Doctor of Philosophy (PhD)
We use the Renormalization Group (RG) method within the perturbation theory framework to study properties of a balanced, two-dimensional Fermi gas with short-range, attractive interactions in non-superfluid (normal) phase. We find that the RG method allows for the evaluation of logarithmic corrections to Equations of State in various regimes of density and temperature. We present two calculations using RG with perturbation theory. The first being a simplified RG scheme with an interpolation of crossover between RG flow in different regimes. The second calculation features a rigorous derivation whereby the Green's function within a standard perturbation theory is renormalized to derive the density Equation of State. Calculations of associated observables like particle number density and isothermal compressibility via both of our approaches show agreement with experimental data using trapped balanced gases to varying degrees.
Uppalapati, Sri Laalitya, "Examining Interaction Effects in 2D Fermi Gases Using Renormalization Group Theory" (2020). LSU Doctoral Dissertations. 5150.