Wigner-Weyl calculus in Keldysh technique

C. Banerjee, I. V. Fialkovsky, M. Lewkowicz, C. X. Zhang, M. A. Zubkov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We discuss the non-equilibrium dynamics of condensed matter/quantum field systems in the framework of Keldysh technique. In order to deal with the inhomogeneous systems we use the Wigner-Weyl formalism. Unification of the mentioned two approaches is demonstrated on the example of Hall conductivity. We express Hall conductivity through the Wigner transformed two-point Green’s functions. We demonstrate how this expression is reduced to the topological number in thermal equilibrium at zero temperature. At the same time both at finite temperature and out of equilibrium the topological invariance is lost. Moreover, Hall conductivity becomes sensitive to interaction corrections.

Original languageEnglish
Pages (from-to)2255-2283
Number of pages29
JournalJournal of Computational Electronics
Issue number6
StatePublished - Dec 2021


  • Green functions
  • Hallconductivity
  • Keldysh technique
  • Moyal product
  • Wigner-Weyl calculus


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