PT Journal
AU Hinarejos, M
   Bañuls, MC
   Perez, A
TI Wigner formalism for a particle on an infinite lattice: dynamics and spin
SO New Journal of Physics
JI New J. Phys.
PY 2015
BP 013037
EP 16pp
VL 17
DI 10.1088/1367-2630/17/1/013037
LA English
DE Wigner functions; dynamics on a lattice; spin-dependent forces
AB 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.
ER