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- W2964072612 abstract "We construct pairs of compact Kahler-Einstein manifolds (Mi, gi, ωi) (i = 1, 2) of complex dimension n with the following properties: The canonical line bundle Li = ∧n T Mi has Chern class [ωi/2π], and for each integer k the tensor powers L 1 and L 2 are isospectral for the bundle Laplacian associated with the canonical connection, while M1 and M2 – and hence T M1 and T M2 – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent. Moreover, we construct many examples of line bundles L, pairs of potentials Q1, Q2 on the base manifold, and pairs of connections ∇1, ∇2 on L such that for each integer k the associated Schrodinger operators on L are isospectral. Resume: On construit des couples de varietes de Kahler-Einstein compactes (Mi, gi, ωi) (i = 1, 2) de dimension complexe n avec les proprietes suivantes: La premiere classe de Chern associee au fibre en droites canonique Li = ∧n T Mi est ωi/2π, et pour tout entier k, les puissances tensorielles L 1 et L 2 sont isospectrales pour le Laplacien associe a la connexion canonique, mais M1 et M2 – et, en consequence,T M1 et T M2 – ne sont pas homeomorphes. Dans le contexte de la quantification geometrique, nous interpretons ces examples comme des champs magnetiques qui sont equivalents au sens quantique mais pas au sens classique. En plus, on construit beaucoup d’exemples de fibres en droites L, de couples de potentiels Q1, Q2 sur la variete de base et de couples de connexions ∇1, ∇2 telles que pour tout entier k les operateurs de Schrodinger associes sur L soient isospectraux." @default.
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- W2964072612 date "2010-01-01" @default.
- W2964072612 modified "2023-09-29" @default.
- W2964072612 title "Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent" @default.
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- W2964072612 doi "https://doi.org/10.5802/aif.2612" @default.
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