FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2080408826> ?p ?o ?g. }

• W2080408826 endingPage "1016" @default.
• W2080408826 startingPage "963" @default.
• W2080408826 abstract "We consider the quantum dynamics of an electron in a periodic box of large size L, for long time scales T, in d dimensions of space, d ≥ 3. One obstacle occupying a volume 1 is present in the box. The coupling constant between the electron and the obstacle is A. The model is described by a scaled periodic von Neumann equation with a potential, a time-reversible equation. We investigate the asymptotic dynamics in the typical low-density regime T ∼ L d , L → ∞. The coupling constant has to be rescaled and small, namely λ ∼ L -d+2 → 0. More general regimes are in fact considered. Our analysis is easily adapted in the case of Dirichlet boundary conditions. Loosely speaking, the dynamics of an electron moving in a field of obstacles and in the low-density regime is, in general, asymptotically described by a time-irreversible Boltzmann equation. Large finite boxes are often used in the physical literature to formally justify this statement. However, the above asymptotics has only been proved true for randomly distributed obstacle, say. On the more, the physical derivations relying on taking large finite boxes are mathematically as well as physically questionable. Starting from these observations, we investigate here in a quantitative way the case of an electron moving in a large periodic (or Dirichlet) box, with a given deterministic obstacle. We prove here that both periodicity and the fact that the obstacle is deterministic, create strong phase coherence effects which dominate the asymptotic process. This implies that, (a) the limiting dynamics is not the Boltzmann equation, (b) it is time-reversible, (c) it is the same for any time scale T such that, roughly, T/L 2 → ∞, adn (d) the unusual rescaling of λ is needed as well. However, the convergence proved here only holds as a term-by-term convergence of certain series. Our results relies on the analysis of certain Riemann sums with arithmetic constraints, and number theoretic considerations relating the asymptotic distribution of integer vectors on spheres of large radius happen to play a key role in this paper." @default.
• W2080408826 created "2016-06-24" @default.
• W2080408826 creator A5008872453 @default.
• W2080408826 creator A5089908522 @default.
• W2080408826 date "2002-01-01" @default.
• W2080408826 modified "2023-10-16" @default.
• W2080408826 title "Non-derivation of the quantum Boltzmann equation from the periodic Von Neumann Equation" @default.
• W2080408826 cites W103651397 @default.
• W2080408826 cites W1482636459 @default.
• W2080408826 cites W1486304066 @default.
• W2080408826 cites W1518139628 @default.
• W2080408826 cites W1520468186 @default.
• W2080408826 cites W1537383557 @default.
• W2080408826 cites W161896720 @default.
• W2080408826 cites W1650269408 @default.
• W2080408826 cites W1664764145 @default.
• W2080408826 cites W184743397 @default.
• W2080408826 cites W1965353064 @default.
• W2080408826 cites W1970959040 @default.
• W2080408826 cites W1976021442 @default.
• W2080408826 cites W1983309742 @default.
• W2080408826 cites W1993095706 @default.
• W2080408826 cites W2002571532 @default.
• W2080408826 cites W2004477572 @default.
• W2080408826 cites W2018395999 @default.
• W2080408826 cites W2018535636 @default.
• W2080408826 cites W2036163097 @default.
• W2080408826 cites W2047117738 @default.
• W2080408826 cites W2055046849 @default.
• W2080408826 cites W2067579563 @default.
• W2080408826 cites W2067792418 @default.
• W2080408826 cites W2079738287 @default.
• W2080408826 cites W2083916485 @default.
• W2080408826 cites W2102787760 @default.
• W2080408826 cites W2117572933 @default.
• W2080408826 cites W2132248880 @default.
• W2080408826 cites W2136737502 @default.
• W2080408826 cites W2166848949 @default.
• W2080408826 cites W2472321209 @default.
• W2080408826 cites W2610542513 @default.
• W2080408826 cites W2798456356 @default.
• W2080408826 cites W3003955138 @default.
• W2080408826 doi "https://doi.org/10.1512/iumj.2002.51.2266" @default.
• W2080408826 hasPublicationYear "2002" @default.
• W2080408826 type Work @default.
• W2080408826 sameAs 2080408826 @default.
• W2080408826 citedByCount "9" @default.
• W2080408826 countsByYear W20804088262012 @default.
• W2080408826 countsByYear W20804088262019 @default.
• W2080408826 countsByYear W20804088262021 @default.
• W2080408826 crossrefType "journal-article" @default.
• W2080408826 hasAuthorship W2080408826A5008872453 @default.
• W2080408826 hasAuthorship W2080408826A5089908522 @default.
• W2080408826 hasConcept C121332964 @default.
• W2080408826 hasConcept C132954091 @default.
• W2080408826 hasConcept C134306372 @default.
• W2080408826 hasConcept C165995430 @default.
• W2080408826 hasConcept C202444582 @default.
• W2080408826 hasConcept C21261745 @default.
• W2080408826 hasConcept C33923547 @default.
• W2080408826 hasConcept C37914503 @default.
• W2080408826 hasConcept C62520636 @default.
• W2080408826 hasConcept C80469333 @default.
• W2080408826 hasConcept C84114770 @default.
• W2080408826 hasConcept C99392333 @default.
• W2080408826 hasConceptScore W2080408826C121332964 @default.
• W2080408826 hasConceptScore W2080408826C132954091 @default.
• W2080408826 hasConceptScore W2080408826C134306372 @default.
• W2080408826 hasConceptScore W2080408826C165995430 @default.
• W2080408826 hasConceptScore W2080408826C202444582 @default.
• W2080408826 hasConceptScore W2080408826C21261745 @default.
• W2080408826 hasConceptScore W2080408826C33923547 @default.
• W2080408826 hasConceptScore W2080408826C37914503 @default.
• W2080408826 hasConceptScore W2080408826C62520636 @default.
• W2080408826 hasConceptScore W2080408826C80469333 @default.
• W2080408826 hasConceptScore W2080408826C84114770 @default.
• W2080408826 hasConceptScore W2080408826C99392333 @default.
• W2080408826 hasIssue "4" @default.
• W2080408826 hasLocation W20804088261 @default.
• W2080408826 hasOpenAccess W2080408826 @default.
• W2080408826 hasPrimaryLocation W20804088261 @default.
• W2080408826 hasRelatedWork W1977570627 @default.
• W2080408826 hasRelatedWork W1983366713 @default.
• W2080408826 hasRelatedWork W2018822026 @default.
• W2080408826 hasRelatedWork W2043594297 @default.
• W2080408826 hasRelatedWork W2050770628 @default.
• W2080408826 hasRelatedWork W2318744113 @default.
• W2080408826 hasRelatedWork W2772879479 @default.
• W2080408826 hasRelatedWork W2982326764 @default.
• W2080408826 hasRelatedWork W4236584742 @default.
• W2080408826 hasRelatedWork W2889274241 @default.
• W2080408826 hasVolume "51" @default.
• W2080408826 isParatext "false" @default.
• W2080408826 isRetracted "false" @default.
• W2080408826 magId "2080408826" @default.
• W2080408826 workType "article" @default.