Quantum Monte Carlo study of effective masses in a polarized unitary Fermi gas

Ultracold gases provide an ideal platform for quantum simulations of many-body systems. Here we are interested in a particular system which has been the focus of most experimental and theoretical works on ultracold fermionic gases: the unitary Fermi gas. In this work we study with Quantum Monte Carlo simulations a two-component gas of fermionic atoms at zero temperature in the unitary regime. Specifically, we are interested in studying how the effective masses for the quasi-particles of the two components of the Fermi liquid evolve as the polarization is progressively reduced from full to lower values. A recent theoretical work, based on alternative diagrammatic methods, has indeed suggested that such effective masses should diverge at a critical polarization. To independently verify such predictions, we perform Variational Monte Carlo (VMC) calculations of the energy based on Jastrow-Slater wavefunctions after adding or subtracting a particle with a given momentum to a full Fermi sphere. In this way, we determine the quasi-particle dispersions, from which we extract the effective masses for different polarizations. The resulting effective masses turn out to be quite close to the non-interacting values, even though some evidence of an increase for the effective mass of the minority component appears close to the predicted value for the critical polarization. Preliminary results obtained for the majority component with the Fixed-node Diffusion Monte Carlo (DMC) method seem to indicate that DMC could lead to an increase of the effective masses in comparison with the VMC results. Finally, we point out further improvements of the trial wave-function and boundary conditions that would be necessary in future simulations to draw definite conclusions on the effective masses of the polarized unitary Fermi gas.

WEC-Sim Application for the Assessment of Wave Energy Generation in the Tyrrhenian Sea and the North Sea Through the 2-Body Point Absorber (2BPA) and the Oscillating Surge Wave Energy Converter (OSWEC)

In recent years, developed countries have turned their attention to clean and renewable energy, such as wind energy and wave energy that can be converted to electrical power. Companies and academic groups worldwide are investigating several wave energy ideas today. Accordingly, this thesis studies the numerical simulation of the dynamic response of the wave energy converters (WECs) subjected to the ocean waves. This study considers a two-body point absorber (2BPA) and an oscillating surge wave energy converter (OSWEC). The first aim is to mesh the bodies of the earlier mentioned WECs to calculate their hydrostatic properties using axiMesh.m and Mesh.m functions provided by NEMOH. The second aim is to calculate the first-order hydrodynamic coefficients of the WECs using the NEMOH BEM solver and to study the ability of this method to eliminate irregular frequencies. The third is to generate a *.h5 file for 2BPA and OSWEC devices, in which all the hydrodynamic data are included. The BEMIO, a pre-and post-processing tool developed by WEC-Sim, is used in this study to create *.h5 files. The primary and final goal is to run the wave energy converter Simulator (WEC-Sim) to simulate the dynamic responses of WECs studied in this thesis and estimate their power performance at different sites located in the Mediterranean Sea and the North Sea. The hydrodynamic data obtained by the NEMOH BEM solver for the 2BPA and OSWEC devices studied in this thesis is imported to WEC-Sim using BEMIO. Lastly, the power matrices and annual energy production (AEP) of WECs are estimated for different sites located in the Sea of Sicily, Sea of Sardinia, Adriatic Sea, Tyrrhenian Sea, and the North Sea. To this end, the NEMOH and WEC-Sim are still the most practical tools to estimate the power generation of WECs numerically.