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Wigner function-based device modeling. In: M. Rieth and W. Schommers (eds), Handbook of Theoretical and Computational Nanotechnology 10, 731. -W. (1995). Theory and application of the quantum phase-space distribution functions, Physics Reports, Vol. 259, 147. -L. & Paul, T. (1993). Sur les mesures de Wigner. Rev. Mat. Iberoamer, Vol. 9, 553. , Morandi, O. , (2011). High field transport and optical phonon scattering in graphene, Phys. Rew. B, Vol. 84, 045406. , Ringhofer, C. & Schmeiser, C. (1990).
2009). Transport Equations for Semiconductors, Springer-Verlag, Berlin. Kosina H. , (2006). Wigner function-based device modeling. In: M. Rieth and W. Schommers (eds), Handbook of Theoretical and Computational Nanotechnology 10, 731. -W. (1995). Theory and application of the quantum phase-space distribution functions, Physics Reports, Vol. 259, 147. -L. & Paul, T. (1993). Sur les mesures de Wigner. Rev. Mat. Iberoamer, Vol. 9, 553. , Morandi, O. , (2011). High field transport and optical phonon scattering in graphene, Phys.
In fig. 4 the comparison of the classical and the pseudo electric field obtained by using the Boltzmann distribution function is presented. A glance at the figure reveals that, compared with the bare potential U, the effective pseudo-potential is smoother and extends beyond the support of U. As a consequence, the particle in the presence of the quantum corrected potential are decelerated or accelerated before they reach the classical force field −∇r U, making evident the non-local action of the quantum potential.