Lattice Wigner equation
arXiv:1709.05934 · doi:10.1103/PhysRevE.97.013308
Abstract
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretisation, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one and two dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three- dimensional open systems is also illustrated.
References in corpus (18)
- Sub-Planck spots of Schroedinger cats and quantum decoherence
- Entanglement with Negative Wigner Function of Three Thousand Atoms Heralded by One Photon
- Lattice Boltzmann Equation for Quantum Mechanics
- Lattice Boltzmann scheme for relativistic fluids
- Nonlinear Matter Wave Dynamics with a Chaotic Potential
- Isotropic discrete Laplacian operators from lattice hydrodynamics
- Wigner-function formalism applied to semiconductor quantum devices: Failure of the conventional boundary-condition scheme
- Semiclassical propagator of the Wigner function
- Three Dimensional Lattice-Boltzmann Model for Electrodynamics
- Efficient method to generate time evolution of the Wigner function for open quantum systems
- Semiclassical propagation of Wigner functions
- Explicit Solution of the Time Evolution of the Wigner Function
- Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations
- Semi-Spectral Method for the Wigner equation
- Wigner function quantum molecular dynamics
- Poiseuille flow in curved spaces
- A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals
- Lattice Boltzmann Model for Numerical Relativity