Topics in Quantum Chaos and Thermoelectricity

Thesis Advisors: Profs. E. J. Heller and H. Ehrenreich This thesis consists of two parts. Part I is concerned with quantum chaos in two model systems in two dimensions, the stadium billiard and a chaotic doublewell potential. We study the localization properties of eigenfunctions in the stadium billiard, and conclude that there is more localization of the local density of states as a function of position in phase space than can be accounted for on the basis of random matrix theory. A part of this can be attributed to scars, but most of the excess localization is found to be due to symmetry eects originating in the parity and time-reversal symmetries. As for the double-well potentials, we study the connection between scarring of eigenfunctions and tunneling through the barrier, as reected in the level splittings. The level splittings oscillate as a function of energy, with period h in units of action, as expected if scarring plays a role in determining the size of the splitting. Indeed, the size of the splitting is directely correlated with the strength of scarring. Our results are interpreted within the framework of semiclassical theory