We consider chiral liquids, that is liquids consisting of massless fermions and right-left asymmetric. In such media, one expects existence of electromagnetic current flowing along an external magnetic field, associated with the chiral anomaly. The current is predicted to be dissipation-free. We consider dynamics of chiral liquids, concentrating on the issues of possible instabilities and infrared sensitivity. Instabilities arise, generally speaking, already in the limit of vanishing electromagnetic constant, $α_{el}\to 0$. In particular, liquids with non-vanishing chiral chemical potential might decay into right-left asymmetric states containing vortices.
We prove that ideal chiral hydrodynamics, as derived from chiral kinetic theory, is acausal and its initial-value problem is ill-posed both in the linearized case around a local equilibrium solution and also in the full nonlinear regime. Therefore, such theory cannot be used to determine how the chiral anomaly affects the hydrodynamic evolution. We show that these fundamental issues can be fixed by using different definitions (frames) for the hydrodynamic fields. This leads to a causal theory of ideal chiral hydrodynamics where the vorticity strength is constrained by the coefficient that enco…
The conservation of an axial current modified by the gravitational chiral anomaly implies the universal transport phenomenon (Kinematical Vortical Effect) dependent solely on medium vorticity and acceleration but not dependent explicitly on its temperature and density. This general analysis is verified for the case of massless fermions with spin 1/2.
Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly
众所周知，由于手征磁效应，手征异常可以通过能量和电荷输运来宏观检测。另一方面，在全息多体系统中，混沌模式可能只与能量守恒有关。这表明，也许人们可以通过诊断这种系统中的量子混沌来检测微观异常。为了研究这一想法，我们考虑在AdS时空中的磁化膜与陈-西蒙斯耦合的散装。通过研究这种背景下的激波几何，我们首先计算了在$μ\ll T$和$ B \ll T^2$极限下，存在外磁场$B$时相应的蝶形速度。我们发现，在$B$的方向上的蝴蝶传播有一个不同的速度比在相反的方向。蝴蝶速度的分裂证实了手征反常可以通过量子混沌在宏观上表现出来的观点。然后，我们表明，极点跳跃点的能量密度格林函数的边界理论准确地符合混沌点。这可能被认为是反常系统中量子混沌的流体动力学起源。另外，在上述背景下，通过研究标量场的近视界动力学，我们发现了与对偶边界算子的两点函数相联系的跳极点谱。我们发现，特定松原频率处跳极点对应的波数之和是一个普适量，与对偶边界算子的标度维度无关。然后，我们表明，这个量遵循一个封闭的公式，可以被视为另一个宏观表现的手征异常。
We employ path integral methods to calculate the Casimir energy and force densities in a chiral extension of QED. Manifestly gauge invariant perfect electromagnetic boundary conditions, a natural generalization of perfect electric and perfect magnetic conditions, are implemented directly in the action by the usage of auxiliary fields. The chiral properties of the vacuum are modelled using a background $θ$ field, and we introduce techniques to efficiently calculate the path integral in this chiral medium. The flexibility of our method allows us to naturally obtain results for a variety of confi…
We analyze the combined effects of hydrodynamic fluctuations and chiral magnetic effect (CME) for a chiral medium in the presence of a background magnetic field. Based on the recently developed non-equilibrium effective field theory, we show fluctuations give rise to a CME-related positive contribution to magnetoresistance, while the early studies without accounting for the fluctuations find a CME-related negative magnetoresistance. At zero axial relaxation rate, the fluctuations contribute to the transverse conductivity in addition to the longitudinal one.
Integrable hydrodynamic equations for initial chiral currents and infinite hydrodynamic chains from WZNW model and string model of WZNW type with $SU(2),$ $SO(3),$ $SP(2),$ $SU(\infty)$, $SO(\infty)$, $SP(\infty)$ constant torsions
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_π$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the …
Relativistic Covariance from Hamiltonian Hydrodynamics in the Chiral Limit
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transpo…
In the framework of Carrol-Field-Jackiw electrodynamics we calculate the spectral distribution of the Cherenkov radiation (CHR) produced by a charge moving at constant velocity in a chiral medium. We find zero, one or two Cherenkov angles according to the relation between the velocity of the particle and the refraction index of the medium.
