Wigner formalism for a particle on an infinite lattice: dynamics and spin. (20th January 2015) - Hinarejos, M
Abstract: The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Bañuls M C and Pérez 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.