The Fermi–Pasta–Ulam System as a Model for Glasses View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-12

AUTHORS

A. Carati, A. Maiocchi, L. Galgani, G. Amati

ABSTRACT

We show that the standard Fermi–Pasta–Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape of the minima of the potential energy and to deal concretely with any one of them, determining the spectrum of frequencies and the normal modes. A relevant role is played by the harmonic energy ℰ relative to a given minimum, i.e., the expansion of the Hamiltonian about the minimum up to second order. Indeed we find that there exists an energy threshold in ℰ such that below it the harmonic energy ℰ appears to be an approximate integral of motion for the whole observation time. Consequently, the system remains trapped near the minimum, in what may be called a vitreous or glassy state. Instead, for larger values of ℰ the system rather quickly relaxes to a final equilibrium state. Moreover we find that the vitreous states present peculiar statistical behaviors, still involving the harmonic energy ℰ. Indeed, the vitreous states are described by a Gibbs distribution with an effective Hamiltonian close to ℰ and with a suitable effective inverse temperature. The final equilibrium state presents instead statistical properties which are in very good agreement with the Gibbs distribution relative to the full Hamiltonian of the system. More... »

PAGES

31

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11040-015-9201-x

DOI

http://dx.doi.org/10.1007/s11040-015-9201-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006935347


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/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "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": "University of Milan", 
          "id": "https://www.grid.ac/institutes/grid.4708.b", 
          "name": [
            "Department of Mathematics, Universit\u00e0 degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Carati", 
        "givenName": "A.", 
        "id": "sg:person.01364554612.00", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01364554612.00"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Milan", 
          "id": "https://www.grid.ac/institutes/grid.4708.b", 
          "name": [
            "Department of Mathematics, Universit\u00e0 degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Maiocchi", 
        "givenName": "A.", 
        "id": "sg:person.015366730074.31", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015366730074.31"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Milan", 
          "id": "https://www.grid.ac/institutes/grid.4708.b", 
          "name": [
            "Department of Mathematics, Universit\u00e0 degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Galgani", 
        "givenName": "L.", 
        "id": "sg:person.010346707747.76", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010346707747.76"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Milan", 
          "id": "https://www.grid.ac/institutes/grid.4708.b", 
          "name": [
            "Corso di Laurea in Fisica, Universit\u00e0 degli Studi di Milano, Via Celoria 16, 20133, Milano, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Amati", 
        "givenName": "G.", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01210702", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002642648", 
          "https://doi.org/10.1007/bf01210702"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01210702", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002642648", 
          "https://doi.org/10.1007/bf01210702"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1209/epl/i1997-00471-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014955489"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-72995-2_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021282964", 
          "https://doi.org/10.1007/978-3-540-72995-2_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-72995-2_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021282964", 
          "https://doi.org/10.1007/978-3-540-72995-2_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.88.055502", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038277513"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.88.055502", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038277513"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10955-011-0277-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041003802", 
          "https://doi.org/10.1007/s10955-011-0277-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10955-014-0958-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048020450", 
          "https://doi.org/10.1007/s10955-014-0958-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1051/jphys:01982004305070700", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1056990681"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1672587", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057749047"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1743274", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057805719"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2015-12", 
    "datePublishedReg": "2015-12-01", 
    "description": "We show that the standard Fermi\u2013Pasta\u2013Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape of the minima of the potential energy and to deal concretely with any one of them, determining the spectrum of frequencies and the normal modes. A relevant role is played by the harmonic energy \u2130 relative to a given minimum, i.e., the expansion of the Hamiltonian about the minimum up to second order. Indeed we find that there exists an energy threshold in \u2130 such that below it the harmonic energy \u2130 appears to be an approximate integral of motion for the whole observation time. Consequently, the system remains trapped near the minimum, in what may be called a vitreous or glassy state. Instead, for larger values of \u2130 the system rather quickly relaxes to a final equilibrium state. Moreover we find that the vitreous states present peculiar statistical behaviors, still involving the harmonic energy \u2130. Indeed, the vitreous states are described by a Gibbs distribution with an effective Hamiltonian close to \u2130 and with a suitable effective inverse temperature. The final equilibrium state presents instead statistical properties which are in very good agreement with the Gibbs distribution relative to the full Hamiltonian of the system.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s11040-015-9201-x", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1135920", 
        "issn": [
          "1385-0172", 
          "1572-9656"
        ], 
        "name": "Mathematical Physics, Analysis and Geometry", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "18"
      }
    ], 
    "name": "The Fermi\u2013Pasta\u2013Ulam System as a Model for Glasses", 
    "pagination": "31", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "210977510d2c0afc53cacd276535560e9a4673c97f225ff9ae3997f8af371aad"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11040-015-9201-x"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1006935347"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11040-015-9201-x", 
      "https://app.dimensions.ai/details/publication/pub.1006935347"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T18:20", 
    "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_8675_00000510.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs11040-015-9201-x"
  }
]
 

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.10.1007/s11040-015-9201-x'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11040-015-9201-x'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11040-015-9201-x'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11040-015-9201-x'


 

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

113 TRIPLES      21 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11040-015-9201-x schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Na9aef722727847a3b9b311318e29502d
4 schema:citation sg:pub.10.1007/978-3-540-72995-2_4
5 sg:pub.10.1007/bf01210702
6 sg:pub.10.1007/s10955-011-0277-9
7 sg:pub.10.1007/s10955-014-0958-2
8 https://doi.org/10.1051/jphys:01982004305070700
9 https://doi.org/10.1063/1.1672587
10 https://doi.org/10.1063/1.1743274
11 https://doi.org/10.1103/physrevlett.88.055502
12 https://doi.org/10.1209/epl/i1997-00471-9
13 schema:datePublished 2015-12
14 schema:datePublishedReg 2015-12-01
15 schema:description We show that the standard Fermi–Pasta–Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape of the minima of the potential energy and to deal concretely with any one of them, determining the spectrum of frequencies and the normal modes. A relevant role is played by the harmonic energy ℰ relative to a given minimum, i.e., the expansion of the Hamiltonian about the minimum up to second order. Indeed we find that there exists an energy threshold in ℰ such that below it the harmonic energy ℰ appears to be an approximate integral of motion for the whole observation time. Consequently, the system remains trapped near the minimum, in what may be called a vitreous or glassy state. Instead, for larger values of ℰ the system rather quickly relaxes to a final equilibrium state. Moreover we find that the vitreous states present peculiar statistical behaviors, still involving the harmonic energy ℰ. Indeed, the vitreous states are described by a Gibbs distribution with an effective Hamiltonian close to ℰ and with a suitable effective inverse temperature. The final equilibrium state presents instead statistical properties which are in very good agreement with the Gibbs distribution relative to the full Hamiltonian of the system.
16 schema:genre research_article
17 schema:inLanguage en
18 schema:isAccessibleForFree true
19 schema:isPartOf N33b13363bd95476384e2ff09bc018a56
20 Ncec3c7f9a3774a87a74533f09e788760
21 sg:journal.1135920
22 schema:name The Fermi–Pasta–Ulam System as a Model for Glasses
23 schema:pagination 31
24 schema:productId N068b8deac1884f8cbcdbcefaa07e195f
25 N396405c0cf3f475fb208f7c3cb9bb95f
26 N564f08be1ed34ad4b93201e831ac2868
27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006935347
28 https://doi.org/10.1007/s11040-015-9201-x
29 schema:sdDatePublished 2019-04-10T18:20
30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
31 schema:sdPublisher N074e827523f7441490ae43e7ea5ca194
32 schema:url http://link.springer.com/10.1007%2Fs11040-015-9201-x
33 sgo:license sg:explorer/license/
34 sgo:sdDataset articles
35 rdf:type schema:ScholarlyArticle
36 N068b8deac1884f8cbcdbcefaa07e195f schema:name doi
37 schema:value 10.1007/s11040-015-9201-x
38 rdf:type schema:PropertyValue
39 N074e827523f7441490ae43e7ea5ca194 schema:name Springer Nature - SN SciGraph project
40 rdf:type schema:Organization
41 N33b13363bd95476384e2ff09bc018a56 schema:issueNumber 1
42 rdf:type schema:PublicationIssue
43 N396405c0cf3f475fb208f7c3cb9bb95f schema:name dimensions_id
44 schema:value pub.1006935347
45 rdf:type schema:PropertyValue
46 N564f08be1ed34ad4b93201e831ac2868 schema:name readcube_id
47 schema:value 210977510d2c0afc53cacd276535560e9a4673c97f225ff9ae3997f8af371aad
48 rdf:type schema:PropertyValue
49 N7556a06835b1454f846d00b2d3da90fb rdf:first sg:person.015366730074.31
50 rdf:rest N908c2fb2a1d44c038b62811c33de25f4
51 N8d54d5fe9e754b86b77be89f2f384f15 schema:affiliation https://www.grid.ac/institutes/grid.4708.b
52 schema:familyName Amati
53 schema:givenName G.
54 rdf:type schema:Person
55 N908c2fb2a1d44c038b62811c33de25f4 rdf:first sg:person.010346707747.76
56 rdf:rest Naef4605ad9db4097be635dcfe5ca811e
57 Na9aef722727847a3b9b311318e29502d rdf:first sg:person.01364554612.00
58 rdf:rest N7556a06835b1454f846d00b2d3da90fb
59 Naef4605ad9db4097be635dcfe5ca811e rdf:first N8d54d5fe9e754b86b77be89f2f384f15
60 rdf:rest rdf:nil
61 Ncec3c7f9a3774a87a74533f09e788760 schema:volumeNumber 18
62 rdf:type schema:PublicationVolume
63 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
64 schema:name Mathematical Sciences
65 rdf:type schema:DefinedTerm
66 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
67 schema:name Statistics
68 rdf:type schema:DefinedTerm
69 sg:journal.1135920 schema:issn 1385-0172
70 1572-9656
71 schema:name Mathematical Physics, Analysis and Geometry
72 rdf:type schema:Periodical
73 sg:person.010346707747.76 schema:affiliation https://www.grid.ac/institutes/grid.4708.b
74 schema:familyName Galgani
75 schema:givenName L.
76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010346707747.76
77 rdf:type schema:Person
78 sg:person.01364554612.00 schema:affiliation https://www.grid.ac/institutes/grid.4708.b
79 schema:familyName Carati
80 schema:givenName A.
81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01364554612.00
82 rdf:type schema:Person
83 sg:person.015366730074.31 schema:affiliation https://www.grid.ac/institutes/grid.4708.b
84 schema:familyName Maiocchi
85 schema:givenName A.
86 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015366730074.31
87 rdf:type schema:Person
88 sg:pub.10.1007/978-3-540-72995-2_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021282964
89 https://doi.org/10.1007/978-3-540-72995-2_4
90 rdf:type schema:CreativeWork
91 sg:pub.10.1007/bf01210702 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002642648
92 https://doi.org/10.1007/bf01210702
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/s10955-011-0277-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041003802
95 https://doi.org/10.1007/s10955-011-0277-9
96 rdf:type schema:CreativeWork
97 sg:pub.10.1007/s10955-014-0958-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048020450
98 https://doi.org/10.1007/s10955-014-0958-2
99 rdf:type schema:CreativeWork
100 https://doi.org/10.1051/jphys:01982004305070700 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056990681
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1063/1.1672587 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057749047
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1063/1.1743274 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057805719
105 rdf:type schema:CreativeWork
106 https://doi.org/10.1103/physrevlett.88.055502 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038277513
107 rdf:type schema:CreativeWork
108 https://doi.org/10.1209/epl/i1997-00471-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014955489
109 rdf:type schema:CreativeWork
110 https://www.grid.ac/institutes/grid.4708.b schema:alternateName University of Milan
111 schema:name Corso di Laurea in Fisica, Università degli Studi di Milano, Via Celoria 16, 20133, Milano, Italy
112 Department of Mathematics, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy
113 rdf:type schema:Organization
 




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


...