Hi folks. I've come across a method to determine the controllability of a quantum system that depends on the Lie group generated by the commutator of the skew-Hermetian versions of the field free and interaction (dipole) Hamiltonians. If, for an N dimensional system the dimension of the group generated is N^2, then the dynamical Lie group is U(N) (is it correct to say “is” or should I say “is isomorphic to”?) and “every unitary operator can be dynamically generated”. My questions are: What symmetry are we exploring here with this group? What does the commutator tell us about the symmetry of the operators that determines if they’re fully controllable? What does this mean physically?(adsbygoogle = window.adsbygoogle || []).push({});

I have little experience with this sort of argument (that is, deriving physical information from the structure of a group with the same symmetry), so any insight is much appreciated. Thanks.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Commutators, Lie groups, and quantum systems

Loading...

Similar Threads for Commutators groups quantum | Date |
---|---|

I Commuting Operators and CSCO | Feb 20, 2018 |

A Commutator vector product | Jan 29, 2018 |

Commutation relation | Jan 18, 2018 |

I Solving the Schrödinger eqn. by commutation of operators | Jan 8, 2018 |

How to Determine Group from Commutation Relations? | Jan 20, 2015 |

**Physics Forums - The Fusion of Science and Community**