Quantum dynamics from fixed points and their stability View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-09-04

AUTHORS

Rohit Chawla, Jayanta K. Bhattacharjee

ABSTRACT

We approach quantum dynamics in one spatial dimension from a systematic study of moments starting from the dynamics of the mean position. This is complementary to the approach of Brizuela whose starting point was generalized recursion relations between moments. The infinite set of coupled equations is truncated which allows us to use the techniques used in the study of dynamical systems. In particular we predict for what initial variance the purely quartic oscillator will time develop with minimal change in the shape of the initial packet and what the frequency of oscillation of the mean position will be. We show how quantum fluctuations will cause a particle to escape from the well of a volcano potential and how they will cause an oscillation between the two wells of a double well potential. Further, we consider an oscillatory external field in addition to the double well potential and work near the separatrix where the classical system is known to be chaotic. We show how the quantum fluctuations suppresses the chaotic behaviour after a time interval inversely proportional to the strength of the quantum fluctuations. Graphical abstract More... »

PAGES

196

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1140/epjb/e2019-100340-6

DOI

http://dx.doi.org/10.1140/epjb/e2019-100340-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1120774587


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Jadavpur, Kolkata, India", 
          "id": "http://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": "Chawla", 
        "givenName": "Rohit", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Jadavpur, Kolkata, India", 
          "id": "http://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.", 
        "id": "sg:person.015365735162.55", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015365735162.55"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01329203", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006364072", 
          "https://doi.org/10.1007/bf01329203"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4614-7116-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006634009", 
          "https://doi.org/10.1007/978-1-4614-7116-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4757-0576-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042261003", 
          "https://doi.org/10.1007/978-1-4757-0576-8"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-09-04", 
    "datePublishedReg": "2019-09-04", 
    "description": "Abstract\nWe approach quantum dynamics in one spatial dimension from a systematic study of moments starting from the dynamics of the mean position. This is complementary to the approach of Brizuela whose starting point was generalized recursion relations between moments. The infinite set of coupled equations is truncated which allows us to use the techniques used in the study of dynamical systems. In particular we predict for what initial variance the purely quartic oscillator will time develop with minimal change in the shape of the initial packet and what the frequency of oscillation of the mean position will be. We show how quantum fluctuations will cause a particle to escape from the well of a volcano potential and how they will cause an oscillation between the two wells of a double well potential. Further, we consider an oscillatory external field in addition to the double well potential and work near the separatrix where the classical system is known to be chaotic. We show how the quantum fluctuations suppresses the chaotic behaviour after a time interval inversely proportional to the strength of the quantum fluctuations.\nGraphical abstract", 
    "genre": "article", 
    "id": "sg:pub.10.1140/epjb/e2019-100340-6", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1129956", 
        "issn": [
          "1155-4304", 
          "1286-4862"
        ], 
        "name": "The European Physical Journal B", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "9", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "92"
      }
    ], 
    "keywords": [
      "double-well potential", 
      "quantum dynamics", 
      "quantum fluctuations", 
      "well potential", 
      "oscillatory external field", 
      "dynamical systems", 
      "classical systems", 
      "infinite set", 
      "quartic oscillator", 
      "chaotic behavior", 
      "volcano potential", 
      "recursion relations", 
      "external field", 
      "mean position", 
      "frequency of oscillation", 
      "spatial dimensions", 
      "initial variance", 
      "initial packet", 
      "dynamics", 
      "oscillations", 
      "moment", 
      "equations", 
      "separatrix", 
      "fluctuations", 
      "systematic study", 
      "quantum", 
      "starting point", 
      "oscillator", 
      "time interval", 
      "point", 
      "system", 
      "field", 
      "packets", 
      "set", 
      "dimensions", 
      "wells", 
      "shape", 
      "approach", 
      "stability", 
      "position", 
      "variance", 
      "technique", 
      "particles", 
      "behavior", 
      "work", 
      "frequency", 
      "potential", 
      "intervals", 
      "relation", 
      "time", 
      "strength", 
      "addition", 
      "study", 
      "minimal changes", 
      "changes", 
      "approach of Brizuela", 
      "Brizuela", 
      "Graphical abstract Quantum dynamics", 
      "abstract Quantum dynamics"
    ], 
    "name": "Quantum dynamics from fixed points and their stability", 
    "pagination": "196", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1120774587"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1140/epjb/e2019-100340-6"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1140/epjb/e2019-100340-6", 
      "https://app.dimensions.ai/details/publication/pub.1120774587"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:51", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_802.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1140/epjb/e2019-100340-6"
  }
]
 

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.10.1140/epjb/e2019-100340-6'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1140/epjb/e2019-100340-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1140/epjb/e2019-100340-6'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1140/epjb/e2019-100340-6'


 

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

135 TRIPLES      22 PREDICATES      87 URIs      76 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1140/epjb/e2019-100340-6 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N12ed935390de4d298c294a26ddc00c0f
4 schema:citation sg:pub.10.1007/978-1-4614-7116-5
5 sg:pub.10.1007/978-1-4757-0576-8
6 sg:pub.10.1007/bf01329203
7 schema:datePublished 2019-09-04
8 schema:datePublishedReg 2019-09-04
9 schema:description Abstract We approach quantum dynamics in one spatial dimension from a systematic study of moments starting from the dynamics of the mean position. This is complementary to the approach of Brizuela whose starting point was generalized recursion relations between moments. The infinite set of coupled equations is truncated which allows us to use the techniques used in the study of dynamical systems. In particular we predict for what initial variance the purely quartic oscillator will time develop with minimal change in the shape of the initial packet and what the frequency of oscillation of the mean position will be. We show how quantum fluctuations will cause a particle to escape from the well of a volcano potential and how they will cause an oscillation between the two wells of a double well potential. Further, we consider an oscillatory external field in addition to the double well potential and work near the separatrix where the classical system is known to be chaotic. We show how the quantum fluctuations suppresses the chaotic behaviour after a time interval inversely proportional to the strength of the quantum fluctuations. Graphical abstract
10 schema:genre article
11 schema:inLanguage en
12 schema:isAccessibleForFree true
13 schema:isPartOf N783e2eb4e5114746be9ddcc92a96481c
14 N97e3cfde4136412abfd55657dcb1d413
15 sg:journal.1129956
16 schema:keywords Brizuela
17 Graphical abstract Quantum dynamics
18 abstract Quantum dynamics
19 addition
20 approach
21 approach of Brizuela
22 behavior
23 changes
24 chaotic behavior
25 classical systems
26 dimensions
27 double-well potential
28 dynamical systems
29 dynamics
30 equations
31 external field
32 field
33 fluctuations
34 frequency
35 frequency of oscillation
36 infinite set
37 initial packet
38 initial variance
39 intervals
40 mean position
41 minimal changes
42 moment
43 oscillations
44 oscillator
45 oscillatory external field
46 packets
47 particles
48 point
49 position
50 potential
51 quantum
52 quantum dynamics
53 quantum fluctuations
54 quartic oscillator
55 recursion relations
56 relation
57 separatrix
58 set
59 shape
60 spatial dimensions
61 stability
62 starting point
63 strength
64 study
65 system
66 systematic study
67 technique
68 time
69 time interval
70 variance
71 volcano potential
72 well potential
73 wells
74 work
75 schema:name Quantum dynamics from fixed points and their stability
76 schema:pagination 196
77 schema:productId Nd9de2d40620f4ddcabf7f0fafe0faba7
78 Ne56f849bff7349d498c9b3528cf8e1e0
79 schema:sameAs https://app.dimensions.ai/details/publication/pub.1120774587
80 https://doi.org/10.1140/epjb/e2019-100340-6
81 schema:sdDatePublished 2022-01-01T18:51
82 schema:sdLicense https://scigraph.springernature.com/explorer/license/
83 schema:sdPublisher N4a9725958baa4b089221c961d551cfda
84 schema:url https://doi.org/10.1140/epjb/e2019-100340-6
85 sgo:license sg:explorer/license/
86 sgo:sdDataset articles
87 rdf:type schema:ScholarlyArticle
88 N12ed935390de4d298c294a26ddc00c0f rdf:first Nb7fc9d10a39e4fad861f9c5ad3cb7f56
89 rdf:rest N4c604e86e6cb4624bf619465ca934b08
90 N4a9725958baa4b089221c961d551cfda schema:name Springer Nature - SN SciGraph project
91 rdf:type schema:Organization
92 N4c604e86e6cb4624bf619465ca934b08 rdf:first sg:person.015365735162.55
93 rdf:rest rdf:nil
94 N783e2eb4e5114746be9ddcc92a96481c schema:volumeNumber 92
95 rdf:type schema:PublicationVolume
96 N97e3cfde4136412abfd55657dcb1d413 schema:issueNumber 9
97 rdf:type schema:PublicationIssue
98 Nb7fc9d10a39e4fad861f9c5ad3cb7f56 schema:affiliation grid-institutes:grid.417929.0
99 schema:familyName Chawla
100 schema:givenName Rohit
101 rdf:type schema:Person
102 Nd9de2d40620f4ddcabf7f0fafe0faba7 schema:name doi
103 schema:value 10.1140/epjb/e2019-100340-6
104 rdf:type schema:PropertyValue
105 Ne56f849bff7349d498c9b3528cf8e1e0 schema:name dimensions_id
106 schema:value pub.1120774587
107 rdf:type schema:PropertyValue
108 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
109 schema:name Mathematical Sciences
110 rdf:type schema:DefinedTerm
111 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
112 schema:name Pure Mathematics
113 rdf:type schema:DefinedTerm
114 sg:journal.1129956 schema:issn 1155-4304
115 1286-4862
116 schema:name The European Physical Journal B
117 schema:publisher Springer Nature
118 rdf:type schema:Periodical
119 sg:person.015365735162.55 schema:affiliation grid-institutes:grid.417929.0
120 schema:familyName Bhattacharjee
121 schema:givenName Jayanta K.
122 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015365735162.55
123 rdf:type schema:Person
124 sg:pub.10.1007/978-1-4614-7116-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006634009
125 https://doi.org/10.1007/978-1-4614-7116-5
126 rdf:type schema:CreativeWork
127 sg:pub.10.1007/978-1-4757-0576-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042261003
128 https://doi.org/10.1007/978-1-4757-0576-8
129 rdf:type schema:CreativeWork
130 sg:pub.10.1007/bf01329203 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006364072
131 https://doi.org/10.1007/bf01329203
132 rdf:type schema:CreativeWork
133 grid-institutes:grid.417929.0 schema:alternateName Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Jadavpur, Kolkata, India
134 schema:name Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Jadavpur, Kolkata, India
135 rdf:type schema:Organization
 




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


...