On a Spectral Method for Calculating the Electrical Resistivity of a Low Temperature Metal from the Linearized Boltzmann Equation
| dc.contributor.advisor | Belitz, Dietrich | |
| dc.contributor.author | Amarel, James | |
| dc.date.accessioned | 2022-05-10T15:03:48Z | |
| dc.date.available | 2022-05-10T15:03:48Z | |
| dc.date.issued | 2022-05-10 | |
| dc.description.abstract | While it is well known that transport equations may be derived diagrammatically, both this approach and that of Boltzmann inevitably encounter an integral equation that both is difficult to solve and, for the most part, has yielded only to uncontrolled approximations. Even though the popular approximations, which are typically either variational in nature or involve dropping memory effects, can be expected to capture the temperature scaling of the kinetic coefficients, it is desirable to exactly obtain the prefactor by way of a mathematically justifiable approximation. For the purpose of so precisely resolving the distribution function that governs the elementary excitations of a metal perturbed by an externally applied static electric field, a spectral method was developed that makes use of the temperature as a control parameter to facilitate an asymptotic inversion of the collision operator; the technique leverages a singularity that is inherent to the Boltzmann equation in the low temperature limit, i.e. when the dissipating Boson bath is all but frozen out. This present dissertation is mainly concerned with the anomalous transport behavior that is commonly observed in quantum magnets; throughout a wide range of their phase diagram, materials such as the metallic ferromagnet ZrZn$_2$ display a power law behavior of the electrical resistivity $\rho \propto T^s$ with $s < 2$. As is thoroughly established, this non-Fermi-liquid like exponent $s$ does not arise solely due to the scattering of conduction electrons by phonons, magnons, or screened Coulomb fluctuations, for each of these soft excitations leads to $s > 2$ at temperatures $T \approx 10K$ (where ZrZn$_2$ exhibits $1.5 < s < 1.7$). After preliminarily investigating the electron-phonon system by way of rigorous reasoning, I will argue that the observed scaling of the residual resistivity $\rho \propto T^{3/2}$ in metallic ferromagnets can be attributed to interference between two scattering mechanisms: ferromagnons and static impurities. This dissertation includes previously published co-authoredmaterial. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/27145 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.title | On a Spectral Method for Calculating the Electrical Resistivity of a Low Temperature Metal from the Linearized Boltzmann Equation | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Physics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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