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

TL;DR

This paper extends the Wigner function formalism for particles on an infinite lattice to include spin, providing explicit solutions for dynamics with potential and decoherence, and exploring negativity concepts.

Contribution

It introduces a formalism incorporating spin into the Wigner function for lattice particles, with solutions for Hamiltonian and decoherence dynamics.

Findings

Explicit solutions for Hamiltonian evolution with position-dependent potential

Models of decoherence with master equations

Discussion on negativity of the Wigner function with spin

Abstract

The recently proposed Wigner function for a particle in an infinite lattice [NJP 14, 103009 (2012)] is extended here to include an internal degree of freedom, as spin. 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. Discrete processes are also discussed. Finally we discuss the possibility of introducing a negativity concept for the Wigner function in the case in which the spin degree of freedom is included.