Monodromy

So to verify that monodromy actually exists in the control process - we ought to examine the EM geometry. Ideally we will have only two parameters for the potential. See Efstathiou et al, PRA 69, 032504 (2004).

For Monodromy, see also
Dullin et al, Physica D 190, 15-37 (2004),
Cushman et al, Phys. Rev. Lett. 93(2), 024302 (2004),
Giacobbe et al, J. Math. Phys. 45(12), 5076 (2004).

Marketing hoax

I noticed a funny marketing trick played by Tropicana (orange juice) the other day. They released the new 'Light N Healthy' juice, which really pulled me to read the fine prints, which said '43% of orignal juice'. So intrisically you are paying $1 to buy $.43 worth of juice plus the water. LOLz!

Bruce Lee

Just watched the Biography DVD of Bruce Lee by A&E (hah, b-day gift from Y). One line of Lee impressed me the most, which can be paraphrased as 'martial art is about expressing yourself freely and truly, not the fancy movements'. I can not agree more. As a matter of fact, life is about being true and expressive of oneself, not about impressive or influential to others - which, has become a commonly accepted goal of today's power-thirsty humanity. One step further: I believe if one is truly expressive of oneself, he will be more impressive and influential than otherwise; but how many people have truly accepted and followed it? Very few.

Free rotation in 3d space

The problem arises as I have to rotate (randomly) the linear molecule for initial conditions. There have been established ways to do this: Euler angles, unit vector + rotation (essentially the same thing), SO(3) matrices, quaternions etc. I chose Euler angles for my previous simulations, however there is a serious issue: how to make the orientations evenly distributed in the rotation space? Obviously generating evenly distributed φ, θ, ψ is not the answer. Down to the ground, Euler angles → SO(3) is not even a bijective map; for example, (-φ,π,φ) all gives the same rotation.

The proper probability density function: ρ(φ,θ,ψ)=cos(θ).