University of North Carolina, Chapel Hill
Math was Casey Berger’s first love. “That was my area” in elementary, middle and high school, she says. “But I was also involved with theater and sang in a choir, so I really got to explore both sides of my personality.”
When she had to choose a major at Boston University, Berger picked film and television (she later added philosophy and earned dual bachelor’s degrees) and pursued a film production career. But a what-if question from a show-business mentor later prompted her to pursue a doctoral degree in theoretical and computational physics.
Now the Department of Energy Computational Science Graduate Fellowship (DOE CSGF) recipient focuses on the quantum mechanical world, where energy and matter interact as both particles and waves, at the University of North Carolina, Chapel Hill. Quantum physics always fascinated her, Berger says, but “it also blew my mind how little we actually understand about the way important elements of our universe work.” High-performance computing (HPC) is necessary to find answers.
With advisor Joaquín Drut, Berger develops techniques to solve the many-body Schrödinger equation, the canonical formula for describing a quantum system’s state. They focus on rotating bosons – elementary or composite particles, including certain nuclei, that have spin (a form of angular momentum) characterized as a whole number. Rotating bosons are found in large-scale phenomena like superfluids, which flow without losing kinetic energy, and superconducting materials, which allow electrons to move without resistance. Spinning a quantum system radically alters its properties, entering complex regimes that computer power has only recently made accessible.
Suppose someone wants to calculate the properties of a population, such as the average income of United States residents. “That’s a well-defined number,” Drut says. “You have a finite number of people, and you can calculate it easily.”
But for quantum systems, “you have a humongous number of elements that you want to average.” To cope with that larger space, researchers typically sample a range of probabilities and average them. Drut uses the quantum Monte Carlo method, named for the eponymous Monaco casino because it randomly tests probable values in a way that’s similar to games of chance.
But rotating quantum systems suffer from the sign problem. The probability is complex and “you find that the averages are all over the place,” Drut says. “They keep fluctuating.” This statistical noise, with averages oscillating between positive and negative and cancelling each other, obscures the final answer – an expected value, such as a quantum system’s total energy, that an experiment might find.
Berger and Drut tackle the problem with stochastic quantization, using these complex probabilities to help choose the samples. It handles the positive and negative pieces of the physics separately so they don’t cancel. A final step averages the two, zeroing out the negative and producing an expected value.
To test the algorithm, Berger and Drut recreated a model of a relativistic Bose gas, one comprised of bosons moving at a significant fraction of light speed. It showed the same sudden, sharp increase in density that a 2009 computation found.
The rotating bosons Berger focuses on, however, are low-energy systems, with atoms and particles moving at nonrelativistic energies. “That changes what kind of equation you use to solve the quantum mechanics,” she says. Berger rewrote the code and tested it on a problem with a precise answer: a nonrotating, noninteracting free boson gas. The algorithm produced statistical noise, prompting some adjustments to better balance its precision and efficiency.
The next step – adding rotation and particle interaction – increases the difficulty. A preliminary test found the algorithm again generated noisy data, Berger says. She’s since tweaked the code, producing results that agree with previous outcomes.
It’s a long way, physically and intellectually, from the talent management agency where Berger formerly worked. The company connects actors, writers and directors with projects and produces movies and TV shows.
The job was glamorous but Berger missed the intellectual engagement that had been part of her life. When a mentor asked Berger what she’d do if money was no object, she instantly said “go back to school to study astrophysics.”
Berger plans to research computational physics after graduation – in academia, she hopes – with a characteristically broad perspective. “Sometimes there are these wonderful secrets locked away in one area of physics that nobody has heard of in another area of physics,” she says. Methods like hers “can be used to make huge progress somewhere that had been stuck for a long time.”
Image caption: The complex Langevin method takes a complex physical system (in purple) and separates the real part of the physics (blue) from the imaginary part (red). Without this method, the noisy imaginary part of the system would drown out the real physical signal researchers want to understand. Credit: Casey Berger.
Read the entire article in DEIXIS, the DOE CSGF annual. [PDF, pages 10-12]