The He atom revisited Article Swipe
Subhadeep Datta
,
James M. Rejcek
,
J. L. Fry
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1703.08977
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1703.08977
In the Feynman-Kac[1] path integral approach the eigenvalues of a quantum system can be computed using Wiener measure which uses Brownian particle motion. In our previous work[2-3] on such systems we have observed that the Wiener process numerically converges slowly for dimensions greater than two because almost all trajectories will escape to infinity[4]. One can speed up this process by using a Generalized Feynman-Kac (GFK) method[5] in which the new measure associated with the trial function is stationary, so that the convergence rate becomes much faster. We thus achieve an example of Importance Sampling and in the present work we apply it to the Feynman-Kac(FK) path integrals for the ground and first few excited state energies for He to speed up the convergence rate. We calculate the path integrals using space averaging rather than the time averaging as done in the past. The best previous calculations from Variational computations report precisions of Hartrees, whereas in most cases our path integral results obtained for the ground and first excited states of He are lower than these results by about Hartrees or more.
Related Topics
Concepts
Path integral formulation
Feynman diagram
Measure (data warehouse)
Brownian motion
Eigenvalues and eigenvectors
Mathematics
Wiener process
Path (computing)
Excited state
Physics
Rate of convergence
Quantum mechanics
Work (physics)
Statistical physics
Mathematical analysis
Mathematical physics
Quantum
Computer science
Channel (broadcasting)
Computer network
Database
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1703.08977
- https://arxiv.org/pdf/1703.08977
- OA Status
- green
- References
- 2
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2598784207
All OpenAlex metadata
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https://openalex.org/W2598784207Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1703.08977Digital Object Identifier
- Title
-
The He atom revisitedWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2017Year of publication
- Publication date
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2017-03-27Full publication date if available
- Authors
-
Subhadeep Datta, James M. Rejcek, J. L. FryList of authors in order
- Landing page
-
https://arxiv.org/abs/1703.08977Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1703.08977Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1703.08977Direct OA link when available
- Concepts
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Path integral formulation, Feynman diagram, Measure (data warehouse), Brownian motion, Eigenvalues and eigenvectors, Mathematics, Wiener process, Path (computing), Excited state, Physics, Rate of convergence, Quantum mechanics, Work (physics), Statistical physics, Mathematical analysis, Mathematical physics, Quantum, Computer science, Channel (broadcasting), Computer network, Database, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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2Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.a | 9, 61 |
| abstract_inverted_index.He | 117, 170 |
| abstract_inverted_index.In | 0, 23 |
| abstract_inverted_index.We | 86, 124 |
| abstract_inverted_index.an | 89 |
| abstract_inverted_index.as | 137 |
| abstract_inverted_index.be | 13 |
| abstract_inverted_index.by | 59, 176 |
| abstract_inverted_index.in | 66, 95, 139, 154 |
| abstract_inverted_index.is | 76 |
| abstract_inverted_index.it | 101 |
| abstract_inverted_index.of | 8, 91, 151, 169 |
| abstract_inverted_index.on | 27 |
| abstract_inverted_index.or | 179 |
| abstract_inverted_index.so | 78 |
| abstract_inverted_index.to | 51, 102, 118 |
| abstract_inverted_index.up | 56, 120 |
| abstract_inverted_index.we | 30, 99 |
| abstract_inverted_index.One | 53 |
| abstract_inverted_index.The | 142 |
| abstract_inverted_index.all | 47 |
| abstract_inverted_index.and | 94, 110, 165 |
| abstract_inverted_index.are | 171 |
| abstract_inverted_index.can | 12, 54 |
| abstract_inverted_index.few | 112 |
| abstract_inverted_index.for | 40, 107, 116, 162 |
| abstract_inverted_index.new | 69 |
| abstract_inverted_index.our | 24, 157 |
| abstract_inverted_index.the | 1, 6, 34, 68, 73, 80, 96, 103, 108, 121, 126, 134, 140, 163 |
| abstract_inverted_index.two | 44 |
| abstract_inverted_index.best | 143 |
| abstract_inverted_index.done | 138 |
| abstract_inverted_index.from | 146 |
| abstract_inverted_index.have | 31 |
| abstract_inverted_index.most | 155 |
| abstract_inverted_index.much | 84 |
| abstract_inverted_index.path | 3, 105, 127, 158 |
| abstract_inverted_index.rate | 82 |
| abstract_inverted_index.such | 28 |
| abstract_inverted_index.than | 43, 133, 173 |
| abstract_inverted_index.that | 33, 79 |
| abstract_inverted_index.this | 57 |
| abstract_inverted_index.thus | 87 |
| abstract_inverted_index.time | 135 |
| abstract_inverted_index.uses | 19 |
| abstract_inverted_index.will | 49 |
| abstract_inverted_index.with | 72 |
| abstract_inverted_index.work | 98 |
| abstract_inverted_index.(GFK) | 64 |
| abstract_inverted_index.about | 177 |
| abstract_inverted_index.apply | 100 |
| abstract_inverted_index.cases | 156 |
| abstract_inverted_index.first | 111, 166 |
| abstract_inverted_index.lower | 172 |
| abstract_inverted_index.more. | 180 |
| abstract_inverted_index.past. | 141 |
| abstract_inverted_index.rate. | 123 |
| abstract_inverted_index.space | 130 |
| abstract_inverted_index.speed | 55, 119 |
| abstract_inverted_index.state | 114 |
| abstract_inverted_index.these | 174 |
| abstract_inverted_index.trial | 74 |
| abstract_inverted_index.using | 15, 60, 129 |
| abstract_inverted_index.which | 18, 67 |
| abstract_inverted_index.Wiener | 16, 35 |
| abstract_inverted_index.almost | 46 |
| abstract_inverted_index.escape | 50 |
| abstract_inverted_index.ground | 109, 164 |
| abstract_inverted_index.rather | 132 |
| abstract_inverted_index.report | 149 |
| abstract_inverted_index.slowly | 39 |
| abstract_inverted_index.states | 168 |
| abstract_inverted_index.system | 11 |
| abstract_inverted_index.achieve | 88 |
| abstract_inverted_index.because | 45 |
| abstract_inverted_index.becomes | 83 |
| abstract_inverted_index.example | 90 |
| abstract_inverted_index.excited | 113, 167 |
| abstract_inverted_index.faster. | 85 |
| abstract_inverted_index.greater | 42 |
| abstract_inverted_index.measure | 17, 70 |
| abstract_inverted_index.motion. | 22 |
| abstract_inverted_index.present | 97 |
| abstract_inverted_index.process | 36, 58 |
| abstract_inverted_index.quantum | 10 |
| abstract_inverted_index.results | 160, 175 |
| abstract_inverted_index.systems | 29 |
| abstract_inverted_index.whereas | 153 |
| abstract_inverted_index.Brownian | 20 |
| abstract_inverted_index.Hartrees | 178 |
| abstract_inverted_index.Sampling | 93 |
| abstract_inverted_index.approach | 5 |
| abstract_inverted_index.computed | 14 |
| abstract_inverted_index.energies | 115 |
| abstract_inverted_index.function | 75 |
| abstract_inverted_index.integral | 4, 159 |
| abstract_inverted_index.observed | 32 |
| abstract_inverted_index.obtained | 161 |
| abstract_inverted_index.particle | 21 |
| abstract_inverted_index.previous | 25, 144 |
| abstract_inverted_index.Hartrees, | 152 |
| abstract_inverted_index.averaging | 131, 136 |
| abstract_inverted_index.calculate | 125 |
| abstract_inverted_index.converges | 38 |
| abstract_inverted_index.integrals | 106, 128 |
| abstract_inverted_index.method[5] | 65 |
| abstract_inverted_index.work[2-3] | 26 |
| abstract_inverted_index.Importance | 92 |
| abstract_inverted_index.associated | 71 |
| abstract_inverted_index.dimensions | 41 |
| abstract_inverted_index.precisions | 150 |
| abstract_inverted_index.Feynman-Kac | 63 |
| abstract_inverted_index.Generalized | 62 |
| abstract_inverted_index.Variational | 147 |
| abstract_inverted_index.convergence | 81, 122 |
| abstract_inverted_index.eigenvalues | 7 |
| abstract_inverted_index.numerically | 37 |
| abstract_inverted_index.stationary, | 77 |
| abstract_inverted_index.calculations | 145 |
| abstract_inverted_index.computations | 148 |
| abstract_inverted_index.infinity[4]. | 52 |
| abstract_inverted_index.trajectories | 48 |
| abstract_inverted_index.Feynman-Kac[1] | 2 |
| abstract_inverted_index.Feynman-Kac(FK) | 104 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |