FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3103520000> ?p ?o ?g. }

• W3103520000 endingPage "211" @default.
• W3103520000 startingPage "175" @default.
• W3103520000 abstract "The Aharonov-Bohm effect is a fundamental issue in physics that has been extensively studied in the literature and is discussed in most of the textbooks in quantum mechanics. The issues at stake are what are the fundamental electromagnetic quantities in quantum physics, if magnetic fields can act at a distance on charged particles and if the magnetic potentials have a real physical significance. The Aharonov-Bohm effect is a very controversial issue. From the experimental side the issues were settled by the remarkable experiments of Tonomura et al. (Phys Rev Lett 48:1443–1446, 1982; Phys Rev Lett 56:792–795, 1986) with toroidal magnets that gave a strong experimental evidence of the physical existence of the Aharonov-Bohm effect, and by the recent experiment of Caprez et al. (Phys Rev Lett 99:210401, 2007) that shows that the results of the Tonomura et al. experiments can not be explained by the action of a force. Aharonov and Bohm (Phys Rev 115:485-491, 1959) proposed an Ansatz for the solution to the Schrödinger equation in simply connected regions of space where there are no electromagnetic fields. It consists of multiplying the free evolution by the Dirac magnetic factor. The Aharonov-Bohm Ansatz predicts the results of the experiments of Tonomura et al. and of Caprez et al. Recently in Ballesteros and Weder (Math Phys 50:122108, 2009) we gave the first rigorous proof that the Aharonov-Bohm Ansatz is a good approximation to the exact solution for toroidal magnets under the conditions of the experiments of Tonomura et al. We provided a rigorous, simple, quantitative, error bound for the difference in norm between the exact solution and the Aharonov-Bohm Ansatz. In this paper we prove that these results do not depend on the particular geometry of the magnets and on the velocities of the incoming electrons used on the experiments, and on the gaussian shape of the wave packets used to obtain our quantitative error bound. We consider a general class of magnets that are a finite union of handlebodies. Each handlebody is diffeomorphic to a torus or a ball, and some of them can be patched though the boundary. We formulate the Aharonov-Bohm Ansatz that is appropriate to this general case and we prove that the exact solution to the Schrödinger equation is given by the Aharonov-Bohm Ansatz up to an error bound in norm that is uniform in time and that decays as a constant divided by v ρ , 0 < ρ < 1, with v the velocity. The results of Tonomura et al., of Caprez et al., our previous results and the results of this paper give a firm experimental and theoretical basis to the existence of the Aharonov-Bohm effect and to its quantum nature. Namely, that magnetic fields act at a distance on charged particles, and that this action at a distance is carried by the circulation of the magnetic potential which gives a real physical significance to magnetic potentials." @default.
• W3103520000 created "2020-11-23" @default.
• W3103520000 creator A5027081783 @default.
• W3103520000 creator A5029382973 @default.
• W3103520000 date "2010-12-14" @default.
• W3103520000 modified "2023-10-18" @default.
• W3103520000 title "Aharonov-Bohm Effect and High-Velocity Estimates of Solutions to the Schrödinger Equation" @default.
• W3103520000 cites W1555703232 @default.
• W3103520000 cites W1575147392 @default.
• W3103520000 cites W1694512337 @default.
• W3103520000 cites W1968947080 @default.
• W3103520000 cites W1976017069 @default.
• W3103520000 cites W1985802081 @default.
• W3103520000 cites W1997802669 @default.
• W3103520000 cites W2004424573 @default.
• W3103520000 cites W2028948400 @default.
• W3103520000 cites W2029450225 @default.
• W3103520000 cites W2031867899 @default.
• W3103520000 cites W2050341534 @default.
• W3103520000 cites W2055529983 @default.
• W3103520000 cites W2076622372 @default.
• W3103520000 cites W2087675085 @default.
• W3103520000 cites W2092272609 @default.
• W3103520000 cites W2110399667 @default.
• W3103520000 cites W2141832944 @default.
• W3103520000 cites W2159285249 @default.
• W3103520000 cites W2160794025 @default.
• W3103520000 cites W3101926118 @default.
• W3103520000 cites W4231442273 @default.
• W3103520000 cites W4247458820 @default.
• W3103520000 doi "https://doi.org/10.1007/s00220-010-1166-9" @default.
• W3103520000 hasPublicationYear "2010" @default.
• W3103520000 type Work @default.
• W3103520000 sameAs 3103520000 @default.
• W3103520000 citedByCount "17" @default.
• W3103520000 countsByYear W31035200002012 @default.
• W3103520000 countsByYear W31035200002013 @default.
• W3103520000 countsByYear W31035200002015 @default.
• W3103520000 countsByYear W31035200002016 @default.
• W3103520000 countsByYear W31035200002017 @default.
• W3103520000 countsByYear W31035200002019 @default.
• W3103520000 countsByYear W31035200002020 @default.
• W3103520000 countsByYear W31035200002022 @default.
• W3103520000 countsByYear W31035200002023 @default.
• W3103520000 crossrefType "journal-article" @default.
• W3103520000 hasAuthorship W3103520000A5027081783 @default.
• W3103520000 hasAuthorship W3103520000A5029382973 @default.
• W3103520000 hasBestOaLocation W31035200002 @default.
• W3103520000 hasConcept C115260700 @default.
• W3103520000 hasConcept C121332964 @default.
• W3103520000 hasConcept C130979935 @default.
• W3103520000 hasConcept C139989952 @default.
• W3103520000 hasConcept C15001198 @default.
• W3103520000 hasConcept C2780791683 @default.
• W3103520000 hasConcept C37914503 @default.
• W3103520000 hasConcept C62520636 @default.
• W3103520000 hasConcept C63036615 @default.
• W3103520000 hasConcept C82601208 @default.
• W3103520000 hasConcept C82706917 @default.
• W3103520000 hasConcept C84114770 @default.
• W3103520000 hasConceptScore W3103520000C115260700 @default.
• W3103520000 hasConceptScore W3103520000C121332964 @default.
• W3103520000 hasConceptScore W3103520000C130979935 @default.
• W3103520000 hasConceptScore W3103520000C139989952 @default.
• W3103520000 hasConceptScore W3103520000C15001198 @default.
• W3103520000 hasConceptScore W3103520000C2780791683 @default.
• W3103520000 hasConceptScore W3103520000C37914503 @default.
• W3103520000 hasConceptScore W3103520000C62520636 @default.
• W3103520000 hasConceptScore W3103520000C63036615 @default.
• W3103520000 hasConceptScore W3103520000C82601208 @default.
• W3103520000 hasConceptScore W3103520000C82706917 @default.
• W3103520000 hasConceptScore W3103520000C84114770 @default.
• W3103520000 hasIssue "1" @default.
• W3103520000 hasLocation W31035200001 @default.
• W3103520000 hasLocation W31035200002 @default.
• W3103520000 hasLocation W31035200003 @default.
• W3103520000 hasOpenAccess W3103520000 @default.
• W3103520000 hasPrimaryLocation W31035200001 @default.
• W3103520000 hasRelatedWork W1582990172 @default.
• W3103520000 hasRelatedWork W1982119637 @default.
• W3103520000 hasRelatedWork W1988480871 @default.
• W3103520000 hasRelatedWork W2056440057 @default.
• W3103520000 hasRelatedWork W2111466411 @default.
• W3103520000 hasRelatedWork W2165328413 @default.
• W3103520000 hasRelatedWork W2170880167 @default.
• W3103520000 hasRelatedWork W2193125515 @default.
• W3103520000 hasRelatedWork W2950103711 @default.
• W3103520000 hasRelatedWork W4283709755 @default.
• W3103520000 hasVolume "303" @default.
• W3103520000 isParatext "false" @default.
• W3103520000 isRetracted "false" @default.
• W3103520000 magId "3103520000" @default.
• W3103520000 workType "article" @default.