Geometry of variational methods: dynamics of closed quantum systems

摘要: We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary we show how approach highlights necessity distinguish between two classes manifolds: Kahler non-Kahler. Traditional methods typically require family be manifold, where multiplication by unit preserves tangent spaces. This covers vast majority cases studied in literature. However, recently proposed generalized Gaussian states make it necessary also include non-Kahler case, which has already been encountered occasionally. illustrate our detail with range concrete examples structures considered manifolds are particularly relevant. These go from group theoretic coherent states.