The representation of quantum mechanics in the phase space (position-momentum) is carried out in terms of the Wigner function. This formulation has the advantage of providing an intuitive visualization of the state and allowing the introduction of interactions with the environment in the context of open quantum dynamics. However, the phase space has the disadvantage of requiring significantly more computational power. Fortunately, new algorithms and modern computational techniques such as GPU computing can be used to overcome this difficulty as I show in a sequence of papers [1,2]. These techniques can be even applied to relativistic systems [3].

The following is a list of some sample simulations. Please click on the links to see the videos.

- Free particle evolution of an INCOHERENT superposition

[1]

*Efficient method to generate time evolution of the Wigner function for open quantum systems*, Renan Cabrera, Denys I. Bondar, Kurt Jacobs, and Herschel A. Rabitz, Phys. Rev. A 92, 042122 – Published 28 October 2015

[2]

*Efficient computations of quantum canonical Gibbs state in phase space,*

Denys I. Bondar, Andre G. Campos, Renan Cabrera, and Herschel A. Rabitz

Phys. Rev. E 93, 063304 – Published 13 June 2016

[3]

*Dirac open-quantum-system dynamics: Formulations and simulations,*

Renan Cabrera, Andre G. Campos, Denys I. Bondar, and Herschel A. Rabitz

Phys. Rev. A 94, 052111 – Published 14 November 2016