SU(1,1), SU(2), and SU(3) coherence-preserving Hamiltonians and time-ordering techniques

A Classical View of the Euler Angles and the Euler Kinematic Equations in NMR

“…The simple modeled as a rotation in a Euclidean space, and how the answer is that the same kinematical relations must be relevant Rabi rotation matrix (31)(32)(33) can be deduced from obtained in both the quantum-mechanical and the classi-the Wei-Norman ordered form of the evolution operator for cal picture; in the next section, both sets of kinematical SU(2) Hamiltonians (34). Further work (35,36) showed relations derived via the rotation-operator approach will how the Wei-Norman ordering equations could be cast in be rederived from the Bloch equations using a classical the form of a generalized Bloch equation, thereby establishpoint of view. A more profound answer can be found ing a clear link between the wave-function and vector-model in the work of Ansbacher ( 29 ) , who demonstrated the methods.…”

Computable negativity in two-mode squeezing subject to dissipation

“…Equation (14) shows that at t = 0 the state is completely separable, i.e., N = 0, while in the steady state it is inseparable provided that |ξ | > 4κn th , which is a parameter reduced expression (12) and (13). Moreover, at zero bath temperature, i.e., n th = 0 states violate the separability condition in all parameter regimes.…”

“…In the past, the Wei-Norman method has been applied to study Lie algebra valued problems [9][10][11][12][13][14], many of which found applications in optical systems. These problems, however, mainly involved Lie algebras spanned by no more than three generators, and if any extensions to the algebras were considered, only their few operator reductions were studied [15,16].…”

“…κ 1 = κ 2 = 0, decouples operators H 2,3,6 , H 7-10 , and H 13,14 . The remaining operators form again an so(2,2) ⊂ so(4,2) Lie algebra which decomposes into two sets of operators acting separately from the right or from the left of the 033829-7 ,…”

“…δ = 0 decouples operators H 11-15 from the algebra [H 15 vanishes directly from the equation of motion, and H [11][12][13][14] do not enter the dynamics due to their commutation relation properties (see Table I)].…”