Mathematics – Dynamical Systems
Scientific paper
2002-05-23
Mathematics
Dynamical Systems
17 pages
Scientific paper
Completely 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.
Giachetta Giovanni
Mangiarotti Luigi
Sardanashvily Gennadi
No associations
LandOfFree
Holonomy control operators in classical and quantum completely integrable Hamiltonian systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Holonomy control operators in classical and quantum completely integrable Hamiltonian systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holonomy control operators in classical and quantum completely integrable Hamiltonian systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-454563