The Local Coherent-State Approach to System-Bath Quantum Dynamics and Its Extensions

So called system-bath problems arise naturally in chemistry and physics, e.g. in gas-surface processes or reactions in condensed phase. Solution of these problems is enormously difficult in quantum mechanics. The most elegant and promising approaches relying on reduced equations of motion for the system density operator are presently limited to severe approximations, e.g. weak system-bath coupling and short bath correlation time. Here we consider the possibility of approximately following the unitary evolution of the whole system-bath state(s), in the spirit of the surrogate hamiltonian approach (R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)), and discuss a number of approximations specifically tailored for this problem. These approximations are mainly in the bath description, whose dynamics is not of direct relevance for our purposes. Starting with the recently introduced Local Coherent-State Approximation (LCSA) (R. Martinazzo, M. Nest, P. Saalfrank and G.F. Tantardini, J. Chem. Phys. 125, 194102 (2006)) for the T=0 K dynamics, we introduce a number of its generalizations. These include (i) a non-local variant using time-dependent system states, which more closely resembles the Gaussian MultiConfuration Time-Dependent Hartree (G-MCDTH) method (I. Burghardt, H.-D. Meyer and L.S. Cederbaum, J. Chem. Phys. 111, 2927 (1999)) with selected configurations; (ii) locally multiconfigurational variants which relaxe the Hartree approximation for the local bath states; (iii) generalized mixed quantum-classical approaches, in which locality is reduced and each bath configuration is used for groups of system DVR states. All these approaches are designed to scale linearly with respect to the bath dimensions. Applications to model system-bath problems at T=0 K (e.g. vibrational relaxation, tunneling and surface sticking) are discussed and results are compared with exact MCTDH ones in systems with 50-100 bath degrees of freedom. Futher extensions to T > 0 K dynamics are introduced.