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Wigner formalism for a particle on an infinite lattice: dynamics and spin

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Wigner formalism for a particle on an infinite lattice: dynamics and spin

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Hinarejos Doménech, Margarida; Bañuls Polo, María Carmen; Pérez Cañellas, Armando

Aquest document és un/a article, creat/da en: 2015

The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.

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