Theses and Dissertations from UMD
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Item Lattice Quantum Chromodynamics (QCD) Calculations of Parton Physics with Leading Power Accuracy in Large Momentum Expansion(2023) Zhang, Rui; Ji, Xiangdong XJ; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Parton distributions describing how momenta of quarks and gluons are distributed inside a hadron moving at the speed of light, are important inputs to the Standard Model prediction of collider physics. Their non-perturbative nature makes traditional perturbative calculations from quantum field theory impossible. Besides a global fitting to experimental data, it is also possible to calculate parton physics from lattice QCD, a first-principle non-perturbative Monte Carlo simulation of the strong interaction on super computers. Among the different strategies to extract information for parton physics, the large momentum effective theory, based on a large momentum expansion of non-local Euclidean correlation functions, allows us to directly calculate the momentum-fraction or $x$-dependence. When matching the lattice-QCD calculations to the physical parton physics in the large momentum expansion, there are unavoidable power corrections in the expansion parameter $\Lambda_{\rm QCD}/P_z$, which is determined by the QCD characteristic non-perturbative scale $\Lambda_{\rm QCD}\approx300$~MeV and the hadron momentum $P_z$, and the leading term appears as $\mathcal{O}(\Lambda_{\rm QCD}/(2xP_z))$ due to the linear divergent self-energy of Wilson line in the Euclidean lattice correlators. For current lattice calculations of $P_z\sim 2-3$~GeV, this correction can be as large as $30\%$ at small $x$, dominating the uncertainties in the calculation. Achieving power accuracy in linear order of $\Lambda_{\rm QCD}/P_z$ is thus crucial for a high precision calculation of the parton physics from lattice QCD. In this dissertation, I summarize our work to eliminate this linear correction by consistently defining the renormalization for the linear divergence in lattice data and the resummation scheme of the factorially growing infrared-renormalon series in the perturbative matching. We show that the method significantly reduces the linear uncertainty by a factor of $\sim3-5$ and improves the convergence of the perturbation theory. We then apply the strategy to the calculation of pion distribution amplitude, which describes the pion light-cone wave function in a quark-antiquark pair. The method improves the short distance behavior of the renormalized lattice correlations, which is now consistent with the prediction of the short distance operator product expansion, showing a reasonable value for the moments of pion distribution amplitude. We also develop the first strategy to resum the large logarithms in the matching to physical pion distribution amplitude when the momentum of quark or antiquark in the pion are small, that could improve the accuracy of the prediction near the endpoint regions. After extracting the $x$-dependence from the large momentum expansion in mid-$x$ region, we complete the endpoint regions by fitting to the short distance correlations. Then a complete $x$-dependence is obtained for the pion distribution amplitude, which suggests a broader distribution compared to previous lattice QCD calculations or model predictions.Item LOSS IN SUPERCONDUCTING QUANTUM DEVICES FROM NON-EQUILIBRIUM QUASIPARTICLES AND INHOMOGENEITY IN ENERGY GAP(2020) Zhang, Rui; Wellstood, Frederick C.; Palmer, Benjamin S.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon T1 relaxation time and resonator quality factor QI, I observed reduced microwave loss as the temperature increased from 20 mK to approximately Tc/10 at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles. I measured the temperature dependence of the relaxation time T1 of the excited state of an Al/AlOx/Al transmon and found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best T1 of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short T1. Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing T1. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons. I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation (λ=1.55 μm). With no applied IR light, the internal quality factor increased from QI = 800,000 at T < 70 mK up to QI=(2×10^6 ) at 600 mK. The resonant frequency f0 increased by 2 parts per million over the same temperature range. Above 600 mK both QI and f0 decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below 1 aW μm^(-2) and T < 400 mK, QI increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.Item Mathematical Programming Models for Influence Maximization on Social Networks(2016) Zhang, Rui; Raghavan, Subramanian; Business and Management: Decision & Information Technologies; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we apply mathematical programming techniques (i.e., integer programming and polyhedral combinatorics) to develop exact approaches for influence maximization on social networks. We study four combinatorial optimization problems that deal with maximizing influence at minimum cost over a social network. To our knowl- edge, all previous work to date involving influence maximization problems has focused on heuristics and approximation. We start with the following viral marketing problem that has attracted a significant amount of interest from the computer science literature. Given a social network, find a target set of customers to seed with a product. Then, a cascade will be caused by these initial adopters and other people start to adopt this product due to the influence they re- ceive from earlier adopters. The idea is to find the minimum cost that results in the entire network adopting the product. We first study a problem called the Weighted Target Set Selection (WTSS) Prob- lem. In the WTSS problem, the diffusion can take place over as many time periods as needed and a free product is given out to the individuals in the target set. Restricting the number of time periods that the diffusion takes place over to be one, we obtain a problem called the Positive Influence Dominating Set (PIDS) problem. Next, incorporating partial incentives, we consider a problem called the Least Cost Influence Problem (LCIP). The fourth problem studied is the One Time Period Least Cost Influence Problem (1TPLCIP) which is identical to the LCIP except that we restrict the number of time periods that the diffusion takes place over to be one. We apply a common research paradigm to each of these four problems. First, we work on special graphs: trees and cycles. Based on the insights we obtain from special graphs, we develop efficient methods for general graphs. On trees, first, we propose a polynomial time algorithm. More importantly, we present a tight and compact extended formulation. We also project the extended formulation onto the space of the natural vari- ables that gives the polytope on trees. Next, building upon the result for trees---we derive the polytope on cycles for the WTSS problem; as well as a polynomial time algorithm on cycles. This leads to our contribution on general graphs. For the WTSS problem and the LCIP, using the observation that the influence propagation network must be a directed acyclic graph (DAG), the strong formulation for trees can be embedded into a formulation on general graphs. We use this to design and implement a branch-and-cut approach for the WTSS problem and the LCIP. In our computational study, we are able to obtain high quality solutions for random graph instances with up to 10,000 nodes and 20,000 edges (40,000 arcs) within a reasonable amount of time.