Discrete Wigner function by symmetric informationally complete positive operator valued measureA discrete formulation of the Wigner distribution function ͑WDF͒ and the Wigner transport equation ͑WTE͒ is proposed, where the "discreteness" of the WDF and WTE is not just a practical, mathematical feature of discretization for the possible computations, but reveals a fundamental physics regarding the maximum correlation length of potentials ͑an essential quantum-mechanical feature of the WTE͒: it is set by the positional uncertainty due to the discrete values of momentum in evaluating the discrete WDF. Our formulation also shows that the weighting function to the potential-correlation term can be derived naturally from a mathematical necessity related to the antiperiodicity of the discrete density operator. In addition, we propose a mutually independent discretization scheme for the diagonal and cross-diagonal coordinates of the density operator, which results in a numerically effective discrete WTE in that it requires much less computational resources without significant loss in accuracy.
Electron-confined longitudinal optical phonon interaction and strong magnetic field effects on the binding energy in GaAs quantum wells Effect of parallel-perpendicular kinetic energy coupling under effective mass approximation at heterostructure boundaries in a quantum wire
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