Multilevel tunneling and coherence: Dissipative spin-hopping dynamics at finite temperatures

Abstract

The real-time dynamics of a quantum-mechanical particle in a dissipative double-well potential at finite temperatures is solved ab initio by means of a multisite spin-hopping analysis. Both the macroscopic-quantum-coherence and macroscopic-quantum-tunneling regimes are covered. The theory gives a unified picture of tunneling transport and vibrational relaxation. The analysis is based on the Ohmic-model Hamiltonian [A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983); R. Zwanzig, J. Stat. Phys. 9, 215 (1973)] or the equivalent ``particle-on-a-string'' model [H. Dekker, Phys. Rev. A 31, 1067 (1985)]. The reduced quantum Liouville equation for the particle is derived and written in the energy representation. The usual truncation to the ground-state doublet of the vibrational ladder is not made. The interdoublet vibrational dynamics considerably simplifies upon coarse-graining and in the harmonic-well approximation. The intradoublet pseudospin dynamics is treated in the ``noninteracting-blip approximation'' [A. J. Leggett et al., Rev. Mod. Phys. 59, 1 (1987)]. The coarse-grained vibrational processes give rise to a Markovian one-step spin hopping between adjacent doublets (or sites). Inter alia ``inhomogeneous broadening'' and ``motional narrowing'' [P. E. Parris and R. Silbey, J. Chem. Phys. 83, 5619 (1985)] are discussed as special cases.