MULTISITE SPIN HOPPING ANALYSIS OF MULTILEVEL DISSIPATIVE QUANTUM TUNNELING AND COHERENCE AT FINITE TEMPERATURES .1. GENERAL-THEORY

A novel treatment is present of the real-time dynamics of a quantum mechanical (quasi-) particle in a dissipative bistable potential. Both the macroscopic quantum coherence (MQC) and the macroscopic quantum tunneling (MQT) regimes are covered. The theory allows for a unified treatment of the interplay of (either coherent or incoherent) tunneling transport and vibrational relaxation. Finite temperature effects are included ab initio. The analysis is based on the model-Hamiltonian for motion in a double-well potential coupled to a harmonic environment at nonzero temperature. The coupling is taken linear in both the system and the bath coordinates (a la Zwanzig-Caldeira-Leggett), while its spectral density will be of the ohmic type. The equivalent "particle-on-a-string" model (a la Dekker) is also discussed. Both the particle's operator Langevin equation and the equation of motion for the partially reduced density operator (still showing the free environmental operator fluctuations) are obtained. The ensuing density matrix equation is written in the energy representation. The energy spectrum consists of a ladder of vibrational doublets, the doublet splitting being determined by the tunneling (overlap of localized states). The localized states are treated in the harmonic-well approximation, which admits an explicit evaluation of the inter-doublet vibrational relaxation. The usual truncation to the ground state doublet (a la Leggett et al.) is not required. Upon coarsegraining (on a time scale of many vibrational periods) the inter-doublet dynamics considerably simplifies and represents a Markovian one-step hopping between adjacent doublets, which resemble sites on a lattice. The on-site intra-doublet dynamics represents a (pseudo-)spin-1/2 particle interacting with a bosonic bath.