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The theory of quantum chromodynamics (QCD) encodes the strong interactions that bind quarks and gluons into nucleons and that bind nucleons into nuclei. Predictive control of QCD would allow nuclear structure and reactions as well as properties of supernovae and neutron stars to be theoretically studied from first principles. Lattice QCD can represent generic QCD predictions in terms of well-defined path integrals, but the sign and signal-to-noise problems have obstructed lattice QCD calculations of large nuclei and nuclear matter in practice. This thesis presents a statistical study of lattice QCD correlation functions, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in baryon correlation functions is demonstrated to arise from a sign problem associated with Monte Carlo sampling of complex correlation functions. The phases of complex correlation functions are analyzed in the framework of circular statistics, and the time evolution of the phase is shown to resemble a heavy-tailed random walk on the unit circle. Building on these observations, a new technique called phase reweighting is investigated that involves calculations of phase differences over fixed-length time intervals. Phase reweighting allows results for hadronic observables to be extracted from large-time correlation functions with constant signal-to-noise ratios. The signal-to-noise problem re-emerges as the length of the phase-difference interval is increased. Applications of phase reweighting to meson, baryon, and two-baryon systems are discussed.
Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo est
Path integrals describing quantum many-body systems can be calculated with Monte Carlo sampling techniques, but average quantities are often subject to signal-to-noise ratios that degrade exponentially with time. A phase-reweighting technique inspire
Ideas and recent results for light-front Hamiltonian quantisation of lattice gauge theories.
The long standing problem is solved why the number and the location of monopoles observed in Lattice configurations depend on the choice of the gauge used to detect them, in contrast to the obvious requirement that monopoles, as physical objects, mus
We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ Me