PT Journal
AU Hinarejos, M
   Perez, A
   Bañuls, MC
TI Wigner function for a particle in an infinite lattice
SO New Journal of Physics
JI New J. Phys.
PY 2012
BP 103009
EP 19pp
VL 14
DI 10.1088/1367-2630/14/10/103009
LA English
AB We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.
ER