Semi-classical determination of exponentially small intermode transitions for 1+1 space-time scattering systems
| dc.creator | Marx, Magali | |
| dc.creator | Joye, Alain | |
| dc.date | 2005-08-24 | |
| dc.date.accessioned | 2026-07-07T04:32:17Z | |
| dc.date.available | 2026-07-07T04:32:17Z | |
| dc.description | We consider the semiclassical limit of systems of autonomous PDE's in 1+1 space-time dimensions in a scattering regime. We assume the matrix valued coefficients are analytic in the space variable and we further suppose that the corresponding dispersion relation admits real-valued modes only with one-dimensional polarization subspaces. Hence a BKW-type analysis of the solutions is possible. We typically consider time-dependent solutions to the PDE which are carried asymptotically in the past and as $x\to -\infty$ along one mode only and determine the piece of the solution that is carried for $x\to +\infty$ along some other mode in the future. Because of the assumed non-degeneracy of the modes, such transitions between modes are exponentially small in the semiclassical parameter; this is an expression of the Landau-Zener mechanism. We completely elucidate the space-time properties of the leading term of this exponentially small wave, when the semiclassical parameter is small, for large values of $x$ and $t$, when some avoided crossing of finite width takes place between the involved modes. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0508047 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0508047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58136 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Qxx; 35L30; 81U30 | |
| dc.title | Semi-classical determination of exponentially small intermode transitions for 1+1 space-time scattering systems | |
| dc.type | text |