Adiabatic control of quantum systems Article Swipe
The main purpose of the thesis is to study the links between the singularities of the spectrum of a controlled quantum Hamiltonian and the controllability issues of the associated Schrodinger equation.The principal issue that is developed is how to control a parameter-dependent family of quantum systems with a common control input. This problem of ensemble controllability is linked to the design of a robust control strategy when a parameter (a resonance frequency or a control field inhomogeneity for instance) is unknown, and is an important issue for experimentalists.Thanks to the study one-parametric families of Hamiltonians and their generic singularities, we give an explicit control strategy for the ensemble controllability problem when geometric conditions on the spectrum of the Hamiltonian are satisfied. The result is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian. The proposed technique works for systems evolving both in finite-dimensional and infinite-dimensional Hilbert spaces. Then we study the problem of ensemble controllability under less restrictive hypotheses on the spectrum, namely the presence of non-conical singularities. Under generic conditions such non-conical singularities are not present for single systems, but appear for one-parametric families of systems.For the study of a single system, we focus on a class of curves in the space of controls, called the non-mixing curves (defined in cite{Bos}), that can optimize the adiabatic dynamics near conical and non-conical intersections. They are linked to the geometry of the eigenspaces of the controlled Hamiltonian and the adiabatic approximation holds with higher precision along them.We propose to study the compatibility of the adiabatic approximation with the rotating wave approximation. Such approximations are usually done in cascade by physicists. My work shows that this is justified for finite dimensional quantum systems only under certain conditions on the time scales. We also study ensemble control issues in this case.
Related Topics
Concepts
Controllability
Hamiltonian (control theory)
Gravitational singularity
Adiabatic process
Mathematics
Hilbert space
Eigenvalues and eigenvectors
Parametric statistics
Adiabatic quantum computation
Quantum system
Quantum
Hamiltonian system
Conical intersection
Conical surface
Mathematical analysis
Quantum mechanics
Physics
Quantum computer
Geometry
Applied mathematics
Mathematical optimization
Statistics
Metadata
- Type
- preprint
- Language
- fr
- Landing Page
- https://tel.archives-ouvertes.fr/tel-02434725
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2999400414
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2999400414Canonical identifier for this work in OpenAlex
- Title
-
Adiabatic control of quantum systemsWork title
- Type
-
preprintOpenAlex work type
- Language
-
frPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-09-27Full publication date if available
- Authors
-
Nicolas AugierList of authors in order
- Landing page
-
https://tel.archives-ouvertes.fr/tel-02434725Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://tel.archives-ouvertes.fr/tel-02434725Direct OA link when available
- Concepts
-
Controllability, Hamiltonian (control theory), Gravitational singularity, Adiabatic process, Mathematics, Hilbert space, Eigenvalues and eigenvectors, Parametric statistics, Adiabatic quantum computation, Quantum system, Quantum, Hamiltonian system, Conical intersection, Conical surface, Mathematical analysis, Quantum mechanics, Physics, Quantum computer, Geometry, Applied mathematics, Mathematical optimization, StatisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2999400414 |
|---|---|
| doi | |
| ids.mag | 2999400414 |
| ids.openalex | https://openalex.org/W2999400414 |
| fwci | 0.0 |
| type | preprint |
| title | Adiabatic control of quantum systems |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11416 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9398999810218811 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2612 |
| topics[0].subfield.display_name | Numerical Analysis |
| topics[0].display_name | Numerical methods for differential equations |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C48209547 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7846753597259521 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1331104 |
| concepts[0].display_name | Controllability |
| concepts[1].id | https://openalex.org/C130787639 |
| concepts[1].level | 2 |
| concepts[1].score | 0.7470773458480835 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q5645293 |
| concepts[1].display_name | Hamiltonian (control theory) |
| concepts[2].id | https://openalex.org/C12843 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6785640716552734 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q201721 |
| concepts[2].display_name | Gravitational singularity |
| concepts[3].id | https://openalex.org/C109663097 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5537914037704468 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q182453 |
| concepts[3].display_name | Adiabatic process |
| concepts[4].id | https://openalex.org/C33923547 |
| concepts[4].level | 0 |
| concepts[4].score | 0.5494741797447205 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[4].display_name | Mathematics |
| concepts[5].id | https://openalex.org/C62799726 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5119510889053345 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q190056 |
| concepts[5].display_name | Hilbert space |
| concepts[6].id | https://openalex.org/C158693339 |
| concepts[6].level | 2 |
| concepts[6].score | 0.5053096413612366 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q190524 |
| concepts[6].display_name | Eigenvalues and eigenvectors |
| concepts[7].id | https://openalex.org/C117251300 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4960978925228119 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1849855 |
| concepts[7].display_name | Parametric statistics |
| concepts[8].id | https://openalex.org/C192353077 |
| concepts[8].level | 4 |
| concepts[8].score | 0.4785274267196655 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q4682635 |
| concepts[8].display_name | Adiabatic quantum computation |
| concepts[9].id | https://openalex.org/C2778926657 |
| concepts[9].level | 3 |
| concepts[9].score | 0.4689217209815979 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[9].display_name | Quantum system |
| concepts[10].id | https://openalex.org/C84114770 |
| concepts[10].level | 2 |
| concepts[10].score | 0.45920661091804504 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q46344 |
| concepts[10].display_name | Quantum |
| concepts[11].id | https://openalex.org/C121770821 |
| concepts[11].level | 2 |
| concepts[11].score | 0.4405825734138489 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q2072471 |
| concepts[11].display_name | Hamiltonian system |
| concepts[12].id | https://openalex.org/C24857813 |
| concepts[12].level | 3 |
| concepts[12].score | 0.43265625834465027 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q3153596 |
| concepts[12].display_name | Conical intersection |
| concepts[13].id | https://openalex.org/C124961601 |
| concepts[13].level | 2 |
| concepts[13].score | 0.4093865752220154 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q2518149 |
| concepts[13].display_name | Conical surface |
| concepts[14].id | https://openalex.org/C134306372 |
| concepts[14].level | 1 |
| concepts[14].score | 0.31007036566734314 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[14].display_name | Mathematical analysis |
| concepts[15].id | https://openalex.org/C62520636 |
| concepts[15].level | 1 |
| concepts[15].score | 0.3095656633377075 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[15].display_name | Quantum mechanics |
| concepts[16].id | https://openalex.org/C121332964 |
| concepts[16].level | 0 |
| concepts[16].score | 0.30444806814193726 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[16].display_name | Physics |
| concepts[17].id | https://openalex.org/C58053490 |
| concepts[17].level | 3 |
| concepts[17].score | 0.23862382769584656 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q176555 |
| concepts[17].display_name | Quantum computer |
| concepts[18].id | https://openalex.org/C2524010 |
| concepts[18].level | 1 |
| concepts[18].score | 0.23061150312423706 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[18].display_name | Geometry |
| concepts[19].id | https://openalex.org/C28826006 |
| concepts[19].level | 1 |
| concepts[19].score | 0.20628300309181213 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[19].display_name | Applied mathematics |
| concepts[20].id | https://openalex.org/C126255220 |
| concepts[20].level | 1 |
| concepts[20].score | 0.15857362747192383 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[20].display_name | Mathematical optimization |
| concepts[21].id | https://openalex.org/C105795698 |
| concepts[21].level | 1 |
| concepts[21].score | 0.0 |
| concepts[21].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[21].display_name | Statistics |
| keywords[0].id | https://openalex.org/keywords/controllability |
| keywords[0].score | 0.7846753597259521 |
| keywords[0].display_name | Controllability |
| keywords[1].id | https://openalex.org/keywords/hamiltonian |
| keywords[1].score | 0.7470773458480835 |
| keywords[1].display_name | Hamiltonian (control theory) |
| keywords[2].id | https://openalex.org/keywords/gravitational-singularity |
| keywords[2].score | 0.6785640716552734 |
| keywords[2].display_name | Gravitational singularity |
| keywords[3].id | https://openalex.org/keywords/adiabatic-process |
| keywords[3].score | 0.5537914037704468 |
| keywords[3].display_name | Adiabatic process |
| keywords[4].id | https://openalex.org/keywords/mathematics |
| keywords[4].score | 0.5494741797447205 |
| keywords[4].display_name | Mathematics |
| keywords[5].id | https://openalex.org/keywords/hilbert-space |
| keywords[5].score | 0.5119510889053345 |
| keywords[5].display_name | Hilbert space |
| keywords[6].id | https://openalex.org/keywords/eigenvalues-and-eigenvectors |
| keywords[6].score | 0.5053096413612366 |
| keywords[6].display_name | Eigenvalues and eigenvectors |
| keywords[7].id | https://openalex.org/keywords/parametric-statistics |
| keywords[7].score | 0.4960978925228119 |
| keywords[7].display_name | Parametric statistics |
| keywords[8].id | https://openalex.org/keywords/adiabatic-quantum-computation |
| keywords[8].score | 0.4785274267196655 |
| keywords[8].display_name | Adiabatic quantum computation |
| keywords[9].id | https://openalex.org/keywords/quantum-system |
| keywords[9].score | 0.4689217209815979 |
| keywords[9].display_name | Quantum system |
| keywords[10].id | https://openalex.org/keywords/quantum |
| keywords[10].score | 0.45920661091804504 |
| keywords[10].display_name | Quantum |
| keywords[11].id | https://openalex.org/keywords/hamiltonian-system |
| keywords[11].score | 0.4405825734138489 |
| keywords[11].display_name | Hamiltonian system |
| keywords[12].id | https://openalex.org/keywords/conical-intersection |
| keywords[12].score | 0.43265625834465027 |
| keywords[12].display_name | Conical intersection |
| keywords[13].id | https://openalex.org/keywords/conical-surface |
| keywords[13].score | 0.4093865752220154 |
| keywords[13].display_name | Conical surface |
| keywords[14].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[14].score | 0.31007036566734314 |
| keywords[14].display_name | Mathematical analysis |
| keywords[15].id | https://openalex.org/keywords/quantum-mechanics |
| keywords[15].score | 0.3095656633377075 |
| keywords[15].display_name | Quantum mechanics |
| keywords[16].id | https://openalex.org/keywords/physics |
| keywords[16].score | 0.30444806814193726 |
| keywords[16].display_name | Physics |
| keywords[17].id | https://openalex.org/keywords/quantum-computer |
| keywords[17].score | 0.23862382769584656 |
| keywords[17].display_name | Quantum computer |
| keywords[18].id | https://openalex.org/keywords/geometry |
| keywords[18].score | 0.23061150312423706 |
| keywords[18].display_name | Geometry |
| keywords[19].id | https://openalex.org/keywords/applied-mathematics |
| keywords[19].score | 0.20628300309181213 |
| keywords[19].display_name | Applied mathematics |
| keywords[20].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[20].score | 0.15857362747192383 |
| keywords[20].display_name | Mathematical optimization |
| language | fr |
| locations[0].id | mag:2999400414 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306402512 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| locations[0].source.host_organization | https://openalex.org/I1294671590 |
| locations[0].source.host_organization_name | Centre National de la Recherche Scientifique |
| locations[0].source.host_organization_lineage | https://openalex.org/I1294671590 |
| locations[0].license | other-oa |
| locations[0].pdf_url | |
| locations[0].version | submittedVersion |
| locations[0].raw_type | |
| locations[0].license_id | https://openalex.org/licenses/other-oa |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| locations[0].landing_page_url | https://tel.archives-ouvertes.fr/tel-02434725 |
| authorships[0].author.id | https://openalex.org/A5000540514 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-9396-5439 |
| authorships[0].author.display_name | Nicolas Augier |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Augier, Nicolas |
| authorships[0].is_corresponding | True |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://tel.archives-ouvertes.fr/tel-02434725 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Adiabatic control of quantum systems |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-10-10T17:16:08.811792 |
| primary_topic.id | https://openalex.org/T11416 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9398999810218811 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2612 |
| primary_topic.subfield.display_name | Numerical Analysis |
| primary_topic.display_name | Numerical methods for differential equations |
| related_works | https://openalex.org/W1975933568, https://openalex.org/W2161111492, https://openalex.org/W1966014094, https://openalex.org/W4392385300, https://openalex.org/W2085556107, https://openalex.org/W1506448353, https://openalex.org/W2058068274, https://openalex.org/W2317426883, https://openalex.org/W2068030512, https://openalex.org/W2033554775 |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | mag:2999400414 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306402512 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| best_oa_location.source.host_organization | https://openalex.org/I1294671590 |
| best_oa_location.source.host_organization_name | Centre National de la Recherche Scientifique |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I1294671590 |
| best_oa_location.license | other-oa |
| best_oa_location.pdf_url | |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | |
| best_oa_location.license_id | https://openalex.org/licenses/other-oa |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| best_oa_location.landing_page_url | https://tel.archives-ouvertes.fr/tel-02434725 |
| primary_location.id | mag:2999400414 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306402512 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| primary_location.source.host_organization | https://openalex.org/I1294671590 |
| primary_location.source.host_organization_name | Centre National de la Recherche Scientifique |
| primary_location.source.host_organization_lineage | https://openalex.org/I1294671590 |
| primary_location.license | other-oa |
| primary_location.pdf_url | |
| primary_location.version | submittedVersion |
| primary_location.raw_type | |
| primary_location.license_id | https://openalex.org/licenses/other-oa |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| primary_location.landing_page_url | https://tel.archives-ouvertes.fr/tel-02434725 |
| publication_date | 2019-09-27 |
| publication_year | 2019 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 18, 40, 47, 62, 67, 73, 200, 206 |
| abstract_inverted_index.(a | 69 |
| abstract_inverted_index.My | 279 |
| abstract_inverted_index.We | 299 |
| abstract_inverted_index.an | 83, 101 |
| abstract_inverted_index.by | 277 |
| abstract_inverted_index.in | 151, 210, 220, 275, 305 |
| abstract_inverted_index.is | 6, 34, 36, 56, 79, 82, 123, 284 |
| abstract_inverted_index.of | 3, 14, 17, 26, 43, 53, 61, 93, 116, 133, 135, 139, 162, 175, 195, 199, 208, 213, 239, 242, 261 |
| abstract_inverted_index.on | 113, 125, 130, 169, 205, 295 |
| abstract_inverted_index.or | 72 |
| abstract_inverted_index.to | 7, 38, 58, 88, 236, 257 |
| abstract_inverted_index.we | 99, 158, 203 |
| abstract_inverted_index.The | 0, 121, 143 |
| abstract_inverted_index.and | 22, 81, 95, 129, 153, 230, 246 |
| abstract_inverted_index.are | 119, 184, 234, 272 |
| abstract_inverted_index.but | 190 |
| abstract_inverted_index.can | 223 |
| abstract_inverted_index.for | 77, 86, 105, 147, 187, 192, 286 |
| abstract_inverted_index.how | 37 |
| abstract_inverted_index.not | 185 |
| abstract_inverted_index.the | 4, 9, 12, 15, 23, 27, 59, 89, 106, 114, 117, 131, 140, 160, 170, 173, 197, 211, 216, 225, 237, 240, 243, 247, 259, 262, 266, 296 |
| abstract_inverted_index.Such | 270 |
| abstract_inverted_index.Then | 157 |
| abstract_inverted_index.They | 233 |
| abstract_inverted_index.This | 51 |
| abstract_inverted_index.also | 300 |
| abstract_inverted_index.both | 150 |
| abstract_inverted_index.done | 274 |
| abstract_inverted_index.give | 100 |
| abstract_inverted_index.less | 166 |
| abstract_inverted_index.main | 1 |
| abstract_inverted_index.near | 228 |
| abstract_inverted_index.only | 291 |
| abstract_inverted_index.such | 181 |
| abstract_inverted_index.that | 33, 222, 282 |
| abstract_inverted_index.this | 283, 306 |
| abstract_inverted_index.time | 297 |
| abstract_inverted_index.wave | 268 |
| abstract_inverted_index.when | 66, 110 |
| abstract_inverted_index.with | 46, 251, 265 |
| abstract_inverted_index.work | 280 |
| abstract_inverted_index.Under | 178 |
| abstract_inverted_index.along | 254 |
| abstract_inverted_index.based | 124 |
| abstract_inverted_index.case. | 307 |
| abstract_inverted_index.class | 207 |
| abstract_inverted_index.field | 75 |
| abstract_inverted_index.focus | 204 |
| abstract_inverted_index.holds | 250 |
| abstract_inverted_index.issue | 32, 85 |
| abstract_inverted_index.links | 10 |
| abstract_inverted_index.shows | 281 |
| abstract_inverted_index.space | 212 |
| abstract_inverted_index.study | 8, 90, 159, 198, 258, 301 |
| abstract_inverted_index.their | 96 |
| abstract_inverted_index.under | 165, 292 |
| abstract_inverted_index.works | 146 |
| abstract_inverted_index.appear | 191 |
| abstract_inverted_index.called | 215 |
| abstract_inverted_index.common | 48 |
| abstract_inverted_index.curves | 134, 209, 218 |
| abstract_inverted_index.design | 60 |
| abstract_inverted_index.family | 42 |
| abstract_inverted_index.finite | 287 |
| abstract_inverted_index.higher | 252 |
| abstract_inverted_index.input. | 50 |
| abstract_inverted_index.issues | 25, 304 |
| abstract_inverted_index.linked | 57, 235 |
| abstract_inverted_index.namely | 172 |
| abstract_inverted_index.result | 122 |
| abstract_inverted_index.robust | 63 |
| abstract_inverted_index.single | 188, 201 |
| abstract_inverted_index.theory | 128 |
| abstract_inverted_index.thesis | 5 |
| abstract_inverted_index.Hilbert | 155 |
| abstract_inverted_index.between | 11 |
| abstract_inverted_index.cascade | 276 |
| abstract_inverted_index.certain | 293 |
| abstract_inverted_index.conical | 136, 229 |
| abstract_inverted_index.control | 39, 49, 64, 74, 103, 303 |
| abstract_inverted_index.generic | 97, 179 |
| abstract_inverted_index.present | 186 |
| abstract_inverted_index.problem | 52, 109, 161 |
| abstract_inverted_index.propose | 256 |
| abstract_inverted_index.purpose | 2 |
| abstract_inverted_index.quantum | 20, 44, 289 |
| abstract_inverted_index.scales. | 298 |
| abstract_inverted_index.spaces. | 156 |
| abstract_inverted_index.system, | 202 |
| abstract_inverted_index.systems | 45, 148, 290 |
| abstract_inverted_index.them.We | 255 |
| abstract_inverted_index.usually | 273 |
| abstract_inverted_index.(defined | 219 |
| abstract_inverted_index.dynamics | 227 |
| abstract_inverted_index.ensemble | 54, 107, 163, 302 |
| abstract_inverted_index.evolving | 149 |
| abstract_inverted_index.explicit | 102 |
| abstract_inverted_index.families | 92, 194 |
| abstract_inverted_index.geometry | 238 |
| abstract_inverted_index.optimize | 224 |
| abstract_inverted_index.presence | 132, 174 |
| abstract_inverted_index.proposed | 144 |
| abstract_inverted_index.rotating | 267 |
| abstract_inverted_index.spectrum | 16, 115 |
| abstract_inverted_index.strategy | 65, 104 |
| abstract_inverted_index.systems, | 189 |
| abstract_inverted_index.unknown, | 80 |
| abstract_inverted_index.adiabatic | 126, 226, 248, 263 |
| abstract_inverted_index.controls, | 214 |
| abstract_inverted_index.developed | 35 |
| abstract_inverted_index.frequency | 71 |
| abstract_inverted_index.geometric | 111 |
| abstract_inverted_index.important | 84 |
| abstract_inverted_index.instance) | 78 |
| abstract_inverted_index.justified | 285 |
| abstract_inverted_index.parameter | 68 |
| abstract_inverted_index.precision | 253 |
| abstract_inverted_index.principal | 31 |
| abstract_inverted_index.resonance | 70 |
| abstract_inverted_index.spectrum, | 171 |
| abstract_inverted_index.technique | 145 |
| abstract_inverted_index.associated | 28 |
| abstract_inverted_index.conditions | 112, 180, 294 |
| abstract_inverted_index.controlled | 19, 141, 244 |
| abstract_inverted_index.eigenvalue | 137 |
| abstract_inverted_index.hypotheses | 168 |
| abstract_inverted_index.non-mixing | 217 |
| abstract_inverted_index.satisfied. | 120 |
| abstract_inverted_index.Hamiltonian | 21, 118, 245 |
| abstract_inverted_index.Schrodinger | 29 |
| abstract_inverted_index.cite{Bos}), | 221 |
| abstract_inverted_index.dimensional | 288 |
| abstract_inverted_index.eigenspaces | 241 |
| abstract_inverted_index.non-conical | 176, 182, 231 |
| abstract_inverted_index.physicists. | 278 |
| abstract_inverted_index.restrictive | 167 |
| abstract_inverted_index.systems.For | 196 |
| abstract_inverted_index.Hamiltonian. | 142 |
| abstract_inverted_index.Hamiltonians | 94 |
| abstract_inverted_index.equation.The | 30 |
| abstract_inverted_index.approximation | 127, 249, 264 |
| abstract_inverted_index.compatibility | 260 |
| abstract_inverted_index.inhomogeneity | 76 |
| abstract_inverted_index.intersections | 138 |
| abstract_inverted_index.singularities | 13, 183 |
| abstract_inverted_index.approximation. | 269 |
| abstract_inverted_index.approximations | 271 |
| abstract_inverted_index.intersections. | 232 |
| abstract_inverted_index.one-parametric | 91, 193 |
| abstract_inverted_index.singularities, | 98 |
| abstract_inverted_index.singularities. | 177 |
| abstract_inverted_index.controllability | 24, 55, 108, 164 |
| abstract_inverted_index.finite-dimensional | 152 |
| abstract_inverted_index.parameter-dependent | 41 |
| abstract_inverted_index.infinite-dimensional | 154 |
| abstract_inverted_index.experimentalists.Thanks | 87 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5000540514 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |