On the properties of level spacings for decomposable systems
| dc.creator | Mezzadri, Francesco | |
| dc.creator | Scotti, Antonio | |
| dc.date | 1996-02-22 | |
| dc.date.accessioned | 2026-07-07T09:07:53Z | |
| dc.date.available | 2026-07-07T09:07:53Z | |
| dc.description | In this paper we show that the quantum theory of chaos, based on the statistical theory of energy spectra, presents inconsistencies difficult to overcome. In classical mechanics a system described by an hamiltonian $H = H_1 + H_2$ (decomposable) cannot be ergodic, because there are always two dependent integrals of motion besides the constant of energy. In quantum mechanics we prove the existence of decomposable systems \linebreak $H^q = H^q_1 + H^q_2$ whose spacing distribution agrees with the Wigner law and we show that in general the spacing distribution of $H^q$ is not the Poisson law, even if it has often the same qualitative behaviour. We have found that the spacings of $H^q$ are among the solutions of a well defined class of homogeneous linear systems. We have obtained an explicit formula for the bases of the kernels of these systems, and a chain of inequalities which the coefficients of a generic linear combination of the basis vectors must satisfy so that the elements of a particular solution will be all positive, i.e. can be considered a set of spacings. | |
| dc.description | LateX, 13 pages | |
| dc.identifier | https://arxiv.org/abs/chao-dyn/9602021 | |
| dc.identifier | http://arxiv.org/abs/chao-dyn/9602021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150530 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | On the properties of level spacings for decomposable systems | |
| dc.type | text |