Holonomy control operators in classical and quantum completely integrable Hamiltonian systems

Simple item page
dc.creatorGiachetta, G.
dc.creatorMangiarotti, L.
dc.creatorSardanashvily, G.
dc.date2002-05-23
dc.date.accessioned2026-07-07T04:48:39Z
dc.date.available2026-07-07T04:48:39Z
dc.descriptionCompletely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at will. Action-angle coordinates are most convenient for this purpose. Written with respect to these coordinates, a Hamiltonian and first integrals depend only on the action ones. We introduce a suitable perturbation of a Hamiltonian by a term containing time-dependent parameters so that an evolution of action variables is nothing else than a displacement along a curve in a parameter space. Therefore, one can define this evolution in full by an appropriate choice of parameter functions. Similar holonomy controllability of finite level quantum systems is of special interes in connection with quantum computation. We provide geometric quantization of a time-dependent completely integrable Hamiltonian system in action-angle variables. Its Hamiltonian and first integrals have time-independent countable spectra. The holonomy control operator in this countable level quantum system is constructed.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0205244
dc.identifierhttp://arxiv.org/abs/math/0205244
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64134
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject53D50; 70Q05; 81S10
dc.titleHolonomy control operators in classical and quantum completely integrable Hamiltonian systems
dc.typetext

Files

Collections

arXiv