| Abstract | Experimental measurements of the lifetime of positrons and positronium and the mobility of electrons show dramatic changes when the host fluid is in the vicinity of the liquid-vapor critical point. Since the compressibility diverges at the critical point, we understand that a low-mass quantum particle (qp) disturbs the local fluid density and stabilizes in a mesoscopic droplet or bubble. We refer to this phenomenon as ?self-trapping?. Theoretical formulations of self-trapping have taken two different routes: mean field theory where the Schrodinger equation governing the qp is solved in the averaged local potential produced by the fluid bubble or droplet, or path integral Monte Carlo (PIMC) where the qp is represented by an imaginary time Feynman-Kac path integral interacting with the (classical) fluid molecules. While the complete range of fluctuations is taken into account by PIMC, convergence is prohibitively difficult to obtain. A primitive model of a fluid with a critical point that can be conveniently modeled is provided by the two-dimensional lattice gas. To explore self-trapping in a lattice gas, in this dissertation PIMC was reformulated for a quantum particle that lives on a lattice and interacts with the coexisting ?atoms?. To test the viability of the formulation, the predictions of the lattice PIMC were compared with two analytically solvable, one-dimensional, quenched models. Finally it was shown that the fully annealed hybrid, two-dimensional lattice gas-qp system exhibits the phenomena of self-trapping and captures the essential features of the experimental measurements.--Abstract. |
