Mixed quantum-classical dynamics and statistical mechanics

grantor: University of TorontoMixed quantum-classical equations of motion are derived for a quantum subsystem of light particles interacting with a classical bath of massive particles. The resulting Liouville equation serves as a starting point for both dynamical and statistical mechanical studies. To elucidate the nature of the dynamics, the differential equation is reformulated as an iterated integral which involves a concatenation of classical evolution segments for the bath phase space coordinates separated by operators that change the quantum state and bath momenta. A hybrid molecular dynamics-Monte Carlo algorithm is constructed to solve the integral equation. The non-equilibrium statistical mechanics of mixed quantum-classical systems in the linear response regime is developed in analogy to full quantum mechanics by appealing to the formal algebraic structure of both theories. The structure of the equilibrium density matrix in the canonical ensemble and the common forms for equilibrium time correlation functions are analyzed. Some numerical results are presented for a two-level quantum subsystem coupled to low dimensional classical baths.Ph.D