Dominant Interaction Hamiltonians

Jan-Michael Rost
Max Planck Institute for the Physics of Complex Systems

We propose a partition of a given Hamiltonian based on dominant interactions in different parts of phase space. Depending on the nature of these dominant interaction hamiltonians (DIH) the full problem is considerably simplified which can lead to drastic speed up of the computation or analytical representation of wave functions which are not possible in the full problem. Since DIH is a local approach it rests on a semiclassical treatment with a classical backbone of trajectories, propagated under the different DIHs. Along with the realization of DIH comes automatically a classification of the trajectories with the sequence of DIHs a trajectory is passing. In the talk I will discuss two examples exploring DIH, namely planar electron - ion scattering (a two-electron problem) [1], and high-harmonic generation [2]. For the latter we are able to formulate for the first time an analytical time-dependent wave function in extension to the well known three-step model [3]. [1] M. Gerlach, S. W├╝ster, J. M. Rost, J. Phys. B 45, 235204 (2012) [2] C. Zagoya, C.-M. Goletz, F. Grossmann, and J. M. Rost, PRA(R) 85, 041401 (2012) [3] C. Zagoya, C.-M. Goletz, F. Grossmann, and J. M. Rost, New J. Phys. 14, 093050 (2012)

Presentation (PDF File)

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