Pedro Sáenz’s lab is making waves with math, using the behavior of fluids to improve our understanding of quantum particles.
Photo by Megan Mendenhall/UNC Research Stories
UNC Research Stories sat down with Pedro Sáenz, associate professor in the UNC College of Arts and Sciences’ math department, to learn more about his work at the Physical Mathematics Lab and why student research experiences matter.
Q: What’s the main goal of your research?
A: We study seemingly simple systems — like a dish of liquid on a vibrating table — to uncover complex behaviors that reflect some of nature’s biggest mysteries. It’s about finding big ideas hiding in systems that at first seem almost trivial.
Q: What projects are you working on now?
A: My team studies how tiny droplets “walk” across the surface by bouncing and creating waves that push them forward. These droplets behave in ways that resemble quantum particles — the fundamental building blocks of matter and energy, such as electrons and photons. This gives us a new way to explore the strange and fascinating world of quantum physics, but in a system we can actually see and measure. Our main focus is how these “walking droplets” mimic quantum behaviors like tunneling and interference.
We’ve also discovered “galloping bubbles” that move in unexpected ways. Even though the mechanism is different from that of walking droplets, many of the underlying principles are the same. With this new way of making bubbles motile, we’re starting to explore potential engineering applications.
Q: What are the biggest challenges in your research?
A: We’re often exploring phenomena that haven’t been studied before, so there’s no clear roadmap. We keep our setups simple and take small, logical steps to uncover the physics. We also approach problems from every angle — experiments, simulations and theory — which takes time but leads to deeper understanding.
Q: What’s the most surprising discovery your team has made recently?
A: We found that walking droplets can exhibit a behavior called Anderson localization, where droplets get trapped instead of spreading, even though they have enough energy to keep moving. This trapping arises from the waves the droplets themselves generate, and until now we thought that this phenomenon was exclusive to quantum particles. Seeing this in a fluid system was unexpected and shows how rich and subtle these droplet behaviors can be.
Q: If your research could solve one big problem, what would it be?
A: We would love to resolve the odd behaviors and paradoxes of quantum particles from a new perspective. Quantum mechanics is an extremely successful theory, but several of its foundational principles are very strange and difficult to accept. If our work could offer a new way to see and understand these mysteries, it could change how we think about physics.
Q: What’s the coolest tool you use in the lab?
A: Our high-speed cameras let us slow down time and see what’s happening when droplets bounce, waves form or bubbles deform. To the naked eye everything looks chaotic, but when you record thousands of frames per second you suddenly see a precise sequence of events and patterns that were hidden before.
Our custom vibrating tables are just as important because they give us unprecedented precision in how we drive the fluid. Even tiny changes in vibration can completely alter the dynamics, so having that level of control is what makes our experiments possible. Together, these tools let us reveal and measure behaviors that would otherwise remain invisible.
Q: What do students gain from working with you?
A: They learn how to design experiments, use advanced equipment and analyze data. They also usually pick up coding and simulation skills. Just as important, they learn how to tackle open-ended problems where there isn’t a clear answer and stick with a project from start to finish.