High-accuracy simulation techniques for Many-Body Quantum Systems represent a frontier with significant opportunities for applied mathematics. These complex systems, characterized by intricate interactions among numerous particles, demand sophisticated computational methods to accurately capture their behavior. By leveraging high-accuracy techniques, such as advanced coupled cluster methods and quantum Monte Carlo simulations, applied mathematicians can develop and refine algorithms that enhance both precision and efficiency. This research thrust not only deepens our understanding of fundamental quantum phenomena but also drives innovation in fields like materials science, quantum chemistry, and condensed matter physics. By addressing the many-body problem, applied mathematics plays a pivotal role in unlocking new technological advancements and solving some of the most challenging computational problems in science.

At RPI's Mathematics Department, our research is centered at the intersection of mathematics and quantum chemistry, with a particular focus on fermionic many-body phenomena and the numerical methods used to simulate them. Given the highly interdisciplinary nature of this field, we employ two distinct research philosophies. First, we utilize an applied mathematics approach that translates modern quantum chemistry methods into a rigorous mathematical framework, enabling thorough analysis from a numerical perspective. Second, we adopt a computational mathematics approach to understand physical systems at the limits of computational complexity and to develop new numerical methods that extend these boundaries. This dual approach allows us to tackle some of the most challenging problems in computational mathematics and quantum chemistry, driving both theoretical and practical advancements.

Faculty Researchers: 

• Fabian Faulstich