Abstract:
We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon--nucleon interactions by means of Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and can provide quantitative understanding of problems in nuclear structure and astrophysics.

Abstract:
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

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:
While the shell model Monte Carlo approach has been successful in the microscopic calculation of nuclear state densities, it has been difficult to calculate accurately state densities of odd-even heavy nuclei. This is because the projection on an odd number of particles in the shell model Monte Carlo method leads to a sign problem at low temperatures, making it impractical to extract the ground-state energy in direct Monte Carlo calculations. We show that the ground-state energy can be extracted to a good precision by using level counting data at low excitation energies and the neutron resonance data at the neutron threshold energy. This allows us to extend recent applications of the shell-model Monte Carlo method in even-even rare-earth nuclei to the odd-even isotopic chains of $^{149-155}$Sm and $^{143-149}$Nd. We calculate the state densities of the odd-even samarium and neodymium isotopes and find close agreement with the state densities extracted from experimental data.

Abstract:
Quantum Monte Carlo methods have proven to be valuable in the study of strongly correlated quantum systems, particularly nuclear physics and cold atomic gases. Historically, such ab initio simulations have been used to study properties of light nuclei, including spectra and form factors, low-energy scattering, and high-momentum properties including inclusive scattering and one- and two-body momentum distributions. More recently they have been used to study the properties of homogeneous and inhomogeneous neutron matter and cold atomic gases. There are close analogies between these seemingly diverse systems, including the equation of state, superfluid pairing, and linear response to external probes. In this paper, we compare and contrast results found in nuclear and cold atom physics. We show updated lattice results for the energy of the homogeneous unitary Fermi gas and comparisons with neutron matter, as well as for the dependence of the cold atom energy on the mass ratio between paired particles, which yields insights on the structure of the ground state. We also provide new lattice and continuum results for the harmonically trapped unitary gas, again comparing neutron matter and cold atoms.

Abstract:
We present microscopic calculations of light and medium mass nuclei and the equation of state of symmetric and asymmetric nuclear matter using different nucleon-nucleon forces, including a new Argonne version that has the same spin/isospin structure as local chiral forces at next-to-next-to-leading order (N2LO). The calculations are performed using Auxiliary Field Diffusion Monte Carlo (AFDMC) combined with an improved variational wave function. We show that the AFDMC method can now be used to successfully calculate the energies of very light to medium mass nuclei as well as the energy of isospin-asymmetric nuclear matter, demonstrating microscopically the quadratic dependence of the energy on the symmetry energy.

Abstract:
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.

Abstract:
The role of Pauli potentials in the semiclassical simulation of Fermi gases at low temperatures is investigated. An alternative Pauli potential to the usual bivariate Gaussian form by Dorso et al. is proposed. This new Pauli potential allows for a simultaneous good reproduction of not only the kinetic energy per particle but also the momentum distribution and the two-body correlation function. The reproduction of the binding energies in finite nuclei in the low and medium mass range is also analyzed. What is found is that given a reasonable short-range atractive nuclear interaction one can include correlation effects in a suitable chosen density dependent Pauli potential.

Abstract:
The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sdpf- shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems.

Abstract:
Variational Monte Carlo and Green's function Monte Carlo are powerful tools for calculations of properties of light nuclei using realistic two-nucleon and three-nucleon potentials. Recently the GFMC method has been extended to multiple states with the same quantum numbers. The combination of the Argonne v_18 two-nucleon and Illinois-2 three-nucleon potentials gives a good prediction of many energies of nuclei up to 12C. A number of other recent results are presented: comparison of binding energies with those obtained by the no-core shell model; the incompatibility of modern nuclear Hamiltonians with a bound tetra-neutron; difficulties in computing RMS radii of very weakly bound nuclei, such as 6He; center-of-mass effects on spectroscopic factors; and the possible use of an artificial external well in calculations of neutron-rich isotopes.