She memorized 200+ Taylor Swift songs: Now this 18-year-old Los Angeles girl has won $100,000 for her quantum physics research

An eighteen-year-old student from Los Angeles, identified as Rachel Chen, has developed a concrete, visual way to describe quantum physics systems for her Regeneron Science Talent Search mathematics project, according to Society for Science. She also won $100,000 at the Regeneron Science Talent Search for expanding a 1997 mathematical idea involving Temperley-Lieb diagrams. Rachel Chen took decades-old mathematical idea and expanded it into a visual framework for understanding complex quantum systems.

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Her research builds on a 1997 mathematical discovery involving Temperley-Lieb diagrams—simple point-and-curve representations that help illustrate aspects of quantum systems. Chen takes this idea further, using it to explain how an entire system of quantum particles behaves when exposed to a magnetic field. The approach could give researchers a more intuitive way to understand the connections and interactions between different quantum-mechanical states.

How Rachel Chen turned complex quantum physics into diagrams

Since quantum particles interact with their environment in complex ways, it is hard to describe these systems mathematically. A 1997 paper showed that part of the quantum system could be described using simple point-and-curve graphics called Temperley-Lieb diagrams. Researchers across mathematics and physics use these diagrams as an intuitive tool for understanding phase transitions, mathematical knots and other concepts.

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Rachel expanded on the 1997 work, using Temperley-Lieb diagrams to describe how an entire system of quantum particles acts under the influence of a magnetic field. This may be useful as an intuitive framework for researchers to understand the structure and connections among different quantum-mechanical states. She also used her results to understand alternative ways of working with the quantum system.

What are Temperley-Lieb diagrams?

Temperley-Lieb diagrams are simple drawings made with dots placed along lines and curves connecting the dots. While they look basic, they can represent complicated mathematical relationships.

Mathematicians and physicists use these diagrams to study difficult ideas, including phase transitions and mathematical knots. Chen showed that the diagrams can also be used as building blocks to represent a complicated quantum system called a spin representation.

She then connected these diagrams to an important mathematical structure called Lusztig's dual canonical basis.

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A new mathematical formula

A major part of Chen's research focused on the dual canonical basis. Before her work, researchers did not have a direct, non-inductive formula for this basis in the spin representation.

Using her diagram-based method, Chen developed what she described as the first explicit formula for the dual canonical basis of the spin representation.

She also used the diagrams to check earlier mathematical results. Her work showed that the diagram approach agreed with existing research before she used it to develop new findings.

Chen's research also looked at the Hecke algebra, another important mathematical structure. She provided a new way to describe the canonical basis of the spin representation using a set of basic rules, known as an axiomatic description.

Making complex quantum systems easier to understand

The importance of Chen's work is not just that she created simple-looking mathematical diagrams. More importantly, she used those diagrams to make very complicated quantum systems easier to understand and visualize.

Her approach could give researchers a more intuitive way to study how different quantum-mechanical states are connected.

Chen also expanded her ideas to study systems containing multiple electrons. She showed that her diagrams can illustrate how a complicated system of many electrons can be broken down into several single-particle systems.

A Taylor Swift fan

Rachel is an internationally ranked chess player and won the Pan-American Chess Festival in her age group in 2022. She is also Contests Director for Athemath, a nonprofit that builds community for girls interested in math.

The child of Zhaoxu Chen and Jing Che, Rachel attends Marlborough School, where she plays volleyball and founded the math club.

Rachel is a devoted Taylor Swift fan and has memorized more than 200 of her songs. She is also the founder of her school’s math club, which now has over 100 members.