Arts & Sciences Events
[PAST EVENT] Arjun Singh Gambhir: Physics Dissertation Defense
Abstract: In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called ? disconnected diagrams? and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei.
The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.
Bio: Arjun Singh Gambhir was born and raised in Fairfax, Virginia. From 2007-2011 he attended Virginia Tech, where he graduated with a B.S. in physics and minor in astronomy. Subsequently, he spent a year at Georgetown University teaching and researching in physics education. He entered William & Mary in the fall of 2012 and started working with Kostas Orginos and Jefferson Lab's lattice group in the summer of 2013. His research interests include algorithms relevant for high performance computing, hadron structure, and numerical methods in lattice gauge theory. After graduation he will be joining the Department of Physics at University of California, Berkeley as a Visiting Scholar and Lecturer and also the Nuclear and Chemical Sciences Division at Lawrence Livermore National Laboratory as a Postdoctoral Research Staff Member.