My research process
I stay with ideas for a very long time. I keep reading, thinking and experimenting with different interpretations, analogies and applications. I more often than not put them aside and start working on something else. I need at least 2 to 3 ideas to work on simultaneously because I can’t work on one for a long time. I have to hand over the idea to my subconscious for further processing in between. The whole process is very satisfying. As people say, the journey is more important than the destination. Some notables are,
- The time dependent perturbation paper, the general theory part that I wrote with Sitaram. If I remember correctly, Sitaram was planning to write this paper as a single author one. I agreed as all the development were his. Then Indu and Jam gave me multiple number of Smullyan puzzle-books to read. The reading gave rise to thoughts on self-referential systems and then to the idea of perturbing a Hamiltonian by itself. It gave some insights. I feel there is more to it. I need to explore it further. Thanks Indu and Jam. Thanking Sitaram would be such an understatement.
- The quaternion paper has a history of more than a decade. While working with Radha, I kept looking at the ODEs for the classical spin and the steady state equations and thinking there has to be an underlying mathematical structure here which is more elegant. It was like the hidden beauty was calling out to me but I did not understand the language. This was when I and Radha wrote our Phys. Rev. E. paper. Then at BITS, I started working with two very smart students, one was working on the 3D version of my paper with Radha and the other was working on understanding quaternions (my subconscious was playing games with me J). I finally could see a more elegant way of writing the steady states. So my Phys. Lett. A paper came out with my two students. Thanks Shubhanshu and Sauvik. Thanks Sweetser for your passion for the field and your contribution.
- The Lorenz system with the (misnomer) “forcing term”, was a fun one too. I don’t recollect wherefrom the idea of looking at the analytical manifold came up. It gave rise to a non-trivial closed first return map with Riemanian sheets like structure. This also is worth looking at again. Would be nice if I get an interested student but s/he has to have background in dynamical systems (a first course) Hamiltonian, dissipative, complex analysis (don’t I sound such a snob,… ohhh stop it).
Gautam is responsible for the above title in a way. He keeps flirting with ideas. Sauvik, I believe I see you also flirting now-a-days in virtual space. Hope your muse is treating you well. I am so happy that the black-holes collided. Sometimes it seems that the universe goes way out of its way to make you happy 🙂 . I am feeling so happy these days too.
- Penrose tiles: They have been on my mind since I saw them in a sci. Am. Issue. I have kept drawing them, reading about them and looking for more references on and off. The De-Bruin book has been with me for a while and now the pentagrids have started making sense. Yippie.
- Topological states: Just the name itself is so attractive and physics part of it makes it soooo coooool. Have been reading Kitaev’s work, on and off. Debbie, dear Debbie, I believe some day our paths will collide. (I enjoy annoying my friends). Debbie is going to work on the experimental part of the states, If I can do some coooool theory we may work together, it will be more of a merger than collision. I take back my previous statement. Rads, wish to join in ?
- Neuro-engineering: have always been fascinated by this. Started learning some useful tools. Thanks Sam, Nick and my data team.
Other things which are way back in back-ground but I hope will keep surfacing and contributing are, neural networks (have learnt a little, want to learn more), quantum computers, CPT theorem (I mean truly clear understanding, if such a thing were possible, will be so good). Have been trying to improve on monodromy method of periodic orbit search without much success. Universality (Feigenbaum fame) has always been on my mind, since Arul Lakshminarayan et. al. did the work on Hamiltonian systems. Not even a scratch on the surface yet but thinking about it is such fun. Nice geometry and calculus keep popping in and out.
Thanks Mel for your discussion on making learning visible. Jon Stolk, your passion for intrinsic is infectious (not that I was not already heavily infected).
I hope writing this blog will remind me of this and other work and keep me on some sort of track. Now that I think about it, the title is the exact same in words from a recent mail by Sam !