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Time-Sliced Thawed Gaussian Propagation for Simulations of Quantum Dynamics

Banff International Research Station for Mathematical Innovation and Discovery

We introduce a rigorous method for simulations of quantum dynamics by implementing a simple concatenation of semiclassical thawed Gaussian propagation steps. During each finite-time propagation, the time-dependent wavefunction is represented as a linear superposition of overlapping Gaussians which are evolved, according to their characteristic equations of motion, by using 4th-order Runge-Kutta, or Velocity-Verlet integration. After each propagation step, the expansion coefficients of the linear superposition are updated analytically by using the Fast Gaussian Wavepacket Transform in the limit of closely overlapping basis functions. The method is illustrated as applied to simulations of quantum tunneling, showing quantitative agreement with benchmark calculations based on the Split-Operator Fourier Transform method.

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Yale University

2016-07-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58592

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/