### Speaker

### Description

The quark gluon plasma(QGP) is expected to exhibit a chiral imbalance known as the chiral anomaly which induces various anomalous currents, such as: the chiral magnetic effect(CME), the chiral vortical effect(CVE) , the anomalous Hall effect(AHE) and so on. To describe these anomalous effects, one can use the chiral magnetohydrodynamics (CMHD).

We study the collective excitations and instabilities in a CMHD and focus on the anomalous Hall instability(AHI) which is due to the AHE in this talk.

Like the CME's instability, the AHI is dependent on the value of $k$ and appears in a limited scope which is decided by the AHE coefficient ${\xi}_{H}$. Notably, the AHE does not trigger an instability by itself in a pure electrodynamic context without fluid, but it does in the CMHD. For small $k$ expansion, we show that the Alfven wave modified by the AHE leads to an unstable solution. In particular, one can introduce an axion field $\theta(x)$ which interacts with the electromagnetic field in the form of $\theta E \cdot B$, to reproduce the AHE $\nabla\theta \times {E}$, the chiral chemical potential $\mu_{5}(x)\equiv \partial_{t}\theta$ , where $E,B$ are electric and magnetic fields, the AHE coefficient is $\xi_{H}\equiv\nabla\theta$. Because the AHI happens in a small scope and the total helicity is conserved, these give rise to a novel type of inverse cascade: the fermionic helicity will be transferred to various helicities of the small $k$ modes. Then the AHI ceases eventually by depleting the value of $\mu_{5},\xi_{H}$.

Finally, we briefly discuss three different instabilities such as: the chiral plasma instability(CPI), the chiral magnetovortical instability(CMVI), the AHI and the possible relevance in QGP and other physical systems.