English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We develop the approach of Felix Buot to construction of Wigner-Weyl calculusfor the lattice models. We apply this approach to the tight-binding models withfinite number of lattice cells. For simplicity we restrict ourselves to thecase of rectangular lattice. We start from the original Buot definition of thesymbol of operator. This definition is corrected in order to maintainself-consistency of the algebraic constructions. It appears, however, that theBuot symbol for simple operators does not have a regular limit when the latticesize tends to infinity. Therefore, using a more dense auxiliary lattice wemodify the Buot symbol of operator in order to build our new discrete Weylsymbol. The latter obeys several useful identities inherited from the continuumtheory. Besides, the limit of infinitely large lattice becomes regular. Weformulate Keldysh technique for the lattice models using the proposed Weylsymbols of operators. Within this technique the simple expression for theelectric conductivity of a two dimensional non - equilibrium and non -homogeneous system is derived. This expression smoothly approaches thetopological one in the limit of thermal equilibrium at small temperature andlarge system area.

Discrete Wigner-Weyl calculus for the finite lattice