An approach to larger systems

As described in Sec.3.1, standard wavepacket propagation schemes can be employed for the evaluation of fiux correlation functions. These methods employ multi-dimensional grids or basis sets to represent the wavefunction. Thus, the numerical effort of these schemes increases exponentially with the number of degrees of freedom. Given the computational resources presently available, only systems with up to four atoms can be treated accurately. The extension of numerically exact calculations towards larger systems therefore requires other schemes for the solution of the time-dependent or time-independent Schrodinger equation. 

Different approaches have been or are being investigated. Path integral approaches scale favorably with the number of degrees of freedom. However, an efficient real time path integral treatment requires the introduction of a simple reference Hamiltonian. The propagator associated with the reference Hamiltonian has to be known in closed form and the reference Hamiltonian has to yield a resonable zero order approximation for the total dynamics. 

These requirements are usually only fulfilled by model Hamiltonians. Therefore, the number of systems which can be described by accurate path integral treatments is rather small. A relevant example has been the investigation of a double well system coupled linearly to a harmonic bath [23]. 

In addition to the exact schemes described above, a variety of approximate approaches might be employed to describe large system. Recent interest has focused on semiclassical approaches and reduced density matrix propagation, for example. 

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