Generalized forward-backward initial value representation for the calculation of correlation functions in complex systems

摘要

The capability of two different, recently proposed semiclassical (SC) forward—backward (FB) initial value representations (IVR) to describe quantum interference and coherence effects is investigated. It is shown that depending on the way the observable under consideration is represented by unitary operators one can obtain rather different results. Although the FB-IVR based on an integral representation as a rule is capable of describing quantum interference, a closer analysis reveals that it depends on the observable under consideration if all interference that can be described semiclassically is actually included in the calculation. To overcome this problem a new, generalized FB-IVR method (GFB-JVR) is proposed, which combines the capability of the SC-IVR to describe quantum interference effects independent of the observable and the better convergence properties of the FB-IVR. The performance of this new approach is studied in some detail. In particular, it is shown that the GFB-IVR can describe both the coherent and incoherent regime in the dynamics of an anharmonic vibration coupled to a harmonic bath.