Abstract:
In this thesis, I discuss the use of the Auxiliary Field Diffusion Monte Carlo method to compute the ground state of nuclear Hamiltonians, and I show several applications to interesting problems both in nuclear physics and in nuclear astrophysics. In particular, the AFDMC algorithm is applied to the study of several nuclear systems, finite, and infinite matter. Results about the ground state of nuclei ($^4$He, $^8$He, $^{16}$O and $^{40}$Ca), neutron drops (with 8 and 20 neutrons) and neutron rich-nuclei (isotopes of oxygen and calcium) are discussed, and the equation of state of nuclear and neutron matter are calculated and compared with other many-body calculations. The $^1S_0$ superfluid phase of neutron matter in the low-density regime was also studied.

Abstract:
In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the $Li-K$ Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas.

Abstract:
We present an overview of microscopical calculations of the Equation of State (EOS) of neutron matter performed using Quantum Monte Carlo techniques. We focus to the role of the model of the three-neutron force in the high-density part of the EOS up to a few times the saturation density. We also discuss the interplay between the symmetry energy and the neutron star mass-radius relation. The combination of theoretical models of the EOS with recent neutron stars observations permits us to constrain the value of the symmetry energy and its slope. We show that astrophysical observations are starting to provide important insights into the properties of neutron star matter.

Abstract:
We present an ab-initio study of neutron drops. We use Quantum Monte Carlo techniques to calculate the energy up to 54 neutrons in different external potentials, and we compare the results with Skyrme forces. We also calculate the rms radii and radial densities, and we find that a re-adjustment of the gradient term in Skyrme is needed in order to reproduce the properties of these systems given by the ab-initio calculation. By using the ab-initio results for neutron drops for close- and open-shell configurations, we suggest how to improve Skyrme forces when dealing with systems with large isospin-asymmetries like neutron-rich nuclei.

Abstract:
The structure of neutron stars is determined by the equation of state of the matter inside the star, which relies on the knowledge of nuclear interactions. While radii of neutron stars mostly depend on the equation of state of neutron matter at nuclear densities, their maximum mass can be drastically affected by the appearance of hyperons at higher densities in the inner core of the star. We summarize recent quantum Monte Carlo results on the calculation of the equation of state of neutron matter at nuclear and higher densities. We report about the development of realistic hyperon-nucleon interactions based on the available experimental data for light- and medium-heavy hypernuclei and on the effect of $\Lambda$ hyperons to the neutron star structure.

Abstract:
Recent progress in quantum Monte Carlo with modern nucleon-nucleon interactions have enabled the successful description of properties of light nuclei and neutron-rich matter. As a demonstration, we show that the agreement between theoretical calculations of the charge form factor of 12C and the experimental data is excellent. Applying similar methods to isospin-asymmetric systems allows one to describe neutrons confined in an external potential and homogeneous neutron-rich matter. Of particular interest is the nuclear symmetry energy, the energy cost of creating an isospin asymmetry. Combining these advances with recent observations of neutron star masses and radii gives insight into the equation of state of neutron-rich matter near and above the saturation density. In particular, neutron star radius measurements constrain the derivative of the symmetry energy.

Abstract:
We extract the leading effective range corrections to the equation of state of the unitary Fermi gas from ab initio fixed-node quantum Monte Carlo (FNQMC) calculations in a periodic box using a density functional theory (DFT), and show them to be universal by considering several two-body interactions. Furthermore, we find that the DFT is consistent with the best available unbiased QMC calculations, analytic results, and experimental measurements of the equation of state. We also discuss the asymptotic effective-range corrections for trapped systems and present the first QMC results with the correct asymptotic scaling.

Abstract:
Neutron matter is an intriguing nuclear system with multiple connections to other areas of physics. Considerable progress has been made over the last two decades in exploring the properties of pure neutron fluids. Here we begin by reviewing work done to explore the behavior of very low density neutron matter, which forms a strongly paired superfluid and is thus similar to cold Fermi atoms, though at energy scales differing by many orders of magnitude. We then increase the density, discussing work that ties the study of neutron matter with the determination of the properties of neutron-rich nuclei and neutron-star crusts. After this, we review the impact neutron matter at even higher densities has on the mass-radius relation of neutron stars, thereby making contact with astrophysical observations.

Abstract:
An accurate assessment of the hyperon-nucleon interaction is of great interest in view of recent observations of very massive neutron stars. The challenge is to build a realistic interaction that can be used over a wide range of masses and in infinite matter starting from the available experimental data on the binding energy of light hypernuclei. To this end, accurate calculations of the hyperon binding energy in a hypernucleus are necessary. We present a quantum Monte Carlo study of $\Lambda$ and $\Lambda\Lambda$ hypernuclei up to $A=91$. We investigate the contribution of two- and three-body $\Lambda$-nucleon forces to the $\Lambda$ binding energy. Ground state energies are computed solving the Schr\"odinger equation for non-relativistic baryons by means of the auxiliary field diffusion Monte Carlo algorithm extended to the hypernuclear sector. We show that a simple adjustment of the parameters of the $\Lambda NN$ three-body force yields a very good agreement with available experimental data over a wide range of hypernuclear masses. In some cases no experiments have been performed yet, and we give new predictions. The newly fitted $\Lambda NN$ force properly describes the physics of medium-heavy $\Lambda$ hypernuclei, correctly reproducing the saturation property of the hyperon separation energy.

Abstract:
We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: 1) an ab initio Quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and 2) a new Density Functional Theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: \xi_S <= 0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.