Finite Range of Large Perturbations in Hamiltonian Dynamics View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1998-09

AUTHORS

D. Bénisti, D. F. Escande

ABSTRACT

The dynamics defined by the Hamiltonian , where the φm are fixed random phases, is investigated for large values of A, and for . For a given P* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ − nt + φm) with , is a random variable whose r.m.s. with respect to the φm is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing α. For practical purposes α close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated. More... »

PAGES

909-972

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1023092526620

DOI

http://dx.doi.org/10.1023/a:1023092526620

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1044140989


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": {
          "name": [
            "Equipe Turbulence Plasma du Laboratoire de Physique des Interactions Ioniques et Mol\u00e9culaires, UMR 6633 CNRS-Universit\u00e9 de Provence, Centre universitaire de Saint-J\u00e9r\u00f4me, F-13397, Marseille Cedex 20, France;"
          ], 
          "type": "Organization"
        }, 
        "familyName": "B\u00e9nisti", 
        "givenName": "D.", 
        "id": "sg:person.015254560661.08", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015254560661.08"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Equipe Turbulence Plasma du Laboratoire de Physique des Interactions Ioniques et Mol\u00e9culaires, UMR 6633 CNRS-Universit\u00e9 de Provence, Centre universitaire de Saint-J\u00e9r\u00f4me, F-13397, Marseille Cedex 20, France;"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Escande", 
        "givenName": "D. F.", 
        "id": "sg:person.01243642262.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01243642262.71"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01011301", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043338720", 
          "https://doi.org/10.1007/bf01011301"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01011301", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043338720", 
          "https://doi.org/10.1007/bf01011301"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1761932", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057816989"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.870553", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058122682"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.872288", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058124398"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/rm1977v032n06abeh003859", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058194264"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0031-8949/51/1/005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059000578"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0951-7715/6/6/003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059110825"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.159.98", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060435896"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.159.98", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060435896"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.65.3132", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060801718"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.65.3132", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060801718"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.80.4871", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060817565"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.80.4871", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060817565"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1998-09", 
    "datePublishedReg": "1998-09-01", 
    "description": "The dynamics defined by the Hamiltonian , where the \u03c6m are fixed random phases, is investigated for large values of A, and for . For a given P* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ \u2212 nt + \u03c6m) with , is a random variable whose r.m.s. with respect to the \u03c6m is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing \u03b1. For practical purposes \u03b1 close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1023/a:1023092526620", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040979", 
        "issn": [
          "0022-4715", 
          "1572-9613"
        ], 
        "name": "Journal of Statistical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "5-6", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "92"
      }
    ], 
    "name": "Finite Range of Large Perturbations in Hamiltonian Dynamics", 
    "pagination": "909-972", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "d241f8ac35d6a68864e9442526e845a468d25f7de7e21ea8d5029c0a9cab28d4"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1023/a:1023092526620"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1044140989"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1023/a:1023092526620", 
      "https://app.dimensions.ai/details/publication/pub.1044140989"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T22:30", 
    "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_8690_00000507.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1023%2FA%3A1023092526620"
  }
]
 

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:1023092526620'

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:1023092526620'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1023092526620'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1023092526620'


 

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

100 TRIPLES      21 PREDICATES      37 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1023/a:1023092526620 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Nbe1aa6ea2fb649c1aa053e1b7f7d8ccc
4 schema:citation sg:pub.10.1007/bf01011301
5 https://doi.org/10.1063/1.1761932
6 https://doi.org/10.1063/1.870553
7 https://doi.org/10.1063/1.872288
8 https://doi.org/10.1070/rm1977v032n06abeh003859
9 https://doi.org/10.1088/0031-8949/51/1/005
10 https://doi.org/10.1088/0951-7715/6/6/003
11 https://doi.org/10.1103/physrev.159.98
12 https://doi.org/10.1103/physrevlett.65.3132
13 https://doi.org/10.1103/physrevlett.80.4871
14 schema:datePublished 1998-09
15 schema:datePublishedReg 1998-09-01
16 schema:description The dynamics defined by the Hamiltonian , where the φm are fixed random phases, is investigated for large values of A, and for . For a given P* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ − nt + φm) with , is a random variable whose r.m.s. with respect to the φm is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing α. For practical purposes α close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated.
17 schema:genre research_article
18 schema:inLanguage en
19 schema:isAccessibleForFree false
20 schema:isPartOf N43088ad6f774401a910109b53519a036
21 Nf061740b2d434486bba44cded1431bb0
22 sg:journal.1040979
23 schema:name Finite Range of Large Perturbations in Hamiltonian Dynamics
24 schema:pagination 909-972
25 schema:productId N08a0510e0efe43039e95d56ec847a12a
26 N4a52c03261e34adda9c9f27a708b766c
27 Nc9ace95ffc61485993b85339495e5216
28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044140989
29 https://doi.org/10.1023/a:1023092526620
30 schema:sdDatePublished 2019-04-10T22:30
31 schema:sdLicense https://scigraph.springernature.com/explorer/license/
32 schema:sdPublisher Naabbb10d5dab49c9bbb591a32ef642db
33 schema:url http://link.springer.com/10.1023%2FA%3A1023092526620
34 sgo:license sg:explorer/license/
35 sgo:sdDataset articles
36 rdf:type schema:ScholarlyArticle
37 N08a0510e0efe43039e95d56ec847a12a schema:name dimensions_id
38 schema:value pub.1044140989
39 rdf:type schema:PropertyValue
40 N417c7d7884da4d749dd377f3faf81918 schema:name Equipe Turbulence Plasma du Laboratoire de Physique des Interactions Ioniques et Moléculaires, UMR 6633 CNRS-Université de Provence, Centre universitaire de Saint-Jérôme, F-13397, Marseille Cedex 20, France;
41 rdf:type schema:Organization
42 N43088ad6f774401a910109b53519a036 schema:issueNumber 5-6
43 rdf:type schema:PublicationIssue
44 N4a52c03261e34adda9c9f27a708b766c schema:name doi
45 schema:value 10.1023/a:1023092526620
46 rdf:type schema:PropertyValue
47 N9153dbb137aa42e983e9c686fa85aa1d rdf:first sg:person.01243642262.71
48 rdf:rest rdf:nil
49 Naabbb10d5dab49c9bbb591a32ef642db schema:name Springer Nature - SN SciGraph project
50 rdf:type schema:Organization
51 Nbe1aa6ea2fb649c1aa053e1b7f7d8ccc rdf:first sg:person.015254560661.08
52 rdf:rest N9153dbb137aa42e983e9c686fa85aa1d
53 Nc50bdb43e2464a138ebc4be140f493e1 schema:name Equipe Turbulence Plasma du Laboratoire de Physique des Interactions Ioniques et Moléculaires, UMR 6633 CNRS-Université de Provence, Centre universitaire de Saint-Jérôme, F-13397, Marseille Cedex 20, France;
54 rdf:type schema:Organization
55 Nc9ace95ffc61485993b85339495e5216 schema:name readcube_id
56 schema:value d241f8ac35d6a68864e9442526e845a468d25f7de7e21ea8d5029c0a9cab28d4
57 rdf:type schema:PropertyValue
58 Nf061740b2d434486bba44cded1431bb0 schema:volumeNumber 92
59 rdf:type schema:PublicationVolume
60 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
61 schema:name Mathematical Sciences
62 rdf:type schema:DefinedTerm
63 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
64 schema:name Statistics
65 rdf:type schema:DefinedTerm
66 sg:journal.1040979 schema:issn 0022-4715
67 1572-9613
68 schema:name Journal of Statistical Physics
69 rdf:type schema:Periodical
70 sg:person.01243642262.71 schema:affiliation Nc50bdb43e2464a138ebc4be140f493e1
71 schema:familyName Escande
72 schema:givenName D. F.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01243642262.71
74 rdf:type schema:Person
75 sg:person.015254560661.08 schema:affiliation N417c7d7884da4d749dd377f3faf81918
76 schema:familyName Bénisti
77 schema:givenName D.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015254560661.08
79 rdf:type schema:Person
80 sg:pub.10.1007/bf01011301 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043338720
81 https://doi.org/10.1007/bf01011301
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1063/1.1761932 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057816989
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1063/1.870553 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058122682
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1063/1.872288 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058124398
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1070/rm1977v032n06abeh003859 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058194264
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1088/0031-8949/51/1/005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059000578
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1088/0951-7715/6/6/003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059110825
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1103/physrev.159.98 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060435896
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1103/physrevlett.65.3132 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060801718
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1103/physrevlett.80.4871 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060817565
100 rdf:type schema:CreativeWork
 




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


...