Studies of two-dimensional electron gas on the surface of liquid helium, and three-dimensional solid helium-four, focussing on evidence for quantum tunnelling of electrons or helium atoms. The solid helium-four study will be conducted using ultrasonic attenuation, thermal conductivity, heat capacity and heat pulse propagation experiments to look for quasiparticle excitations, defect behavior, and evidence for the formation of a "supersolid"-- the solid state analogue of a superfluid. Measurements of the escape rate of electrons from the surface of liquid helium will be performed in order to characterize the groundstate and excitations of the two-dimensional electron system.
