Spectral properties of the quantum Mixmaster universe

Abstract : We study the spectral properties of the anisotropic part of the Hamiltonian entering the quantum dynamics of the Mixmaster universe. We derive the explicit asymptotic expressions for the energy spectrum in the limit of large and small volumes of the universe. Then, we study the threshold condition between both regimes. Finally, we prove that the spectrum is purely discrete for any volume of the universe. Our results validate and improve the known approximations to the anisotropy potential. They should be useful for any approach to the quantization of the Mixmaster universe.
Keywords : 98.80.Qc
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https://hal.archives-ouvertes.fr/hal-01645213
Contributeur : Inspire Hep <>
Soumis le : jeudi 23 novembre 2017 - 01:25:58
Dernière modification le : mercredi 13 février 2019 - 07:51:11

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Hervé Bergeron, Ewa Czuchry, Jean-Pierre Gazeau, Przemysław Małkiewicz. Spectral properties of the quantum Mixmaster universe. Phys.Rev.D, 2017, 96 (4), pp.043521. 〈10.1103/PhysRevD.96.043521〉. 〈hal-01645213〉

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