Energy conservation and the chiral magnetic effect

Abstract

We analyze the chiral magnetic effect in a homogeneous neutral plasma from the point of view of energy conservation, and construct an effective potential for the growth of maximally helical perturbations of the electromagnetic field. We show that a negative curvature at the origin of the potential, indicating instability of the plasma, is induced by a chiral asymmetry in electron Fermi energy, as opposed to number density, while the potential grows at large field value. It follows that the ground state for a plasma has zero magnetic helicity; a nonzero electron mass will allow an excited state of a plasma with nonzero helicity to relax to that ground state quickly. We conclude that a chiral plasma instability triggered by weak interactions is not a viable mechanism for explaining magnetic fields in stars except possibly when dynamics drives the system far from equilibrium.

Chiral anomalous dispersion

“…A particularly violent modification of the medium dynamics by chiral effects is tied with a set of instabilities [2,[4][5][6][7][8][9][10][11]. For instance, if the anomalous back-reaction of the medium is taken into account, Maxwell equations support an exponentially growing mode of a helical magnetic field [2,4].…”

Spontaneous CPT Violation and Quantum Anomalies in a Model for Matter–Antimatter Asymmetry in the Cosmos

“…On the other hand, as we mentioned above [42,43], the energy of charged fermions E fermion interacting with a constant external magnetic field B is determined by means of the Landau levels, of which only the lowest n = 0, contributes to the CME current. In the presence of a chemical potential µ 5 , the rate of the corresponding energy density is given by…”

“…However, as argued in [42,43], using different methods, the axial vector potential B 0 does not contribute to CME, and instead one has (28), even if B 0 = 0 is present 10 . The subtlety lies in the fact that, in the presence of a background field B 0 , as we have discussed in [26][27][28], the dispersion relations for the fermions are affected nontrivially by the presence of B 0 , which differentiates it from the chiral chemical potential case; moreover, there are subtleties related to the order of taking the massless limit m → 0.…”

“…We are now well equipped to proceed with a study of the CME. It is instructive to follow the energy conservation arguments of [42]: we consider the rate of change of the total energy of the system (36), that is of the sum of the energy density of the electromagnetic field and of the charged fermions in interaction with the external magnetic fields. We restrict ourselves to flat space-times.…”

Impact of domain walls on the chiral magnetic effect in hot QCD matter

“…The unstable modes transfer helicity from the medium to the field in a process known as the inverse cascade [43,59]. Eventually, however, the helicity conservation puts a cap on the inverse cascade [60,61]. As explained in Sec.…”