On the properties of a class of higher-order Mathieu equations originating from a parametric quantum oscillator View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02-26

AUTHORS

Subhadip Biswas, Jayanta K. Bhattacharjee

ABSTRACT

Evolution in time of an arbitrary initial state for a parametrically driven quantum oscillator is an interesting problem since there exist regions in parameter space (defined by the amplitude and frequency of the driving) where the moments of the probability distribution can diverge in time. While the first moment satisfies a Mathieu equation, the higher-order moments follow Mathieu like equations of order greater than two. It is not very often that a physical problem gives rise to higher-order Mathieu equations. Hence, we give a detailed study of the different stability zones associated with the parametric quantum oscillator, using perturbative techniques traditionally associated with the Mathieu equation. We verify our results by numerical analysis, thus demonstrating that for the higher-order Mathieu equations, the traditional perturbation theory methods give a consistent account of the stability zones. More... »

PAGES

1-14

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11071-019-04818-9

DOI

http://dx.doi.org/10.1007/s11071-019-04818-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112417360


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": "University of Sheffield", 
          "id": "https://www.grid.ac/institutes/grid.11835.3e", 
          "name": [
            "Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Biswas", 
        "givenName": "Subhadip", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Indian Association for the Cultivation of Science", 
          "id": "https://www.grid.ac/institutes/grid.417929.0", 
          "name": [
            "Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Jadavpur, Kolkata, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Bhattacharjee", 
        "givenName": "Jayanta K.", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf03322203", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001683259", 
          "https://doi.org/10.1007/bf03322203"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0378-4371(97)00194-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003298963"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11071-013-1002-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005869379", 
          "https://doi.org/10.1007/s11071-013-1002-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1005909355", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-97465-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005909355", 
          "https://doi.org/10.1007/978-3-642-97465-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-97465-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005909355", 
          "https://doi.org/10.1007/978-3-642-97465-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1023216817293", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008407340", 
          "https://doi.org/10.1023/a:1023216817293"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0960-0779(01)00226-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019174955"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1023293901305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026830757", 
          "https://doi.org/10.1023/a:1023293901305"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/1751-8113/45/45/455305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027311596"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-1977-0454208-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029726916"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11071-006-9162-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037840117", 
          "https://doi.org/10.1007/s11071-006-9162-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1098/rspa.2001.0941", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041376931"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11071-005-4338-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043061660", 
          "https://doi.org/10.1007/s11071-005-4338-y"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11071-014-1405-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044777652", 
          "https://doi.org/10.1007/s11071-014-1405-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jmaa.2010.10.035", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047991609"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00046308", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048910675", 
          "https://doi.org/10.1007/bf00046308"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00046308", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048910675", 
          "https://doi.org/10.1007/bf00046308"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0027763000008254", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052729749"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1664991", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057743061"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.66.527", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060802795"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.66.527", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060802795"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.75.281", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060839572"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.75.281", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060839572"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1115/1.3125853", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062102234"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/s0129183116500145", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062905872"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1115/1.4039144", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1100679851"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.physleta.2018.03.011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101509784"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-02-26", 
    "datePublishedReg": "2019-02-26", 
    "description": "Evolution in time of an arbitrary initial state for a parametrically driven quantum oscillator is an interesting problem since there exist regions in parameter space (defined by the amplitude and frequency of the driving) where the moments of the probability distribution can diverge in time. While the first moment satisfies a Mathieu equation, the higher-order moments follow Mathieu like equations of order greater than two. It is not very often that a physical problem gives rise to higher-order Mathieu equations. Hence, we give a detailed study of the different stability zones associated with the parametric quantum oscillator, using perturbative techniques traditionally associated with the Mathieu equation. We verify our results by numerical analysis, thus demonstrating that for the higher-order Mathieu equations, the traditional perturbation theory methods give a consistent account of the stability zones.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s11071-019-04818-9", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040905", 
        "issn": [
          "0924-090X", 
          "1573-269X"
        ], 
        "name": "Nonlinear Dynamics", 
        "type": "Periodical"
      }
    ], 
    "name": "On the properties of a class of higher-order Mathieu equations originating from a parametric quantum oscillator", 
    "pagination": "1-14", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "432656ffd454982d13248d39807645c98a6868083187910a2c928572240c8ac7"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11071-019-04818-9"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1112417360"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11071-019-04818-9", 
      "https://app.dimensions.ai/details/publication/pub.1112417360"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T10:39", 
    "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/v90/0000000349_0000000349/records_113677_00000005.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs11071-019-04818-9"
  }
]
 

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/s11071-019-04818-9'

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/s11071-019-04818-9'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11071-019-04818-9'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11071-019-04818-9'


 

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

143 TRIPLES      21 PREDICATES      48 URIs      16 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11071-019-04818-9 schema:about anzsrc-for:02
2 anzsrc-for:0202
3 schema:author N9e77ee3bcb9e4ba4acdc213db298f7ef
4 schema:citation sg:pub.10.1007/978-3-642-97465-6
5 sg:pub.10.1007/bf00046308
6 sg:pub.10.1007/bf03322203
7 sg:pub.10.1007/s11071-005-4338-y
8 sg:pub.10.1007/s11071-006-9162-5
9 sg:pub.10.1007/s11071-013-1002-9
10 sg:pub.10.1007/s11071-014-1405-2
11 sg:pub.10.1023/a:1023216817293
12 sg:pub.10.1023/a:1023293901305
13 https://app.dimensions.ai/details/publication/pub.1005909355
14 https://doi.org/10.1016/j.jmaa.2010.10.035
15 https://doi.org/10.1016/j.physleta.2018.03.011
16 https://doi.org/10.1016/s0378-4371(97)00194-5
17 https://doi.org/10.1016/s0960-0779(01)00226-0
18 https://doi.org/10.1017/s0027763000008254
19 https://doi.org/10.1063/1.1664991
20 https://doi.org/10.1088/1751-8113/45/45/455305
21 https://doi.org/10.1090/s0002-9939-1977-0454208-7
22 https://doi.org/10.1098/rspa.2001.0941
23 https://doi.org/10.1103/physrevlett.66.527
24 https://doi.org/10.1103/revmodphys.75.281
25 https://doi.org/10.1115/1.3125853
26 https://doi.org/10.1115/1.4039144
27 https://doi.org/10.1142/s0129183116500145
28 schema:datePublished 2019-02-26
29 schema:datePublishedReg 2019-02-26
30 schema:description Evolution in time of an arbitrary initial state for a parametrically driven quantum oscillator is an interesting problem since there exist regions in parameter space (defined by the amplitude and frequency of the driving) where the moments of the probability distribution can diverge in time. While the first moment satisfies a Mathieu equation, the higher-order moments follow Mathieu like equations of order greater than two. It is not very often that a physical problem gives rise to higher-order Mathieu equations. Hence, we give a detailed study of the different stability zones associated with the parametric quantum oscillator, using perturbative techniques traditionally associated with the Mathieu equation. We verify our results by numerical analysis, thus demonstrating that for the higher-order Mathieu equations, the traditional perturbation theory methods give a consistent account of the stability zones.
31 schema:genre research_article
32 schema:inLanguage en
33 schema:isAccessibleForFree false
34 schema:isPartOf sg:journal.1040905
35 schema:name On the properties of a class of higher-order Mathieu equations originating from a parametric quantum oscillator
36 schema:pagination 1-14
37 schema:productId N301fb1437f534ff2bce4d6257bb825a8
38 N4b01d15ff91d408eb80202f5c3cce840
39 Nd136e8f73a1e4a399e69d6bcb4a14983
40 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112417360
41 https://doi.org/10.1007/s11071-019-04818-9
42 schema:sdDatePublished 2019-04-11T10:39
43 schema:sdLicense https://scigraph.springernature.com/explorer/license/
44 schema:sdPublisher N114f37c0545746eabe347fdf0ff107d8
45 schema:url https://link.springer.com/10.1007%2Fs11071-019-04818-9
46 sgo:license sg:explorer/license/
47 sgo:sdDataset articles
48 rdf:type schema:ScholarlyArticle
49 N098dc2e3d9834f19896ca0cd7ff7497e schema:affiliation https://www.grid.ac/institutes/grid.11835.3e
50 schema:familyName Biswas
51 schema:givenName Subhadip
52 rdf:type schema:Person
53 N114f37c0545746eabe347fdf0ff107d8 schema:name Springer Nature - SN SciGraph project
54 rdf:type schema:Organization
55 N1280a269048544a5aea86351ffeb13ad schema:affiliation https://www.grid.ac/institutes/grid.417929.0
56 schema:familyName Bhattacharjee
57 schema:givenName Jayanta K.
58 rdf:type schema:Person
59 N301fb1437f534ff2bce4d6257bb825a8 schema:name readcube_id
60 schema:value 432656ffd454982d13248d39807645c98a6868083187910a2c928572240c8ac7
61 rdf:type schema:PropertyValue
62 N44a974658c174db3ad231b1ff92a153c rdf:first N1280a269048544a5aea86351ffeb13ad
63 rdf:rest rdf:nil
64 N4b01d15ff91d408eb80202f5c3cce840 schema:name doi
65 schema:value 10.1007/s11071-019-04818-9
66 rdf:type schema:PropertyValue
67 N9e77ee3bcb9e4ba4acdc213db298f7ef rdf:first N098dc2e3d9834f19896ca0cd7ff7497e
68 rdf:rest N44a974658c174db3ad231b1ff92a153c
69 Nd136e8f73a1e4a399e69d6bcb4a14983 schema:name dimensions_id
70 schema:value pub.1112417360
71 rdf:type schema:PropertyValue
72 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
73 schema:name Physical Sciences
74 rdf:type schema:DefinedTerm
75 anzsrc-for:0202 schema:inDefinedTermSet anzsrc-for:
76 schema:name Atomic, Molecular, Nuclear, Particle and Plasma Physics
77 rdf:type schema:DefinedTerm
78 sg:journal.1040905 schema:issn 0924-090X
79 1573-269X
80 schema:name Nonlinear Dynamics
81 rdf:type schema:Periodical
82 sg:pub.10.1007/978-3-642-97465-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005909355
83 https://doi.org/10.1007/978-3-642-97465-6
84 rdf:type schema:CreativeWork
85 sg:pub.10.1007/bf00046308 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048910675
86 https://doi.org/10.1007/bf00046308
87 rdf:type schema:CreativeWork
88 sg:pub.10.1007/bf03322203 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001683259
89 https://doi.org/10.1007/bf03322203
90 rdf:type schema:CreativeWork
91 sg:pub.10.1007/s11071-005-4338-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1043061660
92 https://doi.org/10.1007/s11071-005-4338-y
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/s11071-006-9162-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037840117
95 https://doi.org/10.1007/s11071-006-9162-5
96 rdf:type schema:CreativeWork
97 sg:pub.10.1007/s11071-013-1002-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005869379
98 https://doi.org/10.1007/s11071-013-1002-9
99 rdf:type schema:CreativeWork
100 sg:pub.10.1007/s11071-014-1405-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044777652
101 https://doi.org/10.1007/s11071-014-1405-2
102 rdf:type schema:CreativeWork
103 sg:pub.10.1023/a:1023216817293 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008407340
104 https://doi.org/10.1023/a:1023216817293
105 rdf:type schema:CreativeWork
106 sg:pub.10.1023/a:1023293901305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026830757
107 https://doi.org/10.1023/a:1023293901305
108 rdf:type schema:CreativeWork
109 https://app.dimensions.ai/details/publication/pub.1005909355 schema:CreativeWork
110 https://doi.org/10.1016/j.jmaa.2010.10.035 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047991609
111 rdf:type schema:CreativeWork
112 https://doi.org/10.1016/j.physleta.2018.03.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101509784
113 rdf:type schema:CreativeWork
114 https://doi.org/10.1016/s0378-4371(97)00194-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003298963
115 rdf:type schema:CreativeWork
116 https://doi.org/10.1016/s0960-0779(01)00226-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019174955
117 rdf:type schema:CreativeWork
118 https://doi.org/10.1017/s0027763000008254 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052729749
119 rdf:type schema:CreativeWork
120 https://doi.org/10.1063/1.1664991 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057743061
121 rdf:type schema:CreativeWork
122 https://doi.org/10.1088/1751-8113/45/45/455305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027311596
123 rdf:type schema:CreativeWork
124 https://doi.org/10.1090/s0002-9939-1977-0454208-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029726916
125 rdf:type schema:CreativeWork
126 https://doi.org/10.1098/rspa.2001.0941 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041376931
127 rdf:type schema:CreativeWork
128 https://doi.org/10.1103/physrevlett.66.527 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060802795
129 rdf:type schema:CreativeWork
130 https://doi.org/10.1103/revmodphys.75.281 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060839572
131 rdf:type schema:CreativeWork
132 https://doi.org/10.1115/1.3125853 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062102234
133 rdf:type schema:CreativeWork
134 https://doi.org/10.1115/1.4039144 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100679851
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1142/s0129183116500145 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062905872
137 rdf:type schema:CreativeWork
138 https://www.grid.ac/institutes/grid.11835.3e schema:alternateName University of Sheffield
139 schema:name Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK
140 rdf:type schema:Organization
141 https://www.grid.ac/institutes/grid.417929.0 schema:alternateName Indian Association for the Cultivation of Science
142 schema:name Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Jadavpur, Kolkata, India
143 rdf:type schema:Organization
 




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


...