Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2002-05

AUTHORS

L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim

ABSTRACT

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager–Machlup theory in the SNS; a general Hamilton–Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton–Jacobi equation, we obtain a logically independent derivation of this result. More... »

PAGES

635-675

References to SciGraph publications

  • 1990-08. Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1999-04. Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1982-09. Small deviations from local equilibrium for a process which exhibits hydrodynamical behavior. II in JOURNAL OF STATISTICAL PHYSICS
  • 1984-07. A remark on the hydrodynamics of the zero-range processes in JOURNAL OF STATISTICAL PHYSICS
  • 1993-09. Large deviations for a reaction diffusion model in PROBABILITY THEORY AND RELATED FIELDS
  • 1990-11. Dissipation and large thermodynamic fluctuations in JOURNAL OF STATISTICAL PHYSICS
  • 1999-08. Onsager Symmetry from Microscopic TP Invariance in JOURNAL OF STATISTICAL PHYSICS
  • 1954-11. On time reversal in IL NUOVO CIMENTO (1943-1954)
  • 2007-12-01. Entropy and equilibrium states in classical statistical mechanics in STATISTICAL MECHANICS AND MATHEMATICAL PROBLEMS
  • 1997-10. Irreversibility of classical fluctuations studied in analogue electrical circuits in NATURE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1014525911391

    DOI

    http://dx.doi.org/10.1023/a:1014525911391

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1017377324


    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/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "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"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Sapienza University of Rome", 
              "id": "https://www.grid.ac/institutes/grid.7841.a", 
              "name": [
                "Dipartimento di Matematica, Universit\u00e0 di Roma La Sapienza, P.le A. Moro 2, 00185, Roma, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Bertini", 
            "givenName": "L.", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Massachusetts Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.116068.8", 
              "name": [
                "Department of Mathematics, MIT, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "De Sole", 
            "givenName": "A.", 
            "id": "sg:person.07413526755.89", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07413526755.89"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of L'Aquila", 
              "id": "https://www.grid.ac/institutes/grid.158820.6", 
              "name": [
                "Dipartimento di Matematica, Universit\u00e0 dell'Aquila, 67100, Coppito, L'Aquila, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Gabrielli", 
            "givenName": "D.", 
            "id": "sg:person.016523270626.52", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016523270626.52"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Sapienza University of Rome", 
              "id": "https://www.grid.ac/institutes/grid.7841.a", 
              "name": [
                "Dipartimento di Fisica and INFN, Universit\u00e0 di Roma La Sapienza, P.le A. Moro 2, 00185, Roma, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Jona-Lasinio", 
            "givenName": "G.", 
            "id": "sg:person.01017363063.91", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01017363063.91"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Rouen", 
              "id": "https://www.grid.ac/institutes/grid.10400.35", 
              "name": [
                "IMPA, Estrada Dona Castorina 110, J. Botanico, 22460, Rio de Janeiro, Brazil", 
                "Universit\u00e9 de Rouen, CNRS UPRES-A 6085, 76128, Mont-Saint-Aignan Cedex, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Landim", 
            "givenName": "C.", 
            "id": "sg:person.011514320140.11", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011514320140.11"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1038/38963", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001153712", 
              "https://doi.org/10.1038/38963"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1038/38963", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001153712", 
              "https://doi.org/10.1038/38963"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160420202", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002387673"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160420202", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002387673"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0112756", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006102707", 
              "https://doi.org/10.1007/bfb0112756"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0112756", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006102707", 
              "https://doi.org/10.1007/bfb0112756"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.87.040601", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008699672"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.87.040601", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008699672"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01008249", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017081991", 
              "https://doi.org/10.1007/bf01008249"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200050572", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018942951", 
              "https://doi.org/10.1007/s002200050572"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160420303", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020685618"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160420303", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020685618"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1004550307453", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025070126", 
              "https://doi.org/10.1023/a:1004550307453"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01195070", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042027052", 
              "https://doi.org/10.1007/bf01195070"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01195070", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042027052", 
              "https://doi.org/10.1007/bf01195070"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01027291", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042694408", 
              "https://doi.org/10.1007/bf01027291"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02278011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043562108", 
              "https://doi.org/10.1007/bf02278011"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02278011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043562108", 
              "https://doi.org/10.1007/bf02278011"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01015727", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044349796", 
              "https://doi.org/10.1007/bf01015727"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.77.1202", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051180022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.77.1202", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051180022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02781835", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053369243", 
              "https://doi.org/10.1007/bf02781835"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02781835", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053369243", 
              "https://doi.org/10.1007/bf02781835"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/16/18/029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059066633"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrev.91.1505", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060460948"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrev.91.1505", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060460948"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.33.1322", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060474203"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.33.1322", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060474203"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/aop/1176988286", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064403512"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2002-05", 
        "datePublishedReg": "2002-05-01", 
        "description": "We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager\u2013Machlup theory in the SNS; a general Hamilton\u2013Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton\u2013Jacobi equation, we obtain a logically independent derivation of this result.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1023/a:1014525911391", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1040979", 
            "issn": [
              "0022-4715", 
              "1572-9613"
            ], 
            "name": "Journal of Statistical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3-4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "107"
          }
        ], 
        "name": "Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States", 
        "pagination": "635-675", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "52cac5b48169ca00453e4cd57170b135a2e9c45fc56e7b82c2bc11ebbd3133d2"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1014525911391"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1017377324"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1014525911391", 
          "https://app.dimensions.ai/details/publication/pub.1017377324"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T23:22", 
        "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_8693_00000504.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1023/A:1014525911391"
      }
    ]
     

    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:1014525911391'

    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:1014525911391'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1014525911391'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1014525911391'


     

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

    163 TRIPLES      21 PREDICATES      45 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1014525911391 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N25e16e8b2df1441bb7b58c345b65c23e
    4 schema:citation sg:pub.10.1007/bf01008249
    5 sg:pub.10.1007/bf01015727
    6 sg:pub.10.1007/bf01027291
    7 sg:pub.10.1007/bf01195070
    8 sg:pub.10.1007/bf02278011
    9 sg:pub.10.1007/bf02781835
    10 sg:pub.10.1007/bfb0112756
    11 sg:pub.10.1007/s002200050572
    12 sg:pub.10.1023/a:1004550307453
    13 sg:pub.10.1038/38963
    14 https://doi.org/10.1002/cpa.3160420202
    15 https://doi.org/10.1002/cpa.3160420303
    16 https://doi.org/10.1088/0305-4470/16/18/029
    17 https://doi.org/10.1103/physrev.91.1505
    18 https://doi.org/10.1103/physreva.33.1322
    19 https://doi.org/10.1103/physrevlett.77.1202
    20 https://doi.org/10.1103/physrevlett.87.040601
    21 https://doi.org/10.1214/aop/1176988286
    22 schema:datePublished 2002-05
    23 schema:datePublishedReg 2002-05-01
    24 schema:description We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager–Machlup theory in the SNS; a general Hamilton–Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton–Jacobi equation, we obtain a logically independent derivation of this result.
    25 schema:genre research_article
    26 schema:inLanguage en
    27 schema:isAccessibleForFree true
    28 schema:isPartOf N2f074aec8a894f7081e773dca3ef9667
    29 N5f1b0e354d3c47b1994f729f814a1b47
    30 sg:journal.1040979
    31 schema:name Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States
    32 schema:pagination 635-675
    33 schema:productId N58717516bd244f3587aa5887b7d38948
    34 N6d812ad61448421eafa835b6b3495421
    35 N9c5796447f97494db8626fbd561111e2
    36 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017377324
    37 https://doi.org/10.1023/a:1014525911391
    38 schema:sdDatePublished 2019-04-10T23:22
    39 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    40 schema:sdPublisher N10f6b75a29134ae894bc1b1ef3a29bae
    41 schema:url http://link.springer.com/10.1023/A:1014525911391
    42 sgo:license sg:explorer/license/
    43 sgo:sdDataset articles
    44 rdf:type schema:ScholarlyArticle
    45 N03fcd3e8d3bf47fbb1131c0904308812 rdf:first sg:person.07413526755.89
    46 rdf:rest Nc8b9f5dd37ed4cb9b2b9261887f1fc63
    47 N10f6b75a29134ae894bc1b1ef3a29bae schema:name Springer Nature - SN SciGraph project
    48 rdf:type schema:Organization
    49 N25e16e8b2df1441bb7b58c345b65c23e rdf:first N97480d0a155d4100938f3f2098bd39e8
    50 rdf:rest N03fcd3e8d3bf47fbb1131c0904308812
    51 N2f074aec8a894f7081e773dca3ef9667 schema:issueNumber 3-4
    52 rdf:type schema:PublicationIssue
    53 N58717516bd244f3587aa5887b7d38948 schema:name readcube_id
    54 schema:value 52cac5b48169ca00453e4cd57170b135a2e9c45fc56e7b82c2bc11ebbd3133d2
    55 rdf:type schema:PropertyValue
    56 N5f1b0e354d3c47b1994f729f814a1b47 schema:volumeNumber 107
    57 rdf:type schema:PublicationVolume
    58 N6d812ad61448421eafa835b6b3495421 schema:name doi
    59 schema:value 10.1023/a:1014525911391
    60 rdf:type schema:PropertyValue
    61 N97480d0a155d4100938f3f2098bd39e8 schema:affiliation https://www.grid.ac/institutes/grid.7841.a
    62 schema:familyName Bertini
    63 schema:givenName L.
    64 rdf:type schema:Person
    65 N9c5796447f97494db8626fbd561111e2 schema:name dimensions_id
    66 schema:value pub.1017377324
    67 rdf:type schema:PropertyValue
    68 Nb4fed32313a345f38a412d01623815a2 rdf:first sg:person.011514320140.11
    69 rdf:rest rdf:nil
    70 Nc8b9f5dd37ed4cb9b2b9261887f1fc63 rdf:first sg:person.016523270626.52
    71 rdf:rest Nf1163f82b9e046a5ad9daffeebdc0a26
    72 Nf1163f82b9e046a5ad9daffeebdc0a26 rdf:first sg:person.01017363063.91
    73 rdf:rest Nb4fed32313a345f38a412d01623815a2
    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.1040979 schema:issn 0022-4715
    81 1572-9613
    82 schema:name Journal of Statistical Physics
    83 rdf:type schema:Periodical
    84 sg:person.01017363063.91 schema:affiliation https://www.grid.ac/institutes/grid.7841.a
    85 schema:familyName Jona-Lasinio
    86 schema:givenName G.
    87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01017363063.91
    88 rdf:type schema:Person
    89 sg:person.011514320140.11 schema:affiliation https://www.grid.ac/institutes/grid.10400.35
    90 schema:familyName Landim
    91 schema:givenName C.
    92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011514320140.11
    93 rdf:type schema:Person
    94 sg:person.016523270626.52 schema:affiliation https://www.grid.ac/institutes/grid.158820.6
    95 schema:familyName Gabrielli
    96 schema:givenName D.
    97 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016523270626.52
    98 rdf:type schema:Person
    99 sg:person.07413526755.89 schema:affiliation https://www.grid.ac/institutes/grid.116068.8
    100 schema:familyName De Sole
    101 schema:givenName A.
    102 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07413526755.89
    103 rdf:type schema:Person
    104 sg:pub.10.1007/bf01008249 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017081991
    105 https://doi.org/10.1007/bf01008249
    106 rdf:type schema:CreativeWork
    107 sg:pub.10.1007/bf01015727 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044349796
    108 https://doi.org/10.1007/bf01015727
    109 rdf:type schema:CreativeWork
    110 sg:pub.10.1007/bf01027291 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042694408
    111 https://doi.org/10.1007/bf01027291
    112 rdf:type schema:CreativeWork
    113 sg:pub.10.1007/bf01195070 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042027052
    114 https://doi.org/10.1007/bf01195070
    115 rdf:type schema:CreativeWork
    116 sg:pub.10.1007/bf02278011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043562108
    117 https://doi.org/10.1007/bf02278011
    118 rdf:type schema:CreativeWork
    119 sg:pub.10.1007/bf02781835 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053369243
    120 https://doi.org/10.1007/bf02781835
    121 rdf:type schema:CreativeWork
    122 sg:pub.10.1007/bfb0112756 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006102707
    123 https://doi.org/10.1007/bfb0112756
    124 rdf:type schema:CreativeWork
    125 sg:pub.10.1007/s002200050572 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018942951
    126 https://doi.org/10.1007/s002200050572
    127 rdf:type schema:CreativeWork
    128 sg:pub.10.1023/a:1004550307453 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025070126
    129 https://doi.org/10.1023/a:1004550307453
    130 rdf:type schema:CreativeWork
    131 sg:pub.10.1038/38963 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001153712
    132 https://doi.org/10.1038/38963
    133 rdf:type schema:CreativeWork
    134 https://doi.org/10.1002/cpa.3160420202 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002387673
    135 rdf:type schema:CreativeWork
    136 https://doi.org/10.1002/cpa.3160420303 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020685618
    137 rdf:type schema:CreativeWork
    138 https://doi.org/10.1088/0305-4470/16/18/029 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059066633
    139 rdf:type schema:CreativeWork
    140 https://doi.org/10.1103/physrev.91.1505 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060460948
    141 rdf:type schema:CreativeWork
    142 https://doi.org/10.1103/physreva.33.1322 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060474203
    143 rdf:type schema:CreativeWork
    144 https://doi.org/10.1103/physrevlett.77.1202 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051180022
    145 rdf:type schema:CreativeWork
    146 https://doi.org/10.1103/physrevlett.87.040601 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008699672
    147 rdf:type schema:CreativeWork
    148 https://doi.org/10.1214/aop/1176988286 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064403512
    149 rdf:type schema:CreativeWork
    150 https://www.grid.ac/institutes/grid.10400.35 schema:alternateName University of Rouen
    151 schema:name IMPA, Estrada Dona Castorina 110, J. Botanico, 22460, Rio de Janeiro, Brazil
    152 Université de Rouen, CNRS UPRES-A 6085, 76128, Mont-Saint-Aignan Cedex, France
    153 rdf:type schema:Organization
    154 https://www.grid.ac/institutes/grid.116068.8 schema:alternateName Massachusetts Institute of Technology
    155 schema:name Department of Mathematics, MIT, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA
    156 rdf:type schema:Organization
    157 https://www.grid.ac/institutes/grid.158820.6 schema:alternateName University of L'Aquila
    158 schema:name Dipartimento di Matematica, Università dell'Aquila, 67100, Coppito, L'Aquila, Italy
    159 rdf:type schema:Organization
    160 https://www.grid.ac/institutes/grid.7841.a schema:alternateName Sapienza University of Rome
    161 schema:name Dipartimento di Fisica and INFN, Università di Roma La Sapienza, P.le A. Moro 2, 00185, Roma, Italy
    162 Dipartimento di Matematica, Università di Roma La Sapienza, P.le A. Moro 2, 00185, Roma, Italy
    163 rdf:type schema:Organization
     




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


    ...