251b21b4bea8b9fb6ae schema:name Springer Nature - SN SciGraph project
    70 rdf:type schema:Organization
    71 Ne2d420332d47485ea49d1c4c2746e908 schema:name doi
    72 schema:value 10.3103/s1066369x17090080
    73 rdf:type schema:PropertyValue
    74 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Mathematical Sciences
    76 rdf:type schema:DefinedTerm
    77 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    78 schema:name Pure Mathematics
    79 rdf:type schema:DefinedTerm
    80 sg:journal.1295492 schema:issn 0021-3446
    81 1934-810X
    82 schema:name Russian Mathematics
    83 schema:publisher Allerton Press
    84 rdf:type schema:Periodical
    85 sg:person.015116440573.52 schema:affiliation grid-institutes:grid.77443.33
    86 schema:familyName Khalkhuzhaev
    87 schema:givenName A. M.
    88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015116440573.52
    89 rdf:type schema:Person
    90 sg:pub.10.1007/bf01086541 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021202704
    91 https://doi.org/10.1007/bf01086541
    92 rdf:type schema:CreativeWork
    93 sg:pub.10.1007/bfb0022946 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016631416
    94 https://doi.org/10.1007/bfb0022946
    95 rdf:type schema:CreativeWork
    96 sg:pub.10.1007/s11232-008-0064-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009581998
    97 https://doi.org/10.1007/s11232-008-0064-1
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/s11232-009-0018-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011019006
    100 https://doi.org/10.1007/s11232-009-0018-2
    101 rdf:type schema:CreativeWork
    102 grid-institutes:grid.77443.33 schema:alternateName Samarkand State University, Universiteskii bulv. 15, 140101, Samarkand, Republic of Uzbekistan
    103 schema:name Samarkand State University, Universiteskii bulv. 15, 140101, Samarkand, Republic of Uzbekistan
    104 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...