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arXiv · 0707.0752

Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians

Etienne Gindensperger·Lorenz S. Cederbaum
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Abstract

We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state conical intersections. The general situation of an arbitrary number of states and arbitrary number of nuclear degrees of freedom (modes) is considered. The macrosystem is decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the vast number of remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment is constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. By considering the system's Hamiltonian along with a few members of the hierarchy, it is shown mathematically by a moment analysis that the quantum dynamics of the entire macrosystem can be numerically exactly computed on a given time-scale. The time scale wanted defines the number of effective Hamiltonians to be included. The contribution of the environment to the quantum dynamics of the macrosystem translates into a sequential coupling of effective modes. The wavefunction of the macrosystem is known in the full space of modes, allowing for the evaluation of observables such as the time-dependent individual excitation along modes of interest, as well a spectra and electronic-population dynamics.

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Etienne Gindensperger, Lorenz S. Cederbaum. 2007-07-05. Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians. https://doi.org/10.1063/1.2778682

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