Wigner-Weyl calculus in Keldysh technique
arXiv:2009.10704 · doi:10.1007/s10825-021-01775-8
Abstract
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.
Latex, 29 pages
References in corpus (13)
- Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
- Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
- Chiral Magnetic conductivity
- Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory
- Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
- A Possible Higher Order Correction to the chiral Vortical Conductivity in a Gauge Field Plasma
- The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach
- Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism
- Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
- Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
- Chiral Separation effect in non-homogeneous systems
- Precise Wigner-Weyl calculus for lattice models
- Feynman Rules in terms of the Wigner transformed Green functions