Time Optimal Quantum Control Theory

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There exists a Hamiltonian operator, for a given constraint, that drives the system from an initial state to a target final state in least time. This Hamiltonian operator is a time-dependent matrix with symmetry properties that represent the internal spectroscopy of the atomic system.
It is possible to find the time optimal trajectory for the quantum state once the Hamiltonian is defined, and hence calculate a minimum time required for the evolution in question. Results indicate that the time-dependence contained within the Hamiltonian matrix for particular choices of groups on SU(N) is of a periodic nature. This enables great simplication in analysis as many results from the theory of periodic differential equations may be directly applied to physical problems.

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...and have fun with the calculus

SU(3) changed my life!!!