Phase-space analysis of spinning particle dynamics in two-dimensional Weyl systems: Stratonovich–Weyl approach

Abstract This study examines the phase-space representation of the von Neumann equation of motion for the density operator associated with a particle with one-half spin moving in a two-dimensional layer. The general form of this equation is derived from the Stratonovich–Weyl scheme, which allows for the simultaneous consideration of continuous and discrete degrees of freedom. It is also demonstrated that the equations of motion for the marginals of the Wigner distribution function can be expressed as the Moyal equation, framed within the mean-field approximation. Taking into account the Hamiltonian in the Weyl form and using the Markovian approximation, it is shown that the considered equation of motion can be reduced to the diffusion equation with the time-dependent anisotropic diffusion coefficient for the probability density in real space. This equation is, then, solved with the initial condition set as a rescaled Gaussian, miming particle spread within the anomalous diffusion process. The characteristics of these processes are then analyzed using the dynamic overlap measure and the Shannon entropy approach. The advection process is selected as a reference process, as it naturally arises due to the mean-field approximation.