Interplay of disorder and interaction in electron gas on liquid helium and in quantum dots

We study nontrivial effects resulting from the interplay of interactions and disorder in an electron gas. The particular systems we investigate are electrons on liquid helium and closed quantum dots.; In the first part of the thesis we analyze quantum correction to the classical Drude conductance for non-degenerate electrons on the surface of liquid helium. We show that the interference of closed electron paths in this system is suppressed by an exponential cubic factor due to thermal motion of helium vapor atoms. We test our theory by a detailed comparison to experimental data which reveals that the usual exponential dephasing is also present and it is a consequence of electron-electron interaction.; We also derive analytic asymptotic formulae for the conductance peak spacing distribution in closed GaAs quantum dots using Universal Hamiltonian description in conjunction with Random Matrix Theory. Our formulae are in excellent agreement with brute-force numerical simulations and should significantly simplify experimental data analysis. In addition, we find new classes of Universal Hamiltonians that are applicable to silicon MOSFETs. The main difference from the GaAs quantum dots is that in MOSFETs electrons carry a valley index that results in qualitatively different and much richer physics.; As another application of Random Matrix Theory we study the fluctuations of order parameter in isotropic phase of nanodroplets in nematic liquid crystals.