In this work, we develop effective field theory (EFT) methods for the study of a wide variety of condensed matter systems, including superfluids, ordinary fluids, solids, and supersolids. As a first application, we focus on the dynamics of vortex lines in trapped superfluid condensates, studying their precessional motion and working out the frequency of precession from EFT principles. We consider the effects of trapping in two and three dimensions, as well as implications of trapping for the dispersion relation of Kelvin waves along superfluid vortex lines. We also apply our formalism to study the effects of gravitational fields on sound waves in several different media, discovering that localized sound waves propagate with an associated (negative) net mass, which in turn generates a tiny gravitational field. We confirm that this effect is a robust result that can be found from purely classical, non-relativistic methods. We then present three Lorentz invariant, renormalizable, weakly coupled theories that implement the symmetry-breaking pattern of a perturbative homogeneous and isotropic solid, as potential UV-completions of the low-energy effective theory that we studied. We demonstrate that a particular class of homogeneous, isotropic solids at long distances corresponds to states that are also homogeneous at short distances, unlike typical solids found in nature. We find that each case leads to the same rather unorthodox effective theory of a solid with luminal transverse excitations. Finally, we discuss applications of the methods we have developed and the potential for interesting new directions of this research.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-1qfm-g768 |
| Date | January 2020 |
| Creators | Krichevsky, Rafael |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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