Wolfram Computation Meets Knowledge

Wolfram Summer School


Yingyue (Amy) Boretz

Science and Technology

Class of 2016


Yingyue Boretz earned her PhD in theoretical physics in 2013 from the University of Texas at Austin. Currently, she works as a postdoctoral research fellow at UT Austin. During her graduate studies, she developed special interests and expertise in quantum measurement theory and the quantum Zeno and anti-Zeno effects. For her postdoctoral work, she focused on nonlinear classical dynamics. She has developed a general method to study chaos in wave propagations in the periodic medium. Besides physics, she loves food, hiking and horses.

Project: Poincaré Phase Section for 3-DOF System

The Poincaré phase section (PPS) is one of the best tools to study a chaotic system. However, there is a limitation with such a method: we know that for a system that has two degrees of freedom (DOF), there are four dimensions in phase space. For a conserved energy system, we can plot a Poincaré section energy surface. Thus, the dimensions can be reduced to three DOF, and we can further reduce the dimensions to two by choosing one dimension as an intersection condition. Thus, we would be able to make a two-dimensional PPS. However, most systems in nature have three DOF, which are six dimensions in phase space. Plotting out the PPS becomes very challenging.

In our project, the goal is to make a PPS for a 3-DOF system by taking an unconventional approach—namely, using machine learning techniques. We employ principal component analysis (PCA) to reduce the dimensions of our system. We also plan to see how well PCA can reduce the dimensions of “random” differential equations with many more dimensions than six.

The model considers a gas of non-interacting particles of mass m interacting with a body-centered cubic (BCC) lattice formed by the superposition of three pairs of mutually perpendicular laser beams. We want to investigate the dynamics of an atom inside the lattice by changing the couplings between the laser beams. The Hamiltonian can be written as the following: