Transformation of Gorkov's equation for type II superconductors into transport-like equations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1968-04

AUTHORS

Gert Eilenberger

ABSTRACT

The stationary behavior of type II superconductors is completely described by Gorkov's equations for a set of four Green's functions, supplemented by two self-consistency equations for gap parameterΔ(r) and vector potentialA(r). Expanding all quantities as usual at the Fermi surface and averaging over impurity positions, this set of equations is transformed into a simpler set for integrated Green's functions (which still contain much more information than is needed in most cases). The resulting equations, when linearized, yield essentially Lüders' transport equation for de Gennes' correlation function. The full equations contain all the known results and provide a promising starting point for numerical calculations.The thermodynamic potential is constructed as a functional of the integrated Green's functions and the mean fieldsΔ andA and a variational principle is formulated which uses this functional. Finally, paramagnetic scatterers are included (in Born approximation) as an example for possible generalizations of the new equations. More... »

PAGES

195-213

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01379803

DOI

http://dx.doi.org/10.1007/bf01379803

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1041571783


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/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institut f\u00fcr Theoretische Physik der Universit\u00e4t zu K\u00f6ln, Deutschland", 
          "id": "http://www.grid.ac/institutes/None", 
          "name": [
            "Institut f\u00fcr Theoretische Physik der Universit\u00e4t zu K\u00f6ln, Deutschland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Eilenberger", 
        "givenName": "Gert", 
        "id": "sg:person.015466352201.20", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015466352201.20"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1968-04", 
    "datePublishedReg": "1968-04-01", 
    "description": "The stationary behavior of type II superconductors is completely described by Gorkov's equations for a set of four Green's functions, supplemented by two self-consistency equations for gap parameter\u0394(r) and vector potentialA(r). Expanding all quantities as usual at the Fermi surface and averaging over impurity positions, this set of equations is transformed into a simpler set for integrated Green's functions (which still contain much more information than is needed in most cases). The resulting equations, when linearized, yield essentially L\u00fcders' transport equation for de Gennes' correlation function. The full equations contain all the known results and provide a promising starting point for numerical calculations.The thermodynamic potential is constructed as a functional of the integrated Green's functions and the mean fields\u0394 andA and a variational principle is formulated which uses this functional. Finally, paramagnetic scatterers are included (in Born approximation) as an example for possible generalizations of the new equations.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf01379803", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1313831", 
        "issn": [
          "0939-7922", 
          "1431-5831"
        ], 
        "name": "Zeitschrift f\u00fcr Physik A Hadrons and nuclei", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "214"
      }
    ], 
    "keywords": [
      "type-II superconductors", 
      "integrated Green's functions", 
      "II superconductors", 
      "Gorkov equations", 
      "Green's function", 
      "transport equation", 
      "transport-like equations", 
      "correlation functions", 
      "self-consistency equations", 
      "set of equations", 
      "full equations", 
      "variational principle", 
      "impurity position", 
      "possible generalizations", 
      "equations", 
      "Fermi surface", 
      "thermodynamic potential", 
      "stationary behavior", 
      "numerical calculations", 
      "new equation", 
      "superconductors", 
      "simple set", 
      "functionals", 
      "set", 
      "generalization", 
      "scatterers", 
      "starting point", 
      "function", 
      "calculations", 
      "promising starting point", 
      "vector", 
      "principles", 
      "point", 
      "quantity", 
      "anda", 
      "transformation", 
      "behavior", 
      "gap", 
      "results", 
      "position", 
      "surface", 
      "potential", 
      "example"
    ], 
    "name": "Transformation of Gorkov's equation for type II superconductors into transport-like equations", 
    "pagination": "195-213", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1041571783"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01379803"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01379803", 
      "https://app.dimensions.ai/details/publication/pub.1041571783"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-08-04T17:07", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220804/entities/gbq_results/article/article_78.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf01379803"
  }
]
 

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/bf01379803'

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/bf01379803'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01379803'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01379803'


 

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

100 TRIPLES      20 PREDICATES      68 URIs      60 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01379803 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Na4697de59f2444f6a62f8afb951534c1
4 schema:datePublished 1968-04
5 schema:datePublishedReg 1968-04-01
6 schema:description The stationary behavior of type II superconductors is completely described by Gorkov's equations for a set of four Green's functions, supplemented by two self-consistency equations for gap parameterΔ(r) and vector potentialA(r). Expanding all quantities as usual at the Fermi surface and averaging over impurity positions, this set of equations is transformed into a simpler set for integrated Green's functions (which still contain much more information than is needed in most cases). The resulting equations, when linearized, yield essentially Lüders' transport equation for de Gennes' correlation function. The full equations contain all the known results and provide a promising starting point for numerical calculations.The thermodynamic potential is constructed as a functional of the integrated Green's functions and the mean fieldsΔ andA and a variational principle is formulated which uses this functional. Finally, paramagnetic scatterers are included (in Born approximation) as an example for possible generalizations of the new equations.
7 schema:genre article
8 schema:isAccessibleForFree false
9 schema:isPartOf Ne43b2c8931d74dae80bb55d736905b4d
10 Nefbd77a3e7fc4b599652951334ff8976
11 sg:journal.1313831
12 schema:keywords Fermi surface
13 Gorkov equations
14 Green's function
15 II superconductors
16 anda
17 behavior
18 calculations
19 correlation functions
20 equations
21 example
22 full equations
23 function
24 functionals
25 gap
26 generalization
27 impurity position
28 integrated Green's functions
29 new equation
30 numerical calculations
31 point
32 position
33 possible generalizations
34 potential
35 principles
36 promising starting point
37 quantity
38 results
39 scatterers
40 self-consistency equations
41 set
42 set of equations
43 simple set
44 starting point
45 stationary behavior
46 superconductors
47 surface
48 thermodynamic potential
49 transformation
50 transport equation
51 transport-like equations
52 type-II superconductors
53 variational principle
54 vector
55 schema:name Transformation of Gorkov's equation for type II superconductors into transport-like equations
56 schema:pagination 195-213
57 schema:productId N2debdc884652472aac462ac962a39a4b
58 N6671ad0310ec49d6b9f514c6a1902ef7
59 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041571783
60 https://doi.org/10.1007/bf01379803
61 schema:sdDatePublished 2022-08-04T17:07
62 schema:sdLicense https://scigraph.springernature.com/explorer/license/
63 schema:sdPublisher Na6f7d82caa21461da6db9932e9bf4fe5
64 schema:url https://doi.org/10.1007/bf01379803
65 sgo:license sg:explorer/license/
66 sgo:sdDataset articles
67 rdf:type schema:ScholarlyArticle
68 N2debdc884652472aac462ac962a39a4b schema:name doi
69 schema:value 10.1007/bf01379803
70 rdf:type schema:PropertyValue
71 N6671ad0310ec49d6b9f514c6a1902ef7 schema:name dimensions_id
72 schema:value pub.1041571783
73 rdf:type schema:PropertyValue
74 Na4697de59f2444f6a62f8afb951534c1 rdf:first sg:person.015466352201.20
75 rdf:rest rdf:nil
76 Na6f7d82caa21461da6db9932e9bf4fe5 schema:name Springer Nature - SN SciGraph project
77 rdf:type schema:Organization
78 Ne43b2c8931d74dae80bb55d736905b4d schema:issueNumber 2
79 rdf:type schema:PublicationIssue
80 Nefbd77a3e7fc4b599652951334ff8976 schema:volumeNumber 214
81 rdf:type schema:PublicationVolume
82 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
83 schema:name Mathematical Sciences
84 rdf:type schema:DefinedTerm
85 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
86 schema:name Numerical and Computational Mathematics
87 rdf:type schema:DefinedTerm
88 sg:journal.1313831 schema:issn 0939-7922
89 1431-5831
90 schema:name Zeitschrift für Physik A Hadrons and nuclei
91 schema:publisher Springer Nature
92 rdf:type schema:Periodical
93 sg:person.015466352201.20 schema:affiliation grid-institutes:None
94 schema:familyName Eilenberger
95 schema:givenName Gert
96 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015466352201.20
97 rdf:type schema:Person
98 grid-institutes:None schema:alternateName Institut für Theoretische Physik der Universität zu Köln, Deutschland
99 schema:name Institut für Theoretische Physik der Universität zu Köln, Deutschland
100 rdf:type schema:Organization
 




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


...