Thermal Bath Modeling in Open Quantum and Quantum-Classical Systems

A predictive description of a chemical process in the condensed phase requires the elimination of the overwhelming majority of the degrees of freedom in favour of their averaged statistical influence upon a small set of retained coordinates. The quantity characterizing that influence differs according to whether the retained coordinates are propagated classically or quantum mechanically: the classical reduction retains a friction kernel, defined as a conditional equilibrium correlation function of the environmental force, whereas the quantum reduction retains the power spectrum of the bath operator to which the system couples. This thesis establishes the conditions under which these two descriptors characterize the same environment, quantifies the dynamical consequences of their violation, and measures the classical descriptor for a solvated molecular photoswitch. A single projection-operator derivation yields both reductions and supplies microscopic definitions of the friction tensor and of the fluctuating force. A harmonic environment bilinearly coupled to the system coordinate relates the two descriptors exactly, and the conditions this model imposes are enumerated. The correspondence is then tested numerically upon a two-state photoisomerization model, propagated both by a vibronic Redfield equation and by the quantum-stochastic Liouville equation. The form of the system-bath coupling operator alone is found to determine the branching ratio, which spans the full accessible range at fixed bath parameters; quantitative agreement between the two descriptions is attainable, but only at a friction exceeding the value dictated by the correspondence by two orders of magnitude. The descriptor is subsequently measured rather than postulated. A protocol extracting the conformation-dependent friction from the fluctuations of the generalized force along a restrained torsion is developed, validated upon a coarse-grained model, and applied to 4,4'-dihydroxyazobenzene in explicit water. The friction varies by a factor of 6.8 along the isomerizing coordinate, is maximal at the planar geometries and minimal at the perpendicular one, and is steric rather than dielectric in origin. This topology is the inverse of that implied by the coupling operators employed in the preceding benchmark, and thereby excludes them.