| In this thesis various aspects of electrical and thermoelectric transport are studied. Three specific problems are addressed in this regard. The first of these is the Nernst effect in type II superconductors discussed in Chapter 2. In this work the transverse thermoelectric coefficient alpha xy is measured in simulations of type-II superconductors in the vortex liquid regime, using the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise. The results are in reasonably good quantitative agreement with experimental data on cuprate samples, suggesting that this simple model of superconducting fluctuations contains much of the physics behind the large Nernst effect due to superconducting fluctuations observed in these materials.; In Chapter 3, strongly-correlated systems described by the Hubbard model in the atomic limit are studied and exact expressions for the chemical potential and thermopower are obtained. It is shown that these expressions reduce to the established Heikes formula in the appropriate limits (kB T ≫ U) and (kBT ≪ U) and the full temperature dependence in between these regimes is obtained. The effect of a magnetic field is investigated through the introduction of a Zeeman term and it is shown that the thermopower of the multi-orbital Hubbard model displays spikes as a function of magnetic field at certain special values of the field. This effect might be observable in experiments for materials with a large magnetic coupling.; Finally, in Chapter 4, a study of electrical transport at high temperatures in a model of strongly interacting spinless fermions without disorder is presented. Numerical exact diagonalization methods are used to study the statistics of the energy eigenvalues, eigenstates, and the matrix elements of the current. These suggest that the non-random Hamiltonian that is studied behaves like a member of a certain ensemble of Gaussian random matrices. The conductivity sigma(o) is calculated and its behavior is examined, both in finite size samples and as extrapolated to the thermodynamic limit. It is found that sigma(o) has a prominent non-divergent singularity at o = 0 reflecting a power-law long-time tail in the current autocorrelation function that arises from nonlinear couplings between the long-wavelength diffusive modes of the energy and particle number. |
