*Andrew Lucas recognized for proving a conjecture about speed limits on quantum mechanical systems*

AIP Publishing has named Andrew Lucas winner of the 2020 Journal of Mathematical Physics Young Researcher Award.

The award, which comes with a $3,000 cash prize, will be presented to Lucas at the 2021 International Congress of Mathematical Physics (ICMP) in Geneva on August 4 in recognition of his 2020 paper, “Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model.”

“I am humbled to win the Young Researcher Award from JMP for the proof of a fast-scrambling conjecture,” said Lucas. “I was not trained as a mathematician or mathematical physicist. To receive this award for one of my first ventures into mathematical physics is especially meaningful.”

Lucas grew up in a family of engineers and mathematicians and went on to study physics at Stanford University. He received his doctorate from Harvard University in 2016, where he had a diverse array of research focuses, ranging from integrating condensed matter physics with string theory to studying hydrodynamics in quantum electron liquids.

In quantum mechanics, a measurable quantity, called an observable, can start off by initially only affecting one degree of freedom within the system, or one way in which the system can move. As the system evolves, changes – or perturbations – to the observable can eventually cause it to begin to act on all degrees of freedom simultaneously, leading to many complications and inspiring Lucas’ first foray into mathematical physics.

“The question was: Are there speed limits on how fast this process can happen? Namely, what is the time required for a tiny perturbation to affect the behavior of all degrees of freedom?” Lucas said.

The answer, known as the fast-scrambling conjecture, was previously predicted by string theorists but has been difficult to confirm. The novelty in Lucas’ winning paper is a mathematical proof of this conjecture, which required developing a new method for constraining quantum mechanical dynamics.

“The key contribution of this work was to take some handwavy and nonrigorous ideas coming from string theorists and translating those ideas into a mathematically rigorous language where I could show that the string theorists’ conjectures held when [the number of degrees of freedom] is large but finite,” Lucas said.

This opens the door to several new results, with potential implications in string theory and quantum gravity, as well as in experimentally realized quantum systems, including ultracold atoms interacting with light.

“I think it’s a really exciting moment. A lot of old conjectures and puzzles about locality are naturally phrased in terms of quantum walk-type behavior,” he said. “I hope that this recognition will lead to more interactions and, ultimately, collaboration with mathematicians who are interested in similar problems in many-body quantum physics.”

**ABOUT THE AWARD**

The Journal of Mathematical Physics Young Researcher Award aims to recognize outstanding research in mathematical physics by a Journal of Mathematical Physics author or coauthors. Candidates for the award must be within 8 years of receiving their doctoral degree, and the award will be given for a paper accepted in the Journal of Mathematical Physics within the previous year.

**ABOUT THE JOURNAL**

Journal of Mathematical Physics publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. See https://aip.scitation.org/journal/jmp

**ABOUT AIP PUBLISHING**

AIP Publishing is a wholly owned not-for-profit subsidiary of the American Institute of Physics (AIP). AIP Publishing’s mission is to support the charitable, scientific, and educational purposes of AIP through scholarly publishing activities in the fields of the physical and related sciences on its own behalf and on behalf of our publishing partners to help them proactively advance their missions.