Topological aspects of system-bath Hamiltonians and a vector model for multisite systems coupled to local, correlated, or common baths

Some topological features of multisite Hamiltonians consisting of harmonic potential surfaces with constant site-to-site couplings are discussed. Even in the absence of Duschinsky rotation, such a Hamiltonian assumes the system-bath form only if severe constraints exist. The simplest case of a common bath that couples to all sites is realized when the potential minima are collinear. The bath reorganization energy increases quadratically with site distance in this case. Another frequently encountered situation involves exciton-vibration coupling in molecular aggregates, where the intramolecular normal modes of the monomers give rise to local harmonic potentials. In this case, the reorganization energy accompanying excitation transfer is independent of site-to-site separation, thus this situation cannot be described by the usual system-bath Hamiltonian. A vector system-bath representation is introduced, which brings the exciton-vibration Hamiltonian in system-bath form. In this, the system vectors specify the locations of the potential minima, which in the case of identical monomers lie on the vertices of a regular polyhedron. By properly choosing the system vectors, it is possible to couple each bath to one or more sites and to specify the desired initial density. With a collinear choice of system vectors, the coupling reverts to the simple form of a common bath. The compact form of the vector system-bath coupling generalizes the dissipative tight-binding model to account for local, correlated, and common baths. The influence functional for the vector system-bath Hamiltonian is obtained in a compact and simple form.