User talk:NorioTakemoto

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I am a graduate student at the University of Tokyo, Japan.

My major field is physical chemistry.

I am interested in the interactions of atoms, molecules, and clusters with intense laser fields.

[edit] Symplectic integrator

Dear Norio,

I was very surprised to see somebody create an article on symplectic integrators, as it is something that I actually know a bit about. The definition in the symplectic integrator article seems to be a bit different than the definition that I am used to. Specifically, the article only talks about what I would call seperable Hamiltonians, and it only treats what I would call splitting methods. In my opinion, a symplectic integrator is any integrator that preserves the symplectic two-form, like the Yoshida splitting methods that are described in the article or the Störmer-Verlet method, which can be generalized to the partitioned Lobatto IIIA/IIIB method.

What do you think about this? Perhaps the terms are used slightly differently in physical chemistry (my background is mathematics), or maybe the article needs to be expanded?

Finally, as you seem to be new here, I would like to extend a warm welcome to you at Wikipedia. I hope you are here to stay. Please feel free to ask me any questions on my talk page, which can be found at User talk:Jitse Niesen. In particular, I realize that I might be using some terms which with you may not be familiar because of cultural differences (not only Japanese/English but perhaps more importantly chemics/mathematics); please do not hesitate to ask for further clarification. Anyway, I look forward on your future contributions.

さよなら, Jitse Niesen 02:18, 18 Jun 2005 (UTC)

PS: I had another look at the article and I am quite impressed. Well done! -- Jitse Niesen 02:23, 18 Jun 2005 (UTC)

---- (the following is a copy of my reply which I wrote on Jitse's user talk page) ----

Dear Jitse,

Thank you very much for your comment about a symplectic integrator on my talk page.

Actually, when I was writing that article, I had just a separable Hamiltonian in mind and didn't know such integrators as

Störmer-Verlet method or the partitioned Lobatto IIIA/IIIB method. (I would very much like to get acquainted with these

methods, so please let me know some references on these methods.)

I agree to define a symplectic integrator as any integrator that preserves the symplectic two-form, as you pointed out. I think that

the article needs appropriate corrections and expansions. I wonder if you could kindly make these contributions.

I appreciate your kind comments again. I am eager to learn everything that I feel interesting including mathematics. Although there may be

cultural differences among the fields of chemistry, physics, and mathematics, I hope that I could understand and obey a proper convention

in each field.

Tot morgen!

NorioTakemoto 14:58, 21 Jun 2005 (UTC)

I will try to find time in the future to expand the symplectic integrator article (I just wanted to contact you first). If you want to read a bit, some books that cover this from a mathematical perspective are:

• Sanz-Serna and Calvo, Numerical Hamiltonian problems, Chapman & Hall, London, 1994.
• Hairer, Lubich and Wanner, Geometric numerical integration, Springer Verlag, Berlin, 2002.
• Leimkuhler and Reich, Simulating Hamiltonian dynamics, Cambridge University Press, Cambridge, 2004

The first book is nice, but it does not of course contain all the latest developments. I like the second book very much, but it has some heavy mathematics, especially towards the end. I haven't carefully read through the third one yet; it has a chapter on molecular dynamics which may interest you. However, my feeling is that splitting methods are generally the best, if the Hamiltonian is separable. -- Jitse Niesen 15:58, 21 Jun 2005 (UTC)