A direct link between the quantum-mechanical and semiclassical determination of scattering resonances
| dc.creator | Wirzba, Andreas | |
| dc.creator | Henseler, Michael | |
| dc.date | 1997-02-06 | |
| dc.date | 1998-03-17 | |
| dc.date.accessioned | 2026-07-07T09:02:17Z | |
| dc.date.available | 2026-07-07T09:02:17Z | |
| dc.description | We investigate the scattering of a point particle from n non-overlapping, disconnected hard disks which are fixed in the two-dimensional plane and study the connection between the spectral properties of the quantum-mechanical scattering matrix and its semiclassical equivalent based on the semiclassical zeta function of Gutzwiller and Voros. We rewrite the determinant of the scattering matrix in such a way that it separates into the product of n determinants of 1-disk scattering matrices - representing the incoherent part of the scattering from the n disk system - and the ratio of two mutually complex conjugate determinants of the genuine multi-scattering kernel, M, which is of Korringa-Kohn-Rostoker-type and represents the coherent multi-disk aspect of the n-disk scattering. Our result is well-defined at every step of the calculation, as the on-shell T-matrix and the kernel M-1 are shown to be trace-class. We stress that the cumulant expansion (which defines the determinant over an infinite, but trace class matrix) imposes the curvature regularization scheme to the Gutzwiller-Voros zeta function and thus leads to a new, well-defined and direct derivation of the semiclassical spectral function. We show that unitarity is preserved even at the semiclassical level. | |
| dc.description | 23 pages, latex with IOP journal preprint style, no figures; final version - considerably shortened | |
| dc.identifier | https://arxiv.org/abs/chao-dyn/9702004 | |
| dc.identifier | http://arxiv.org/abs/chao-dyn/9702004 | |
| dc.identifier | J. Phys. A: Math. Gen. 31 (1998) 2155-2172 | |
| dc.identifier | doi:10.1088/0305-4470/31/9/007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148577 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | A direct link between the quantum-mechanical and semiclassical determination of scattering resonances | |
| dc.type | text |