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Abstract: For general quantum systems the semiclassical behaviour of eigenfunctions inrelation to the ergodic properties of the underlying classical system is quitedifficult to understand. The Wignerfunctions of eigenstates converge weakly toinvariant measures of the classical system, the so called quantum limits, andone would like to understand which invariant measures can occur that way,thereby classifying the semiclassical behaviour of eigenfunctions. We introducea class of maps on the torus for whose quantisations we can understand the setof quantum limits in great detail. In particular we can construct examples ofergodic maps which have singular ergodic measures as quantum limits, andexamples of non-ergodic maps where arbitrary convex combinations of absolutelycontinuous ergodic measures can occur as quantum limits. The maps we quantiseare obtained by cutting and stacking.



Author: Cheng-Hung Chang, Tyll Krueger, Roman Schubert, Serge Troubetzkoy CPT, FRUMAM, IML

Source: https://arxiv.org/







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