Holonomic control operators in quantum completely integrable Hamiltonian systems
| dc.creator | Sardanashvily, G. | |
| dc.date | 2002-01-12 | |
| dc.date.accessioned | 2026-07-07T06:03:31Z | |
| dc.date.available | 2026-07-07T06:03:31Z | |
| dc.description | We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to the angle polarization. The carrier space of this quantization is the pre-Hilbert space of smooth complex functions on the torus. A Hamiltonian of a completely integrable system in this carrier space has a countable spectrum. If it is degenerate, its eigenvalues are countably degenerate. We study nonadiabatic perturbations of this Hamiltonian by a term depending on classical time-dependent parameters. It is originated by a connection on the parameter space, and is linear in the temporal derivatives of parameters. One can choose it commuting with a degenerate Hamiltonian of a completely integrable system. Then the corresponding evolution operator acts in the eigenspaces of this Hamiltonian, and is an operator of parallel displacement along a curve in the parameter space. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0201050 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0201050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89972 | |
| dc.subject | Quantum Physics | |
| dc.subject | Mathematical Physics | |
| dc.title | Holonomic control operators in quantum completely integrable Hamiltonian systems | |
| dc.type | text |