Classical and Quantum Statistical Mechanics

Usually, making measurements in a quantum system reduces the degree of entanglement between its constituent parts, as measurement leads to a collapse of the wave function. But this does not have to be the case for a system of Majorana fermions, whose state is always defined with respect to a pairwise "parity" between two particles. We showed that, when a system of Marjoanas undergoes a process of random measurement, long-range entanglement is generated by the measurement process. We studied the dynamics of this entanglement, as well as the properties of the final (critically-entangled) state. We were able to solve the problem exactly by mapping it to a classical problem of closely-packed loops in two dimensions. 

Paper: Phys. Rev. Research 2, 023288 (2020).

"Superspreading" is the phenomenon where a small minority of infected individuals produce the vast majority of new infections. Superspreading is generally inferred through laborious contact tracing studies. We developed a direct method to infer the degree of superspreading by looking only at the case count as a function of time for different geographic regions. We applied our method to data from the early stages of the COVID-19 pandemic, and demonstrated pervasive superspreading, to the tune of > 80% of new cases caused by only 10% of infectious individuals. 

Paper: PLoS ONE 16(3): e0248808 (2021). 

Twitter summary here.

In a quantum many-body system, unitary (quantum) evolution tends to increase the amount of entanglement between subsystems. But if an external observer makes occasional measurements on the system, these measurements tend to have the effect of reducing the total entanglement, by collapsing some of the degrees of freedom in the wave function. We found a way to describe the tradeoff between these two tendencies using the language of a random resistor network, where measurements act like "broken links" in a resistor grid. The mapping makes clear that there is a dynamical phase transition between "entangling" and "disentangling" dynamical states as a function of the rate of measurement.

Paper: Phys. Rev. X 9, 031009 (2019).

arXiv: 2009.11311 (2020)

See also this news article at Phys.org

One of the primary functions of prestige in society is to bias the way that a person is evaluated by others. Absent other information, those belonging to a prestigious group are assumed to have more ability than those who don't. We found a way to model this "prestige bias" using the language of Bayesian inference, and we studied its effect over iterated rounds of examination and evaluation. Most strikingly, we found that as a function of decreasing examination precision there is a phase transition in the weight given to prestigious affiliation. At low exam precision, a "runaway bias" effect happens, leading to a "prestige class" that freezes out and excludes others even when their ability is high.

Paper: arxiv:1910:05813 (2019)

Twitter summary here.

We looked at the question of how people navigate through crowds, using tools from the study of correlated electron gases. After analyzing large data sets from around the world, we found a surprisingly simple law that governs the motion of pedestrians in a crowd. Namely, the "interaction energy" between two pedestrians is proportional to the inverse square of their projected time to collision.

Paper: Phys. Rev. Lett. 113, 238701 (2014)

See also articles in the Boston Globe and Nature News

In this game of basketball, choosing which plays to call and which strategies to use is a complicated optimization problem, owing to the interactions between the outcomes of different plays and the game-theoretical interaction between the two competing teams. Some insight can be gained into this optimization problem from the problem of optimizing flow through a congestible network. Most surprisingly, there is an analog of "Braess's Paradox", where forcibly removing a play (or a player) from the offense can improve its performance.

See this book chapter, which summarizes a range of work.