Wigner-Weyl calculus in Keldysh technique

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....

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Bibliographic Details
Published in:Journal of computational electronics 2021-12, Vol.20 (6), p.2255-2283
Main Authors: Banerjee, C., Fialkovsky, I. V., Lewkowicz, M., Zhang, C. X., Zubkov, M. A.
Format: Article
Language:English
Subjects:
Calculus
Condensed matter physics
Electrical Engineering
Electromagnetism
Engineering
Equilibrium
Green's functions
High energy physics
Inhomogeneous systems
Magnetic fields
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mechanical Engineering
Optical and Electronic Materials
Quantum field theory
Quantum physics
Temperature
Theoretical
Topology
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Summary: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.
ISSN:1569-8025
1572-8137
DOI:10.1007/s10825-021-01775-8