Thermodynamic and hydrodynamic behaviour of interacting Fermi gases
University of Cambridge
Department of Applied Mathematics and Theoretical Physics
Doctor of Philosophy (PhD)
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Goulko, O. (2012). Thermodynamic and hydrodynamic behaviour of interacting Fermi gases (Doctoral thesis). https://doi.org/10.17863/CAM.16110
Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.
Cold atoms, Interacting Fermi gas, Unitary Fermi gas, Quantum Monte Carlo, Superfluidity
This work was supported by the German Academic Exchange Service (DAAD), the Engineering and Physical Sciences Research Council (EPSRC) and the Cambridge European Trust. I am grateful to the Department of Applied Mathematics and Theoretical Physics (DAMTP), Wolfson College, the Cambridge Philosophical society, the ECT* in Trento, Durham University, the ENS in Paris and the Institute for Nuclear Theory at the University of Washington for providing me with travel grants and local financial support during conferences and meetings. This work has made use of the resources provided by the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/).
This record's DOI: https://doi.org/10.17863/CAM.16110
Attribution-NonCommercial-NoDerivs 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc-nd/2.0/uk/
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