Equilibrium chiral magnetic effect: Spatial inhomogeneity, finite temperature, interactions

Wigner-Weyl calculus in description of non-dissipative transport phenomena

“…As a result the topological nature of quantity M 4 means that its response to the variation of chiral chemical potential is vanishing, This means the vanishing of the so -called CME conductivity. This result has been obtained in [51], and it extends the result of [120] to the non -homogeneous systems 1 . The similar consideration gives for the case of the two -dimensional system (D=3):…”

“…To conclude, in this paper we review the results obtained by the group working in Ariel University. We summarize here the results reported previously in a series of papers [26,[47][48][49][50][51][52][53] (see also references therein to the other papers of the group). In these works the non -dissipative transport phenomena have been investigated using the technique of Wigner -Weyl calculus.…”

“…In the present paper we review the recent works by the group working in Ariel University on the topological description of non -dissipative transport in non -homogeneous systems. We summarize here the results reported earlier in a series of papers (see [26,[47][48][49][50][51][52][53] and references therein). We used Wigner -Weyl formalism and start from the extension of Eq.…”

“…In Sect. III we consider the QHE at zero temperature [26] and equilibrium CME at finite temperature [51]. In Sect.…”

Chiral Magnetic Effect out of equilibrium

“…More specifically, we use Wigner transformed Green functions for the calculation of the response of electric current to chiral chemical potential and to external magnetic field. It can be shown using this technique that in equilibrium the response of electric current (integrated over the system volume) to magnetic field and chiral chemical potential is a topological invariant, including the case of the non -homogeneous systems at finite temperature and in the presence of interactions [31]. This topological invariant actually equals to zero identically.…”