Complexity, Fractal Dimension for Quantum States View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1997-04

AUTHORS

Masanori Ohya

ABSTRACT

The complexities in information dynamics are reviewed and their examples are given. The fractal dimensions of a quantum state are discussed from a general point of view of complexity. It is shown trough a model that the fractal dimensions of a state provide measures for order structure of chaotic systems.

PAGES

141-157

References to SciGraph publications

  • 1987-12. Dynamical entropy ofC* algebras and von Neumann algebras in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1996-03. Entropy functionals of Kolmogorov-Sinai type and their limit theorems in LETTERS IN MATHEMATICAL PHYSICS
  • 1983-11. Note on quantum probability in LETTERE AL NUOVO CIMENTO (1971-1985)
  • 1992-04. Entropies of general quantum states in OPEN SYSTEMS AND INFORMATION DYNAMICS
  • 1977-02. Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1009635318043

    DOI

    http://dx.doi.org/10.1023/a:1009635318043

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1026734202


    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/2008/0202", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Atomic, Molecular, Nuclear, Particle and Plasma Physics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Tokyo University of Science", 
              "id": "https://www.grid.ac/institutes/grid.143643.7", 
              "name": [
                "Department of Information Sciences, Science University of Tokyo, 278, Noda City, Chiba, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ohya", 
            "givenName": "Masanori", 
            "id": "sg:person.013365420775.41", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013365420775.41"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01609834", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005841559", 
              "https://doi.org/10.1007/bf01609834"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01609834", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005841559", 
              "https://doi.org/10.1007/bf01609834"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-247x(68)90078-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008678982"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0034-4877(96)83635-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012251654"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02228935", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019568133", 
              "https://doi.org/10.1007/bf02228935"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02228935", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019568133", 
              "https://doi.org/10.1007/bf02228935"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00943285", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022557253", 
              "https://doi.org/10.1007/bf00943285"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-247x(81)90170-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024494478"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/aoms/1177729694", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026070931"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0034-4877(89)90034-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031429842"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01225381", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034943987", 
              "https://doi.org/10.1007/bf01225381"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01225381", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034943987", 
              "https://doi.org/10.1007/bf01225381"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02789599", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035227287", 
              "https://doi.org/10.1007/bf02789599"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0019-9958(72)90199-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042858045"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-247x(83)90003-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048934958"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-247x(84)90076-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049249869"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/j.1538-7305.1948.tb01338.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052867467"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tit.1983.1056719", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061648898"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1997-04", 
        "datePublishedReg": "1997-04-01", 
        "description": "The complexities in information dynamics are reviewed and their examples are given. The fractal dimensions of a quantum state are discussed from a general point of view of complexity. It is shown trough a model that the fractal dimensions of a state provide measures for order structure of chaotic systems.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1023/a:1009635318043", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1140079", 
            "issn": [
              "1230-1612", 
              "1573-1324"
            ], 
            "name": "Open Systems and Information Dynamics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "4"
          }
        ], 
        "name": "Complexity, Fractal Dimension for Quantum States", 
        "pagination": "141-157", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "7f5c18301f5adcd48650ec878256fef44260352b31d61d31ed1cbf163a6a159c"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1009635318043"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1026734202"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1009635318043", 
          "https://app.dimensions.ai/details/publication/pub.1026734202"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T16:39", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8669_00000499.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1023/A:1009635318043"
      }
    ]
     

    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.10.1023/a:1009635318043'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1009635318043'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1009635318043'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1009635318043'


     

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

    111 TRIPLES      21 PREDICATES      42 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1009635318043 schema:about anzsrc-for:02
    2 anzsrc-for:0202
    3 schema:author N7a0fcb30c1a3434c8ba764319346d8cb
    4 schema:citation sg:pub.10.1007/bf00943285
    5 sg:pub.10.1007/bf01225381
    6 sg:pub.10.1007/bf01609834
    7 sg:pub.10.1007/bf02228935
    8 sg:pub.10.1007/bf02789599
    9 https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
    10 https://doi.org/10.1016/0022-247x(68)90078-4
    11 https://doi.org/10.1016/0022-247x(81)90170-0
    12 https://doi.org/10.1016/0022-247x(83)90003-3
    13 https://doi.org/10.1016/0022-247x(84)90076-3
    14 https://doi.org/10.1016/0034-4877(89)90034-7
    15 https://doi.org/10.1016/0034-4877(96)83635-4
    16 https://doi.org/10.1016/s0019-9958(72)90199-4
    17 https://doi.org/10.1109/tit.1983.1056719
    18 https://doi.org/10.1214/aoms/1177729694
    19 schema:datePublished 1997-04
    20 schema:datePublishedReg 1997-04-01
    21 schema:description The complexities in information dynamics are reviewed and their examples are given. The fractal dimensions of a quantum state are discussed from a general point of view of complexity. It is shown trough a model that the fractal dimensions of a state provide measures for order structure of chaotic systems.
    22 schema:genre research_article
    23 schema:inLanguage en
    24 schema:isAccessibleForFree false
    25 schema:isPartOf Nb51e6e0966144e51abcaf222ae933794
    26 Ne25c57f945e44feb955b7b65a4f76ad7
    27 sg:journal.1140079
    28 schema:name Complexity, Fractal Dimension for Quantum States
    29 schema:pagination 141-157
    30 schema:productId N81d104c08d254da89de237ccc0068150
    31 Ndfe6ff329b3c469a9422a6854ad9439b
    32 Nebac721f56844ec882a77de9ad8887f7
    33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026734202
    34 https://doi.org/10.1023/a:1009635318043
    35 schema:sdDatePublished 2019-04-10T16:39
    36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    37 schema:sdPublisher N33e86d88650b47ec97a0af82e5709b3d
    38 schema:url http://link.springer.com/10.1023/A:1009635318043
    39 sgo:license sg:explorer/license/
    40 sgo:sdDataset articles
    41 rdf:type schema:ScholarlyArticle
    42 N33e86d88650b47ec97a0af82e5709b3d schema:name Springer Nature - SN SciGraph project
    43 rdf:type schema:Organization
    44 N7a0fcb30c1a3434c8ba764319346d8cb rdf:first sg:person.013365420775.41
    45 rdf:rest rdf:nil
    46 N81d104c08d254da89de237ccc0068150 schema:name doi
    47 schema:value 10.1023/a:1009635318043
    48 rdf:type schema:PropertyValue
    49 Nb51e6e0966144e51abcaf222ae933794 schema:volumeNumber 4
    50 rdf:type schema:PublicationVolume
    51 Ndfe6ff329b3c469a9422a6854ad9439b schema:name dimensions_id
    52 schema:value pub.1026734202
    53 rdf:type schema:PropertyValue
    54 Ne25c57f945e44feb955b7b65a4f76ad7 schema:issueNumber 2
    55 rdf:type schema:PublicationIssue
    56 Nebac721f56844ec882a77de9ad8887f7 schema:name readcube_id
    57 schema:value 7f5c18301f5adcd48650ec878256fef44260352b31d61d31ed1cbf163a6a159c
    58 rdf:type schema:PropertyValue
    59 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Physical Sciences
    61 rdf:type schema:DefinedTerm
    62 anzsrc-for:0202 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Atomic, Molecular, Nuclear, Particle and Plasma Physics
    64 rdf:type schema:DefinedTerm
    65 sg:journal.1140079 schema:issn 1230-1612
    66 1573-1324
    67 schema:name Open Systems and Information Dynamics
    68 rdf:type schema:Periodical
    69 sg:person.013365420775.41 schema:affiliation https://www.grid.ac/institutes/grid.143643.7
    70 schema:familyName Ohya
    71 schema:givenName Masanori
    72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013365420775.41
    73 rdf:type schema:Person
    74 sg:pub.10.1007/bf00943285 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022557253
    75 https://doi.org/10.1007/bf00943285
    76 rdf:type schema:CreativeWork
    77 sg:pub.10.1007/bf01225381 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034943987
    78 https://doi.org/10.1007/bf01225381
    79 rdf:type schema:CreativeWork
    80 sg:pub.10.1007/bf01609834 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005841559
    81 https://doi.org/10.1007/bf01609834
    82 rdf:type schema:CreativeWork
    83 sg:pub.10.1007/bf02228935 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019568133
    84 https://doi.org/10.1007/bf02228935
    85 rdf:type schema:CreativeWork
    86 sg:pub.10.1007/bf02789599 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035227287
    87 https://doi.org/10.1007/bf02789599
    88 rdf:type schema:CreativeWork
    89 https://doi.org/10.1002/j.1538-7305.1948.tb01338.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1052867467
    90 rdf:type schema:CreativeWork
    91 https://doi.org/10.1016/0022-247x(68)90078-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008678982
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1016/0022-247x(81)90170-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024494478
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1016/0022-247x(83)90003-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048934958
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1016/0022-247x(84)90076-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049249869
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1016/0034-4877(89)90034-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031429842
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1016/0034-4877(96)83635-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012251654
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1016/s0019-9958(72)90199-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042858045
    104 rdf:type schema:CreativeWork
    105 https://doi.org/10.1109/tit.1983.1056719 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061648898
    106 rdf:type schema:CreativeWork
    107 https://doi.org/10.1214/aoms/1177729694 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026070931
    108 rdf:type schema:CreativeWork
    109 https://www.grid.ac/institutes/grid.143643.7 schema:alternateName Tokyo University of Science
    110 schema:name Department of Information Sciences, Science University of Tokyo, 278, Noda City, Chiba, Japan
    111 rdf:type schema:Organization
     




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


    ...