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Time-domain semiclassical approach to quantum tunneling in nearly integrable systems

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AR2W02 - Mathematics of beyond all-orders phenomena

Quantum tunneling in nonintegrable systems has characteristics significantly different from that in integrable systems, reflecting the difference in underlying classical dynamics. Here we approach this issue by introducing “ultra-near” integrable systems, in which any visible nonintegrable structures comparable to the size of the Planck cell do not appear in the classical phase space. We perform the time-domain complex semiclassical analysis and explore the role of ergodicity in the complex plane, which is achieved even in ultra-near integrable systems. Concerning the Stokes phenomenon in evaluating semiclassically the time-domain quantum propagator, we start with the “anti-integrable” limit, in which chaos in the corresponding dynamics is ideally realized, and trace the bifurcation of the Stokes geometry by changing a system parameter.  This intends to establish the pruning theory of Stokes geometry. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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