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arXiv:1707.06077 · Computer Physics Communications

WavePacket: A Matlab package for numerical quantum dynamics.II: Open quantum systems, optimal control, and model reduction

Burkhard Schmidt, Carsten Hartmann

Published Mar 8, 2018• 41 citations
arXivHTMLPDF
DOI
10.1016/j.cpc.2018.02.022

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Abstract We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. These examples will be useful for undergraduate and graduate students with a medium or high-level background in MATLAB, and also for researchers interested in numerical studies applied to quantum optics and condensed matter systems.
In order to model the spectroscopic and scattering properties of a quantum system, we propose and explore a new absorbing complex-type optical potential based on a combination of cosine functions. This function provides a high degree of smoothness to joint with a physical real-type potential. The capabilities of this function are investigated in terms of its effect on otherwise freely evolving quantum dynamics. We use our open-source programs to implement the Fourier Grid method with the Optimizer package (in Matlab), freely available at https://sourceforge.net/projects/optimizer-sovkov/ https://sourceforge.net/projects/optimizer-sovkov/. Keywords: quantum dynamics; damping boundary conditions; optical potential; Fourier Grid method; spectroscopy of ultracold ensembles.