Many-body approach to the BCS-BEC crossover for an imbalanced ultra-cold Fermi gas

The aim of this thesis is the study of the normal phase of a mass imbalanced and polarized ultra-cold Fermi gas in the context of the BCS-BEC crossover, using a diagrammatic approach known as t-matrix approximation. More specifically, the calculations are implemented using the fully self-consistent t-matrix (or Luttinger- Ward) approach, which is already experimentally and numerically validated for the balanced case. An imbalance (polarization) between the two spin populations works against pairing and superfluidity. For sufficiently large polarization (and not too strong attraction) the system remains in the normal phase even at zero temperature. This phase is expected to be well described by the Landau’s Fermi liquid theory. By reducing the spin polarization, a critical imbalance is reached where a quantum phase transition towards a superfluid phase occurs and the Fermi liquid description breaks down. Depending on the strength of the interaction, the exotic superfluid phase at the quantum critical point (QCP) can be either a FFLO phase (Fulde-Ferrell-Larkin-Ovchinnikov) or a Sarma phase. In this regard, the presence of mass imbalance can strongly influence the nature of the QCP, by favouring one of these two exotic types of pairing over the other, depending on whether the majority of the two species is heavier or lighter than the minority. The analysis of the system is made by focusing on the temperature-coupling-polarization phase diagram for different mass ratios of the two components and on the study of different thermodynamic quantities at finite temperature. The evolution towards a non-Fermi liquid behavior at the QCP is investigated by calculating the fermionic quasi-particle residues, the effective masses and the self-energies at zero temperature.

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.

Characterization Of Single Use Reactor Used For The Manufacturing Of Formulated Products Within The Pharmaceutical Industry

Mixing is a fundamental unit operation in the pharmaceutical industry to ensure consistent product quality across different batches. It is usually carried out in mechanically stirred tanks, with a large variety of designs according to the process requirements. A key aspect of pharmaceutical manufacturing is the extensive and meticulous cleaning of the vessels between runs to prevent the risk of contamination. Single-use reactors represent an increasing trend in the industry since they do not require cleaning and sterilization, reducing the need for utilities such as steam to sterilize equipment and the time between production batches. In contrast to traditional stainless steel vessels, single-use reactors consist of a plastic bag used as a vessel and disposed of after use. This thesis aims to characterize the fluid dynamics features and the mixing performance of a commercially available single-use reactor. The characterization employs a combination of various experimental techniques. The analysis starts with the visual observation of the liquid behavior inside the vessel, focusing on the vortex shape evolution at different impeller speeds. The power consumption is then measured using a torque meter to quantify the power number. Particle Image Velocimetry (PIV) is employed to investigate local fluid dynamics properties such as mean flow field and mean and rms velocity profiles. The same experimental setup of PIV is exploited for another optical measurement technique, the Planar Laser-Induced Fluorescence (PLIF). The PLIF measurements complete the characterization of the reactor with the qualitative visualization of the turbulent flow and the quantitative assessment of the system performance through the mixing time. The results confirm good mixing performances for the single-use reactor over the investigated impeller speeds and reveal that the filling volume plays a significant role in the fluid dynamics of the system.