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

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 accoun...

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Bibliographic Details
Published in:New journal of physics 2015-01, Vol.17 (1), p.13037-16
Main Authors: Hinarejos, M, Bañuls, M C, Pérez, A
Format: Article
Language:English
Subjects:
Degrees of freedom
dynamics on a lattice
Evolution
Formalism
Lattices
Mathematical analysis
Mathematical models
Particle spin
Particles (of physics)
Physics
Spin dynamics
spin-dependent forces
Wigner functions
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Summary: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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/17/1/013037