Volume 118, Number 1, April 2017
|Number of page(s)||7|
|Published online||30 May 2017|
Semiclassical quantization of highly excited scar states
Departamento de Física, Comisión Nacional de Energía Atómica - Av. del Libertador 8250, (C1429BNP) Buenos Aires, Argentina and Escuela de Ciencia y Tecnología, Universidad Nacional de General San Martín - Alem 3901, (B1653HIM) Villa Ballester, Argentina
Received: 8 February 2017
Accepted: 15 May 2017
The semiclassical quantization of Hamiltonian systems with classically chaotic dynamics is restricted to low excited states, close to the ground state, because the number of required periodic orbits grows exponentially with energy. Nevertheless, here we demonstrate that it is possible to find eigenenergies of highly excited states scarred by a short periodic orbit. Specifically, by using 18146 homoclinic orbits (HO)s of the shortest periodic orbit of the hyperbola billiard, we find eigenenergies of the strongest scars over a range which includes 630 even eigenfunctions. The analysis of data reveals that the used semiclassical formula presents two regimes. First, when all HOs with excursion time smaller than the Heisenberg time tH are included, the error is around 3.3% of the mean level spacing. Second, in the energy region defined by , where is the maximum excursion time included in the calculation, the error is around 15% of the mean level spacing.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 03.65.Sq – Semiclassical theories and applications
© EPLA, 2017
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