Hannover 2020 – scientific programme
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A: Fachverband Atomphysik
A 9: Poster Session - Atomic Physics I
A 9.8: Poster
Monday, March 9, 2020, 16:00–18:00, Empore Lichthof
Solving the semiclassical propagator via Bayesian quadrature — •Benjamin Rabe and Jan-Michael Rost — Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Semiclassical approximations to the quantum mechanical propagator have shown to give intuitive insight of the dynamics of atomic and molecular systems. One formulation of the semiclassical propagator is the initial value representation (IVR) first derived by Herman and Kluk. [1] This IVR makes use of an expression of the initial state in terms of fixed width coherent states, which form N-dimensional fixed width Gaussian wavepackets in position space. Each wavepacket starting from (qi, pi) represents a classical trajectory.
The integration over initial conditions (qi, pi) of classical trajectories is commonly done via Monte-Carlo integration, which requires the inclusion of a tremendous amount of trajectories. As an alternative approach, we propose the integration of an approximation to the Herman-Kluk propagator done by complex valued Gaussian process regression, which can be done analytically for certain choices of covariance functions. This procedure is referred to as Bayesian quadrature. [2] This approach should reduce the number of trajectories needed significantly and therefore allow for a better solution especially for evolution to larger times.
[1] Michael F Herman and Edward Kluk. Chemical Physics, 91(1):27-34, 1984.
[2] Anthony O’Hagan. Journal of statistical planning and inference, 29(3):245-260, 1991.