A time-dependent semiclassical formalism is developed for the theory of incoherentdiffractive imaging (IDI), an atomically-precise imaging technique based on the principles of intensity interferometry. The technique is applied to image inner-shell X-ray fluorescence from heavy atoms excited by the femtosecond pulses of an X-ray free-electron laser (XFEL). Interference between emission from different atoms is expected when the XFEL pulse duration is shorter than the fluorescence lifetime. Simulations for atoms at the vertices of a simple icosahedral virus capsid are used to generate mock IDI diffraction patterns. These are then used to reconstruct the geometry by phase retrieval of the intensity correlation function between photons emitted independently from many different atoms at two different detector pixels. The dependence of the intensity correlation function on fluorescence lifetime relative to XFEL pulse duration is computed, and a simple expression for the visibility (or contrast) of IDI speckle as well as an upper bound on the IDI signal-to-noise ratio are obtained as a function of XFEL flux and lifetime. This indicates that compact XFELs, with reduced flux but attosecond pulses, should be ideally suited to 3D, atomic-resolution mapping of heavy atoms in materials science, chemistry, and biology. As IDI is a new technique, not much has yet been written about it in the literature. The current theoretical and experimental results are reviewed, including a discussion of signal-to-noise issues that have been raised regarding the idea that IDI is suitable for structural biology.

I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to next-to-next-to-leading-order and the Argonne $v_6'$ interaction. Compared with diffusion based quantum Monte Carlo methods such as Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path integral quantum Monte Carlo has the advantage that it can directly calculate the expectation value of operators without tradeoff, whether they commute with the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g., the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo results. For other operator expectations which are important to understand nuclear measurements but do not commute with the Hamiltonian and therefore cannot be accurately calculated by diffusion based quantum Monte Carlo methods without tradeoff, the path integral quantum Monte Carlo method gives reliable results. I show root-mean-square radii, one-particle number density distributions, and Euclidean response functions for single-nucleon couplings. I also systematically describe all the sampling algorithms used in this work, the strategies to make the computation efficient, the error estimations, and the details of the implementation of the code to perform calculations. This work can serve as a benchmark test for future calculations of larger nuclei or finite temperature nuclear matter using path integral quantum Monte Carlo.

Quantum Monte Carlo is one of the most accurate ab initio methods used to study nuclear physics. The accuracy and efficiency depend heavily on the trial wave function, especially in Auxiliary Field Diffusion Monte Carlo (AFDMC), where a simplified wave function is often used to allow calculations of larger systems. The simple wave functions used with AFDMC contain short range correlations that come from an expansion of the full correlations truncated to linear order. I have extended that expansion to quadratic order in the pair correlations. I have investigated this expansion by keeping the full set of quadratic correlations as well an expansion that keeps only independent pair quadratic correlations. To test these new wave functions I have calculated ground state energies of 4He, 16O, 40Ca and symmetric nuclear matter at saturation density ρ = 0.16 fm−3 with 28 particles in a periodic box. The ground state energies calculated with both wave functions decrease with respect to the simpler wave function with linear correlations only for all systems except 4He for both variational and AFDMC calculations. It was not expected that the ground state energy of 4He would decrease due to the simplicity of the alpha particle wave function. These correlations have also been applied to study alpha particle formation in neutron rich matter, with applications to neutron star crusts and neutron rich nuclei. I have been able to show that this method can be used to study small clusters as well as the effect of external nucleons on these clusters.

The structure of glass has been the subject of many studies, however some

details remained to be resolved. With the advancement of microscopic

imaging techniques and the successful synthesis of two-dimensional materials,

images of two-dimensional glasses (bilayers of silica) are now available,

confirming that this glass structure closely follows the continuous random

network model. These images provide complete in-plane structural information

such as ring correlations, and intermediate range order and with computer

refinement contain indirect information such as angular distributions, and

tilting.

This dissertation reports the first work that integrates the actual atomic

coordinates obtained from such images with structural refinement to enhance

the extracted information from the experimental data.

The correlations in the ring structure of silica bilayers are studied

and it is shown that short-range and intermediate-range order exist in such networks.

Special boundary conditions for finite experimental samples are designed so atoms

in the bulk sense they are part of an infinite network.

It is shown that bilayers consist of two identical layers separated by a

symmetry plane and the tilted tetrahedra, two examples of

added value through the structural refinement.

Finally, the low-temperature properties of glasses in two dimensions

are studied. This dissertation presents a new approach to find possible

two-level systems in silica bilayers employing the tools of rigidity theory

in isostatic systems.

In this dissertation two kinds of strongly interacting fermionic systems were studied: cold atomic gases and nucleon systems. In the first part I report T=0 diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. I investigate how vortex core structure properties behave over the BEC-BCS crossover. The vortex excitation energy, density profiles, and vortex core properties related to the current are calculated. A density suppression at the vortex core on the BCS side of the crossover and a depleted core on the BEC limit is found. Size-effect dependencies in the disk geometry were carefully studied. In the second part of this dissertation I turn my attention to a very interesting problem in nuclear physics. In most simulations of nonrelativistic nuclear systems, the wave functions are found by solving the many-body Schrödinger equations, and they describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. By contrast, in this work I present a novel quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. I report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two nucleon sector the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and I fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. I conclude by showing that the method can be readily applied to light-nuclei.

This work presents analysis and results for the NPDGamma experiment, measuring

the spin-correlated photon directional asymmetry in the $\vec{n}p\rightarrow

d\gamma$ radiative capture of polarized, cold neutrons on a parahydrogen

target. The parity-violating (PV) component of this asymmetry

$A_{\gamma,PV}$ is unambiguously related to the $\Delta I = 1$ component of

the hadronic weak interaction due to pion exchange. Measurements in the second

phase of NPDGamma were taken at the Oak Ridge National Laboratory (ORNL)

Spallation Neutron Source (SNS) from late 2012 to early 2014, and then again in

the first half of 2016 for an unprecedented level of statistics in order to

obtain a measurement that is precise with respect to theoretical predictions of

$A_{\gamma,PV}=O(10^{-8})$. Theoretical and experimental background,

description of the experimental apparatus, analysis methods, and results for

the high-statistics measurements are given.

In this thesis, I present the study of nucleon structure from distinct perspectives. I start by elaborating the motivations behind the endeavors and then introducing the key concept, namely the generalized parton distribution functions (GPDs), which serves as the frame- work describing hadronic particles in terms of their fundamental constituents. The second chapter is then devoted to a detailed phenomenological study of the Virtual Compton Scattering (VCS) process, where a more comprehensive parametrization is suggested. In the third chapter, the renormalization kernels that enters the QCD evolution equations at twist- 4 accuracy are computed in terms of Feynman diagrams in momentum space, which can be viewed as an extension of the work by Bukhvostov, Frolov, Lipatov, and Kuraev (BKLK). The results can be used for determining the QCD background interaction for future precision measurements.

Sample delivery is an essential component in biological imaging using serial diffraction from X-ray Free Electron Lasers (XFEL) and synchrotrons. Recent developments have made possible the near-atomic resolution structure determination of several important proteins, including one G protein-coupled receptor (GPCR) drug target, whose structure could not easily have been determined otherwise (Appendix A). In this thesis I describe new sample delivery developments that are paramount to advancing this field beyond what has been accomplished to date. Soft Lithography was used to implement sample conservation in the Gas Dynamic Virtual Nozzle (GDVN). A PDMS/glass composite microfluidic injector was created and given the capability of millisecond fluidic switching of a GDVN liquid jet within the divergent section of a 2D Laval-like GDVN nozzle, providing a means of collecting sample between the pulses of current XFELs. An oil/water droplet immersion jet was prototyped that suspends small sample droplets within an oil jet such that the sample droplet frequency may match the XFEL pulse repetition rate. A similar device was designed to use gas bubbles for synchronized “on/off” jet behavior and for active micromixing. 3D printing based on 2-Photon Polymerization (2PP) was used to directly fabricate reproducible GDVN injectors at high resolution, introducing the possibility of systematic nozzle research and highly complex GDVN injectors. Viscous sample delivery using the “LCP injector” was improved with a method for dealing with poorly extruding sample mediums when using full beam transmission from the Linac Coherent Light Source (LCLS), and a new viscous crystal-carrying medium was characterized for use in both vacuum and atmospheric environments: high molecular weight Polyethylene Glycol.

Spin-orbit interactions are important in determining nuclear structure. They lead to a shift in the energy levels in the nuclear shell model, which could explain the sequence of magic numbers in nuclei. Also in nucleon-nucleon scattering, the large nucleon polarization observed perpendicular to the plane of scattering needs to be explained by adding the spin-orbit interactions in the potential. Their effects change the equation of state and other properties of nuclear matter. Therefore, the simulation of spin-orbit interactions is necessary in nuclear matter.

The auxiliary field diffusion Monte Carlo is an effective and accurate method for calculating the ground state and low-lying exited states in nuclei and nuclear matter. It has successfully employed the Argonne v6' two-body potential to calculate the equation of state in nuclear matter, and has been applied to light nuclei with reasonable agreement with experimental results. However, the spin-orbit interactions were not included in the previous simulations, because the isospin-dependent spin-orbit potential is difficult in the quantum Monte Carlo method. This work develops a new method using extra auxiliary fields to break up the interactions between nucleons, so that the spin-orbit interaction with isospin can be included in the Hamiltonian, and ground-state energy and other properties can be obtained.

Monte Carlo methods often used in nuclear physics, such as auxiliary field diffusion Monte Carlo and Green's function Monte Carlo, have typically relied on phenomenological local real-space potentials containing as few derivatives as possible, such as the Argonne-Urbana family of interactions, to make sampling simple and efficient. Basis set methods such as no-core shell model or coupled-cluster techniques typically use softer non-local potentials because of their more rapid convergence with basis set size. These non-local potentials are typically defined in momentum space and are often based on effective field theory. Comparisons of the results of the two types of methods are complicated by the use of different potentials. This thesis discusses progress made in using such non-local potentials in quantum Monte Carlo calculations of light nuclei. In particular, it shows methods for evaluating the real-space, imaginary-time propagators needed to perform quantum Monte Carlo calculations using non-local potentials and universality properties of these propagators, how to formulate a good trial wave function for non-local potentials, and how to perform a "one-step" Green's function Monte Carlo calculation for non-local potentials.