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A Feynman diagram for the triangle anomaly. In massless QED both the charge current and axial charge current are conserved classically. However, when the system is quantised the axial anomaly is not conserved. The axial charge nevertheless makes an important contribution to the system and can be included in hydrodynamics. To make the system have finite DC conductivity, it is necesary to introduce relaxation terms. Image borrowed from here.
In previous work, I discovered and discussed generalised relaxation terms. These were important for producing finite DC conductivities in systems with the axial anomaly; which in turn is a model for simulating the behaviour of Weyl semi-metals. In this work, I showed how these generalised relaxation terms can emerge naturally from a kinetic theory.
Kinetic theory is one step lower on the microscopic scale than hydrodynamics. It applies to a dilute gas of particles with very localised and weak interactions. Under suitable limits one can derive hydrodynamics from kinetic theory. I showed how this can be extended to derive quasihydrodynamics with generalised relaxations from kinetic theory. Moreover, I developed an extension of the BKG formalism which puts these ideas on a firm theoretical footing.
Most importantly for applications of my approach to Weyl semi-metals, I showed how it was possible to have conservation of charge and finite DC conductivities. For this to happen, assuming that Onsager reciprocity holds, it must be the case that the second law of thermodynamics is violated.
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