Local coherent-state approximation to system-bath quantum dynamics

The Local Coherent-State Approximation (LCSA)(Martinazzo et al., 2006) has been recently introduced to deal with typical system-bath dynamical problems where the quantum nature of the system and/or the low temperature of the bath force one to correctly represent the important system-bath quantum correlations. In the wavefunction description of the zero-temperature case LCSA introduces a coherent-state description of the local bath states obtained with the help of a Discrete Variable Representation of the system state space. This allows one to enormously simplify the bath dynamics while capturing at the same time an important part of the system-bath correlations. In this context, coupled, pseudo-classical equations of motion for the bath and an effective Schr\ddot{\textrm{o}}dinger equation for the system have been derived with the help of the Dirac-Frenkel variational principle, and solved for a number of model problems, ranging from tunneling to vibrational relaxation and sticking dynamics. Comparison with exact, Multi-Configuration-Time-Dependent-Hartree (MCDTH) results has shown the merits and the limits of the approach(Martinazzo et al., 2006) . On the one hand, optimal scaling with respect to the number of bath degrees of freedom, as shown in practice with calculations using tens of thousands of bath oscillators, is very appealing for studying realistic problems with very large baths. On the other hand, numerical stability problems have been preventing straightforward applications of the method if no additional ad hoc assumption is made on the bath dynamics. In this contribution, we summarize the work done up to now on LCSA, with some emphasis on its connections to the closely related Gaussian-MCTDH(Burghardt et al., 1999; Worth and Burghardt, 2003) and Coupled Coherent-State(Shalashilin and Child, 2000; Shalashilin and Child, 2004) methods. We also present some results of our recent work on the search of robust propagation schemes, which naturally leads one to consider the geometrical properties of approximate quantum-dynamical methods derived from a time-dependent variational principle.