A unified 4D phase-space framework for two-level quantum dynamics: open-source library

Abstract

We present a numerical scheme for simulating the 2D quantum dynamics of a two-level particle gas with internal degrees of freedom such as spin, pseudo-spin, or a two-band electronic structure. We adopt the Wigner formulation of quantum mechanics consisting of a 4D phase-space representation of the quantum dynamics. The numerical scheme is based on a spectral splitting method applied to the integro-differential Wigner-Weyl formulation of the dynamics. The computational architecture of our method is independent of specific physical implementations, resulting in broad applicability. We illustrate the versatility of our approach by simulating dynamical systems relevant to nanomaterials science, cold atom physics, interacting gases, spintronics, and topological superconductors.