Abstract
We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism. We discuss some features of the corresponding constitutive relations, derive the explicit expressions for the conductivities and compare with existing results in the literature.
Highlights
Hydrodynamics is an effective description of out-of-equilibrium systems in which it is assumed local thermodynamical equilibrium
We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism
Two relevant phenomena appear at first order in the hydrodynamic expansion as a consequence of chiral anomalies: the chiral magnetic effect, which is responsible for the generation of an electric current induced by a magnetic field [2], and the chiral vortical effect, in which the electric current is induced by a vortex [3]
Summary
Hydrodynamics is an effective description of out-of-equilibrium systems in which it is assumed local thermodynamical equilibrium. It is believed that these phenomena can produce observable effects in heavy ion physics [4], as well as in condensed matter systems [5] These effects are non-dissipative, and the associated conductivities are almost completely fixed by imposing the requirement of zero entropy production. Some methods to compute the transport coefficients from a microscopic theory, either dissipative or non-dissipative, include kinetic theory [7, 8], Kubo formulae [9], diagrammatic methods [10] and fluid/gravity correspondence [11] It has been proposed a new formalism to obtain the non-dissipative part of the anomalous constitutive relations, and it is based on the existence of an equilibrium partition function in a stationary background. We will be able to get explicit results for some of the transport coefficients
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