Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics Article Swipe
Gerard McCaul
,
Denys I. Bondar
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2207.09515
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2207.09515
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time coordinate transformation. We demonstrate that an equivalent transformation can be performed for classical systems in the context of Koopman von-Neumann (KvN) dynamics. We further extend this mapping to dissipative evolutions in both the quantum and classical cases, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics. The derived classical procedure presents a number of opportunities to import squeezing dependent quantum procedures (such as Hamiltonian amplification) into the classical regime.
Related Topics
Concepts
Harmonic oscillator
Unitary transformation
Quantum
Dissipative system
Unitary state
Hamiltonian (control theory)
Classical mechanics
Quantum dynamics
Transformation (genetics)
Von Neumann architecture
Quantum harmonic oscillator
Physics
Context (archaeology)
Quantum system
Mathematics
Quantum mechanics
Pure mathematics
Biology
Paleontology
Gene
Political science
Law
Mathematical optimization
Chemistry
Biochemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2207.09515
- https://arxiv.org/pdf/2207.09515
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4286588436
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4286588436Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2207.09515Digital Object Identifier
- Title
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Free to Harmonic Unitary Transformations in Quantum and Koopman DynamicsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-07-19Full publication date if available
- Authors
-
Gerard McCaul, Denys I. BondarList of authors in order
- Landing page
-
https://arxiv.org/abs/2207.09515Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2207.09515Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2207.09515Direct OA link when available
- Concepts
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Harmonic oscillator, Unitary transformation, Quantum, Dissipative system, Unitary state, Hamiltonian (control theory), Classical mechanics, Quantum dynamics, Transformation (genetics), Von Neumann architecture, Quantum harmonic oscillator, Physics, Context (archaeology), Quantum system, Mathematics, Quantum mechanics, Pure mathematics, Biology, Paleontology, Gene, Political science, Law, Mathematical optimization, Chemistry, BiochemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2023: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.mapping | 65, 80 |
| abstract_inverted_index.quantum | 15, 20, 72, 108 |
| abstract_inverted_index.regime. | 117 |
| abstract_inverted_index.scaling | 85 |
| abstract_inverted_index.systems | 52 |
| abstract_inverted_index.unitary | 33 |
| abstract_inverted_index.followed | 35 |
| abstract_inverted_index.harmonic | 21 |
| abstract_inverted_index.particle | 17 |
| abstract_inverted_index.presents | 99 |
| abstract_inverted_index.classical | 51, 74, 97, 116 |
| abstract_inverted_index.dependent | 107 |
| abstract_inverted_index.dynamics. | 60, 94 |
| abstract_inverted_index.identical | 83 |
| abstract_inverted_index.operation | 34 |
| abstract_inverted_index.performed | 49 |
| abstract_inverted_index.procedure | 98 |
| abstract_inverted_index.squeezing | 106 |
| abstract_inverted_index.coordinate | 9, 39 |
| abstract_inverted_index.equivalent | 45 |
| abstract_inverted_index.evolutions | 68 |
| abstract_inverted_index.parameters | 89 |
| abstract_inverted_index.procedures | 109 |
| abstract_inverted_index.Hamiltonian | 112 |
| abstract_inverted_index.demonstrate | 42 |
| abstract_inverted_index.dissipation | 88 |
| abstract_inverted_index.dissipative | 67 |
| abstract_inverted_index.oscillator. | 22 |
| abstract_inverted_index.von-Neumann | 58 |
| abstract_inverted_index.opportunities | 103 |
| abstract_inverted_index.reformulating | 29 |
| abstract_inverted_index.amplification) | 113 |
| abstract_inverted_index.time-dependent | 84 |
| abstract_inverted_index.transformation | 10, 46 |
| abstract_inverted_index.transformation. | 40 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.53516699 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |