Most of my entries are not quite in the form of a diary as I had planned. However, my posts reflect the fact that I spend lots of time thinking about things, so I argue that these are genuine diary entries. But at least for today, my entry will be more diary-like
When I made my rounds in the lab this afternoon, I noticed a common theme in my discussions with the students -- the amazing consistency of physics. Physics covers a broad range of phenomena (everything in the universe obeys the laws of physics!) that mesh together in the most beautiful ways.
My first stop was the department office on the 12th floor to sign paperwork. In the most recent power change, I once again avoided chairing the department, but as a comprise, I agreed to be the associate chair for a year -- the same deal I had made 8 years ago. But, my true pleasures awaited me on the 7th floor, the location of my labs.
First, I spent time talking with Julian, an undergraduate student, and Shoresh, a graduate student, who are using sum rules as a guide to developing theories of the relationship between the geometry of quantum nanowires and their nonlinear-optical properties. What started out as a simple class project has evolved into a huge undertaking. New subtleties keep popping up. Last week we had to revisit the basics of expectation values of quantum mechanics when applied to loops of wires. The fact that the answers that we are getting continue to be inconstant with the sum rules is a sure sign that we are getting something wrong.
Since sum rules are derived directly from the Schrodinger equation with no approximation, they cannot be violated. About an hour of discussions on the topic led to some new ideas and new approaches that will help us better understand our problems, which hopefully will lead to a solution. While constantly tracing errors in theoretical models is highly unpleasant, the exhilaration of learning makes it all worthwhile. Michael Cohen, a student of Feynman's and a professor of mine at U Penn showed me the value of going back to the basics and testing the assumptions, no matter how trivial. The process always leads to a deeper understanding.
Next I went to Nathan's office, a student who is doing work that we hope will someday lead to ultra-smart materials. After I helped him and Xianjun clean some laser optics, Nathan described his ambiguous experimental results of the previous evening. Then we returned to his office to discuss another project that we had started in nonlinear optics class. He and two of his classmates did calculations to understand if the process of cascading could be used to break the fundamental limits of the nonlinear optical response that I had calculated 10 years prior. Since my calculations were fairly general, I did not believe this to be possible; but, we are obligated to test the hypothesis. Cascading appears to be a topic of growing interest in the nonlinear optics community because of the new avenues it may provide for making better materials. Our work will assess its usefulness and may lead to design guidelines for new nonlinear-optical material paradigms.
There were several false starts - calculations that gave infinities or calculations that yielded limiting cases that were inconsistent with known physics. After a couple of weeks, and many discussions, we finally converged to what appeared to be a robust theory of cascading. After receiving a draft manuscript from the students, I spent several days adding lots of new material, expanding the bibliography, as well as correcting lots of little errors. Just as I was applying the finishing touches in smug satisfaction of the beauty of the final product, I noticed that we failed to consider one important case. So, I sent Nathan an email, and he went back to the drawing board.
Again, the infinities reared their ugly heads. Luckily, my 2006 paper provided us with some guidance. Nathan concluded that indeed, he could remove the infinities with this method; but, again, there are many subtleties and ambiguities regarding the formulation of the model. After a brief discussion, we agreed on an approach and Nathan immediately began implementing the calculations.
Almost 10 years ago, one of my students and I discovered that some materials self heal after photodegradation. This was an exciting discovery because of the apparent reversal of the arrow of time. The result is yet to be fully understood. Three students are presently working on the project. This work requires lots of samples to be made, long experiments that can take several days of continuous operation, and complex analysis of huge data files. Some of these experiments are currently up and running while we are in the planning phases of building a new instrument and upgrading some older experiments.
The experimental results are encouraging but continue to throw more puzzles our way than providing reliable tests of our hypotheses. But, I have a good feeling that we are expanding into new experimental techniques that will hopefully provide lots of answers as well enabling us to pose more interesting new questions.
When I got home from the lab, my inbox had a message labeled "important." Shoresh had found a paper that shed light on our observation of sum rule violation. The paper's abstract was short but to the point, "We discuss application of the Thomas-Reiche-Kuhn sum rule to simple quantum-mechanical models and its apparent violation by the rigid rotator."
Scanning through the paper, I noticed that the first reference in the bibliography was coauthored by Stavros Fallieros -- an incredible coincidence considering that my parents bought his house in 1968 when I was 10 years old. There must have been the essence of sum rules in the walls that were infused into my being during adolescence.
As it turns out, my in-laws were good friends with the Fallieros family, and continued to remain in touch. Several years after I wrote my 2000 paper on fundamental limits, my wife was visiting her mother in a suburb of Philadelphia, where she ran into Stavros. During the exchange of pleasantries, he learned about our common interest in sum rules, and relayed through my wife the message that he wanted a copy of my paper, which I happily mailed to him. Unfortunately, he passed away soon after, and we never had a chance to discuss the work. Ironically, the sum rule paper that he wrote, and which I recently found, was his last journal publication. With the perfect symmetry not often found in life, one of the last papers that he had in his possession was my paper on sum rules.
The interconnectedness of science is mirrored in the relationships between scientists. We are each small cogs in a gargantuan machine that produces new knowledge. One of my former graduate students, Xavi (PhD in 2007), who was the first person to appreciate my use of the sum rules in nonlinear optics will be visiting my group for 6 weeks this summer. Later in the summer, his co-advisor will also be visitng from Belgium. This combination of our two visitors, a new student in my group, Sengting, who is following in the footsteps of Xavi in his pursuit of a joint PhD degree between WSU and the University of Leuven, along with Shoresh and Julian provides us with a formidable crew that will undoubtedly add to the knowledge base of science.
As I sit here at my computer in this small pocket of nostalgic bliss, thinking about international collaborations and our connections with past and future science, I am looking forward to the satisfaction of learning new things as well as tracking divergences in calculations, fixing lasers, and deficit spending to buy components for a new experiments. Another typical day begins!