Introduction
There are two viewpoints: big picture and day-to-day. For the past 1.5 years, I have lived in the day-to-day. I constantly felt like I needed to do some homework set, fix code, run code, learn some cool-but-not-so-general theory, etc. Living in this day-to-day mindset has impaired my ability to reflect. Reflection generates feedback to improve. Coming back from a 10 day vacation, I feel like now is the best shot I’ll have to reflect on my PhD so far and, hopefully, improve.
Pre-PhD
The story should really begin before I got accepted into a PhD program. As a college senior, I had an overinflated sense of my ability to do physics (big fish, small pond). I hoped to work on what I thought was the fundamental problem of physics: establishing a mathematically rigorous quantum field theory. Enamored by the beauty of algebra, I applied to a prestigious program to work on algebraic quantum field theory, among others. When the results came in, my inflated bubble popped. I got some acceptances but I did not get into the programs I had most hoped for. I was saddened by the results because they made me to consider that I did not have as great potential as a physicist as I thought I had. If I had to boil this experience down into a single lesson, I’d say:
Other people are not a reliable measure of my ability. I was told almost verbatim by one of my undergraduate advisors that a prestigious program would be a safety for me. This only fed the inflation and turned out to be very wrong. On the flip side, this also means that rejections are not necessarily reliable measures of my ability. From hereon, I’d try to approach the problem of estimating my own ability more scientifically. Perhaps I can even take inspiration from the theory of parameter estimation…
At the end (after also considering a two-body problem), I choose to attend the University of Rochester. I am quite happy with my choice now, but only due to the sheer luck of a new faculty hire who later became my advisor. Thinking about how pure luck impacted my fate is sobering: I must work harder and smarter to maximize the chance that I get what I want in the future.
Year 0.5 (Fall 2024)
During this semester, I took some core courses and an elective and began talking to a professor that I wanted to work with (before the aforementioned new hire was announced).
The core courses were uninteresting as I knew most of the content from what I self-studied during my undergraduate years. I did take an elective in complex systems. This course was largely uninteresting as well, but I did learn about percolation theory and the Perron-Frobenius theorem–both of which have come back to help me on several occasions already.
I talked with the professor about potential projects that I could work on. I was intrigued by their interest in quantum foundations (what I had worked on in my undergraduate years) but was dissuaded by the practical considerations of pursuing a career in quantum foundations. We eventually landed on a project which aimed to analyze the flow of information through a top quark decay process. Thereafter, I spent most of my time writing my first (unsuccessful) fellowship application and learning miscellaneous physics unrelated to the project, reminiscent of my undergraduate days.
Above all this noise, one note rang clear. I didn’t know what I wanted to make out of my PhD anymore. I didn’t get my dream of working on rigorous QFT, so I felt like I had to fit myself into one of the few options available. This made for an unproductive semester, among other things. As I considered how to move forward with this situation a real deus ex machina event occurred in the form of a new faculty hire.
Year 1.0 (Spring 2025)
During winter break, I met with the new faculty hire to discuss doing research with them. This led to a series of meetings during the spring semester. As a sort-of test, I along with one other student (who is now my fellow group member) worked through and presented Schultz, Mattis, and Lieb’s solution to the 2D Ising model. I would say this was my first real reading of a scientific paper–and a good one at that; it shows many general features (second order phase transition, emergence of quasiparticles from the original degrees of freedom, etc.) and tricks (Jordan-Wigner transformation, Bogoliubov transformations, Fourier transform lattice translation invariant systems, maximum eigenvalue inequalities in the thermodynamic limit, etc.). It was challenging and took about a month, but I came out with a sense of accomplishment. (The parentheticals sound technical but also generate simple conceptual questions like: what determines whether we see a spin chain or a system of free fermions?)
I also finished up my core courses and took condensed matter II, taught by the new hire. Condensed matter II and the 2D Ising model showed me what real physics is and, above all, that real physics is hard. Hereafter, I’d proceed in physics with a sense of intimidation that has, so far, been slowly abating over time.
Oh, and I was able to join the new hire’s group! Hereon, I’d be able to work on condensed matter theory, whose vast use and generation of physics excited me. Incidentally, my undergraduate advisor and John Baez suggested that I look into condensed matter theory. This was good advice.
Year 1.5 (Fall 2025)
With core courses complete, I only took condensed matter I this semester, taught by my advisor. It was a mix of Ashcroft & Mermin and Girvin & Yang as well as the professors own thoughts. I thought it was great overall and left with a more solid foundation in solid state physics. I was particularly interested in topology (integer quantum Hall effect, first Chern number of bands, etc.) and the Landauer formalism for mesoscopic transport.
But most of my time was spent on my current research project. I started on my current project during the summer (5/1/2025) and have worked on it til now (1/1/2026; happy new year!). So, I’ve been working on this project for about 8 months. It’s been a great starter project, giving me time to learn state-of-the-art numerical methods for solving disordered tight-binding models (Monte Carlo and KPM) as well as miscellaneous but far-reaching theory (disordered systems, Bardeen’s theory of tunneling, polarons, etc.).
The most important thing I learned from this semester was to take breaks more seriously. For six days a week, I would wake up at 10 am, arrive at campus at 11 am, and work until 9 pm without breaks (other than lunch and dinner). For the seventh day, I’d go grocery shopping but still work at least 6 hours. I certainly did not output 70 hours/week worth of physics. The reason is simple: I was working beyond my capacity, leading to gradual losses in productivity via deteriorating ability to think. At least, that’s what I think the mechanism is. Assuming this hypothesis for my productivity, I have started to use a time-tracker that also reminds me to take breaks. I am also slowly introducing things not directly related to my research into my day (like writing this blog post). I am hoping that these changes help me sustain my ability to think. The empirical evidence will come at the end of next semester!
Conclusion
I distilled each half-year into a single lesson. I collect them here:
- Other people are not a reliable measure of my ability.
- Minimize the need for luck through working smarter and harder.
- Take breaks and do other things!
Here’s to 2026!
Brian Yong-Ho Lee 