Lattice Wigner equation

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 threedimensional open systems is also illustrated.

Nonclassical effects in geodesic motion

“…Thus, it is necessary to study the time-evolution of Wigner function W (r, p, t). [46,47], especially with the present central force problem. Nevertheless, it is resolvable within the classical limitation 2 → 0 [49][50][51].…”

“…This equation is equivalent to Schrödinger equation for the dynamical evolution of a pure state, and thus sometimes called Wigner Equivalent formalism [45]. At the same time, this equation also works for the mix state [46,47]…”

“…This equation is equivalent to Schrödinger equation for the dynamical evolution of a pure state, and thus sometimes called Wigner Equivalent formalism [45]. At the same time, this equation also works for the mix state [46,47]. Wigner equation looks similar to Newtonian equation in phase space and allows us to make an intuitive comparison between classical and quantum mechanics [48].…”

Dynamic symmetry-breaking in mutually annihilating fluids with selective interfaces

“…Summarizing, it appears reasonable to speculate that, with proper fine-tuning and extensions, the present model could prove useful for computational explorations of the semi-classical aspects of strongly non-equilibrium EWBG scenarios. The inclusion of quantum effects [15] may also be feasible through suitable adaptations of the lattice Wigner equation [18].…”

Additivity of entanglement of formation via an entanglement-breaking space

“…Hitherto, the explicit analytic formulae for EOF have been found for two-qubit system [11] and some special states such as the isotropic states and some 16×16 mixed states [3,12,13]. Nevertheless, the EOF of the tensor product of two states is usually hard to compute, even if their EOF is known.…”