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Subjects
81-XX Quantum theory
81Qxx General mathematical topics and methods in quantum theory
81Q50 Quantum chaos

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On nodal sets and nodal domains on $S^{2}$ and $ℝ^{2}$

Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili (2007)

Annales de l’institut Fourier

We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on $S^{2}$ . We also construct a solution of the equation $Δ u = u$ in $ℝ^{2}$ that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

On quantum twist maps and spectral properties of Floquet operators

Gunther Karner (1998)

Annales de l'I.H.P. Physique théorique

On the dynamical meaning of spectral dimensions

Italo Guarneri (1998)