Holonomic control operators in quantum completely integrable Hamiltonian systems

Details Holonomic control operators in quantum completely integrable Hamiltonian systems Holonomic control operators in quantum completely integrable Hamiltonian systems

2002-01-12

arxiv.org/abs/quant-ph/0201050v1

Physics

Quantum Physics

13 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Holonomic control operators in 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 Holonomic control operators in quantum completely integrable Hamiltonian systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holonomic control operators in quantum completely integrable Hamiltonian systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-656734