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.
arXiv commentLatex, 29 pages
References in corpus (36)
- Nonlinear Gluon Evolution in the Color Glass Condensate: I
- Observation of the chiral magnetic effect in ZrTe5
- Phase space representation of quantum dynamics
- The Chiral Magnetic Effect and Anomaly-Induced Transport
- Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
- Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
- Introduction to Nonequilibrium Quantum Field Theory
- Anomalous Axion Interactions and Topological Currents in Dense Matter
- Chiral Magnetic conductivity
- Quantization Methods: A Guide for Physicists and Analysts
- Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory
- Quantum Mechanics in Phase Space
- (Non)-Renormalization of the Chiral Vortical Effect Coefficient
- Generalized Bloch theorem and chiral transport phenomena
- Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
- A Possible Higher Order Correction to the chiral Vortical Conductivity in a Gauge Field Plasma
- Hawking radiation and secularly growing loop corrections
- The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach
- HBT Correlators -- Current Formalism vs. Wigner Function Formulation
- Chern-Simons current and local parity violation in hot QCD matter
- Wigner Functions for the Landau Problem in Noncommutative Spaces
- Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism
- A panoply of Schwinger-Keldysh transport
- Wigner transformation, momentum space topology, and anomalous transport
- Chiral torsional effect
- Chiral Separation Effect in lattice regularization
- Anatomy of the chiral vortical effect
- Influence of interactions on the anomalous quantum Hall effect
- Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
- The Subtleties of the Wigner Function Formulation of the Chiral Magnetic Effect
- Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
- Chiral Separation effect in non-homogeneous systems
- Gauge covariant formulation of Wigner representation through deformational quantization --Application to Keldysh formalism with electromagnetic field--
- Anomalous Thermal Hall Effect in a Disordered Weyl Ferromagnet
- Precise Wigner-Weyl calculus for lattice models
- Feynman Rules in terms of the Wigner transformed Green functions