Author: nrui

Tales from five years as a Caltech Physics PhD student

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I’m a doctor! Not the usual kind of doctor, but blood, sweat, and tears were certainly involved.

In 2020, I graduated from UC Berkeley with my bachelor’s degree and wrote a blog post summarizing my undergrad years. Finishing grad school has been a similar transitional event in my life, but also one which many fewer people experience. I think now is a good time for reflecting back on my experiences in grad school and hopefully demystifying the whole process a bit.

My PhD is in physics from Caltech, but I spent the vast majority of my time doing astrophysics in the astrophysics building (the Cahill Center for Astronomy and Astrophysics), especially on the half of the third floor allocated to the TAPIR group (a contrived acronym which presently stands for Theoretical AstroPhysics Including Relativity and Cosmology).

Looking back, my grad school experience was mostly ideal. It lasted five years, no longer or shorter than I wanted it to. While I had my own share of frustrating moments of being stuck, my growth as a researcher was monotonic and accumulated steadily over the years to the point where I now feel pretty autonomous and independent as a researcher. Although I was certainly exhausted by the end of this whole thing, I still haven’t had enough of academia. I’ll be starting next month in a prestigious prize postdoc position.

Unlike undergrad, my grad school experience highly deemphasized classes and placed personal recreation at the center of things. My experiences during these years therefore lack a lot of the simple structure that would usually be introduced by a rigid academic calendar. I think this typical of most people in my position. I consider this a fair warning for the following to read much more like a stream-of-conscious regurgitation of all of the things I can remember doing during these years, written during the point in time where the number of such things is maximized.

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Deriving the Ideal Gas Law: A Statistical Story

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The ideal gas law is PV=NkT, where P is the pressure, V is the volume, N is the number of particles, k=1.38\times10^{-23}\,\mathrm{m}^2\,\mathrm{kg}\,\mathrm{s}^{-2}\,\mathrm{K}^{-1}, and T is the temperature. It constitutes one of the simplest and most applied “equations of states” in all of physics, and is (or will become) incredibly familiar to any student of not only physics but also related fields such as chemistry and various engineering disciplines.

Recently, I’ve come to appreciate the ideal gas law as a very good illustrative example of what statistical mechanics is capable of. In the eighteenth and nineteenth (during the industrial revolution), the field of thermodynamics arose in pursuit of answers to how much energy can be extracted from systems. At the time, the notion of temperature was hotly debated, with one ostensibly reasonable theory being that the flow of a fluid, called “caloric,” facilitated heat transfer. It should be appreciated just how many important results could be derived by our predecessors without precise knowledge of the microscopic physics involved.

Statistical mechanics arises from a desire to understand how thermodynamics arises from microscopic physics, either classical or quantum. While classical thermodynamics is able to achieve a great deal, it is philosophically difficult to reconcile the microscopic and macroscopic worlds without some statistical framework that can translate the former to the latter. Moreover, it allows us to determine the thermodynamic behavior of new systems that are hard to reason about a priori—how, for example, should we expect the stars in a star cluster to behave? What about a complicated, novel quantum field theory?

In this article, I will present a number of different derivations of the ideal gas law within the framework of statistical mechanics. In the process, I hope to motivate the different ensembles of statistical mechanics (which ultimately just encode the behavior of possibly large systems for which only a small amount of bulk information is known). In the process, I hope that an overview of these derivations will be a useful introduction for current physics students (or other interested people) to a notoriously (but arguably needlessly) opaque field.

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COVID-19 in the USA, Measured in Tragedies

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The last few months have been devastating to our societies, our economies, and our ability to get out of bed before attending meetings. In anticipation of the tumultuous days that inevitably lie immediately ahead, I wanted to get out some thoughts about the pandemic. COVID-19 is, among many other things, a collection of “big” numbers—more than 40 million cases worldwide, almost 1.2 million deaths, and so on. At least for me, when the numbers get this big, I have trouble visualizing them, and need a kind of visual aid. This post is going to be mostly USA-centric, simply because (1) I live here and (2) our collective response to COVID-19 has been comically egregious. I hope the interested reader can proportionately scale their anguish to the global scale.

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