Quantum Dynamics Methods Based on the Real-Time Path Integral

This Chapter describes path integral methods for studying the dynamics of quantum systems in large (polyatomic or condensed-phase) environments. The path integral formulation allows the analytical elimination of quadratic degrees of freedom at any temperature, offering a major advantage in the case of system-bath Hamiltonians. Stable and efficient fully quantum mechanical algorithms for propagating the reduced density matrix of continuous or discrete systems coupled to one or multiple harmonic baths are described, and available methods for more complex Hamiltonians are discussed.