Dynamical instability and external perturbations: Bimolecular collisions in laser fields

Abstract

The detailed dynamics of F+H2, and to a lesser extent H+H2, in the presence of laser fields are examined in order to establish the relationship between field-free unstable trajectories and the effect of external perturbations. Weak fields are found to alter the dynamics of individual unstable trajectories and, in particular, to induce transitions amongst the unstable trajectory manifold. As a result, the field has little effect, on the average, on gross collision properties. Intense fields substantially alter the qualitative stable/ unstable structure of phase space and hence the reaction probability. An interesting high field limit is also discussed.

Topology of classical molecular optimal control landscapes in phase space

“…at the global maximum, where the functions ψ l (t) are orthonormal (with respect to the · T norm) with the same span as the functions φ i (t) in Eq. (21). The functions ψ l (t) may be obtained by applying the Gram-Schmidt process to the functions φ i (t).…”

“…The present paper considers optimal classical control for steering a system from an initial point in phase space to a final target point. This work builds on previous classical molecular optimal control studies 8,9,[11][12][13][14][15][16][17][18][19][20][21][22] and extensive research into quantum control. [1][2][3]5,[23][24][25][26][27][28][29] An important feature of optimal control analysis is consideration of the underlying control landscape, defined as the physical objective as a functional of the control field.…”

“…However, some studies have shown that under control, even systems that are nominally chaotic may exhibit regular, non-chaotic behavior. 8,13,21 Managing chaotic behavior is relevant for the stability of optimally controlled trajectories.…”