Wigner formalism for a particle on an infinite lattice: dynamics and spin
arXiv:1405.2944 · doi:10.1088/1367-2630/17/1/013037
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.
arXiv comment16 pages, 3 figures
References in corpus (24)
- Quantum walks: a comprehensive review
- Negativity of the Wigner function as an indicator of nonclassicality
- Positive Wigner functions render classical simulation of quantum computation efficient
- Discrete phase space based on finite fields
- Negative Quasi-Probability as a Resource for Quantum Computation
- Hudson's Theorem for finite-dimensional quantum systems
- Teleportation of Nonclassical Wave Packets of light
- Quasi-probability representations of quantum theory with applications to quantum information science
- Quantum computers in phase space
- Classicality in discrete Wigner functions
- Discrete Wigner functions and quantum computational speedup
- Directly estimating non-classicality
- Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
- Inertial and gravitational mass in quantum mechanics
- Phase-space approach to the study of decoherence in quantum walks
- Orbital angular momentum in phase space
- Determination of entangled quantum states of a trapped atom
- Discrete Wigner functions and the phase space representation of quantum computers
- Wigner function for a particle in an infinite lattice
- Relativistic Wigner Function Approach to Neutrino Propagation in Matter
- Discrete Wigner distribution for two qubits: a characterization of entanglement properties
- Direct Observation and Analysis of Spin Dependent Transport of Single Atoms in a 1D Optical Lattice
- Schroedinger-Cat Entangled State Reconstruction in the Penning Trap
- Covariant Wigner Function Approach to the Boltzmann Equation for Mixing Fermions in Curved Spacetime