Eugenio Megias, Manuel Valle
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.
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We study anomalous hydrodynamics with a dyonic charge. We show that the local second law of thermodynamics constrains the structure of the anomaly in addition to the structure of the hydrodynamic constitutive equations. In particular, we show that not only the usual $E\cdot B$ term but also $E^2 -B^2$ term should be present in the anomaly with a specific coefficient for the local entropy production to be positive definite.
We consider the hydrodynamic regime of gauge theories with general triangle anomalies, where the participating currents may be global or gauged, abelian or non-abelian. We generalize the argument of arXiv:0906.5044, and construct at the viscous order the stress-energy tensor, the charge currents and the entropy current.
Starting from low energy effective chiral Lagrangian with gauged Wess-Zumino Witten term, we have derived a hydrodynamic theory for chiral superfluid. It is a non-abelian hydrodynamics at zero temperature with only superfluid components. With an external electromagnetic field and baryonic and axial baryonic chemical potentials turned on, we are able to identify analogs of various anomaly induced term in normal hydrodynamics, including chiral vortical effect, chiral magnetic effect and chiral electric effect. As an example, we solved the hydrodynamic equations for the ground state and observed …
We study the hydrodynamic regime of chiral plasmas at high temperature. We find a new type of gapless collective excitation induced by chiral effects in an external magnetic field. This is a transverse wave, and it is present even in incompressible fluids, unlike the chiral magnetic and chiral vortical waves. The velocity is proportional to the coefficient of the gravitational anomaly. We briefly discuss the possible relevance of this "chiral Alfvén wave" in physical systems.
It has been shown by Son and Surówka that the presence of anomaly in hydrodynamics with global U(1) symmetry can induce vortical and magnetic currents. The induced current is uniquely determined by anomaly from the existence of an entropy current with non-negative divergence. In this work, we extended the analysis to hydrodynamics with U(1) symmetry spontaneously broken, i.e. U(1) superfluid hydrodynamics. We found that all possible first order gradient corrections are determined up to five arbitrary functions, with the entropy current containing one arbitrary function. Furthermore, the stress…
Chiral anomaly from (anomalous) spin hydrodynamics
本文证明旋转黑Dp膜低能涨落由特定时空上的自旋流体动力学描述，并利用全息对偶性从十维引力反常角度给出了四维超对称杨-米尔斯理论中R-电流反常的几何解释。
In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an electron hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. The obtained hydrodynamic equation suggests a nontrivial analogy between electron fluids in noncentrosymmetric metals and chiral fluids in vacuum, and predicts novel hydrodynamic tr…
We study the hydrodynamics of a gas of noninteracting Weyl fermions coupled to the electromagnetic field in $(2N + 1) + 1$ spacetime dimensions using the chiral kinetic theory, which encodes the gauge anomaly in the Chern character of the nonabelian Berry connection over the Fermi surface. We derive the anomalous contributions to the relativistic hydrodynamic currents in equilibrium and at a finite temperature, which agree with and provides an approach complementary to the results derived previously using thermodynamic constraints.
We extend an infrared-deformed soft-wall anti de-Sitter/QCD model at zero temperature to a model at finite temperature and perform hydrodynamics. To have the infalling boundary condition to make the hydrodynamic analysis possible, we treat the infrared energy scale factor in our metric as a temperature-depending parameter. Then, by carrying out the hydrodynamic analysis, we compute the transport coefficients, the diffusion constant, and the shear viscosity, through the linear response theory.
Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
本文建立2+1维中旋转对称性破缺为三角点群的矢量U(1)电荷流体力学理论，揭示手征反常导致模式色散出现弹道项，并通过经典Markov链模拟验证该反常普适类。
Turbulent flows of incompressible liquid in two dimensions are comprised of dense systems of vortices. Such system of vortices can be treated as a fluid and itself could be described in terms of hydrodynamics. We develop the hydrodynamics of the vortex fluid. This hydrodynamics captures characteristics of fluid flows averaged over fast circulations in the inter-vortex space. The hydrodynamics of the vortex fluid features the anomalous stress absent in Euler's hydrodynamics. The anomalous stress yields a number of interesting effects. Some of them are: a deflection of stream lines, a correction…
We show that electrons undergoing a two-particle collision in a crystal experience a coordinate shift that depends on their single-particle Bloch wave functions, and derive a gauge-invariant expression for such shift, valid for arbitrary band structures, and arbitrary two-particle interaction potentials. As an application of the theory, we consider two-particle coordinate shifts for Weyl fermions in space of three spatial dimensions. We demonstrate that such shifts in general contribute to the anomalous Hall conductivity of a clean electron liquid.
We argue that an effective field theory of local fluid elements captures the constraints on hydrodynamic transport stemming from the presence of quantum anomalies in the underlying microscopic theory. Focussing on global current anomalies for an arbitrary flavour group, we derive the anomalous constitutive relations in arbitrary even dimensions. We demonstrate that our results agree with the constraints on anomaly governed transport derived hitherto using a local version of the second law of thermodynamics. The construction crucially uses the anomaly inflow mechanism and involves a novel therm…
In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the momentum density. We also point out that the ano…
We study the collective excitations in a relativistic fluid with an anomalous $U(1)$ current. In $3+1$ dimensions at zero chemical potential, in addition to ordinary sound modes we find two propagating modes in presence of an external magnetic field. The first one which is a transverse degenerate mode, propagates with a velocity proportional to the coefficient of gravitational anomaly; this is in fact the Chiral Alfvén wave recently found in \cite{Yamamoto:2015ria}. Another one is a wave of density perturbation, namely a chiral magnetic wave (CMW). The velocity dependence of CMW on the chiral …
Natural anomalous cyclotron response in a hydrodynamic local quantum critical metal in a periodic potential
本文研究晶格中量子临界金属的直流磁输运，发现流体力学状态下洛伦兹力与晶格耦合产生由热力学量决定的普适反常回旋频率修正，并通过全息数值模拟验证，为铜氧化物奇异金属的反常霍尔效应提供可能解释。
Observations show that, at the beginning of their existence, neutron stars are accelerated briskly to velocities of up to $1000$ km/s. We discuss possible mechanisms contributing to these kicks in a systematic effective-field-theory framework. Anomalies of the underlying microscopic theory result in chiral transport terms in the hydrodynamic description, and we identify these as explanation for the drastic acceleration. In the presence of vorticity or a magnetic field, the chiral transport effects cause neutrino emission along the respective axes. In typical scenarios, the transport effect due…
Leading order magnetic field dependence of conductivities in anomalous hydrodynamics
本文证明反常一阶流体力学中纵向电导率的磁场依赖项是参考系依赖的非物理结果，并提出将磁场纳入平衡态以消除该问题。
Anomalous hydrodynamics effective actions from holography
本研究借助全息对偶推导带反常阿贝尔整体流的带电等离子体有效作用量，明确't Hooft反常项在高斯阶仅影响动量扩散区产生手征剪切波，且在非高斯阶会对声和电荷扩散动力学产生非平凡作用。
The effects of finite magnetization and electric polarization on dissipative and non-dissipative (anomalous) transport coefficients of a chiral fluid are studied. First, using the second law of thermodynamics as well as Onsager's time reversal symmetry principle, the complete set of dissipative transport coefficients of this medium is derived. It is shown that the properties of the resulting shear and bulk viscosities are mainly affected by the anisotropy induced by external electric and magnetic fields. Then, using the fact that the anomaly induced currents do not contribute to entropy produc…
We show that three-dimensional trace anomalies lead to new universal anomalous transport effects on a conformally-flat spacetime with background scalar fields. In contrast to conventional anomalous transports in quantum chromodynamics (QCD) or quantum electrodynamics (QED), our current is independent of background gauge fields. Therefore, our anomalous transport survives even in the absence of vector-like external sources. By manipulating background fields, we suggest a setup to detect our anomalous transport. If one turns on scalar couplings in a finite interval and considers a conformal fact…
We review the Kubo formulae relevant to study anomalous transport properties of relativistic fluids. We apply this formalism to perform a computation of the transport coefficients in a holographic massive gravity model including vorticity and external electromagnetic fields. We find an interesting phase in which the electric DC conductivity is negligible, while the anomalous conductivities turn out to be nonvanishing.
We summarize recent advances in the application of the equilibrium partition function formalism for the study of the transport coefficients of relativistic fluids induced by quantum anomalies, at first and second order in the hydrodynamic expansion. We provide results for theories with Abelian and non-Abelian chiral fermions, and discuss some features of the corresponding constitutive relations.
We derive the constitutive relations of first order charged hydrodynamics for theories with Lifshitz scaling and broken parity in $2+1$ and $3+1$ spacetime dimensions. In addition to the anomalous (in $3+1$) or Hall (in $2+1$) transport of relativistic hydrodynamics, there is an additional non-dissipative transport allowed by the absence of boost invariance. We analyze the non-relativistic limit and use a phenomenological model of a strange metal to argue that these effects can be measured in principle by using electromagnetic fields with non-zero gradients.
Quantum anomalies are one of the subtlest properties of relativistic field theories. They give rise to non-dissipative transport coefficients in the hydrodynamic expansion. In particular a magnetic field can induce an anomalous current via the chiral magnetic effect. In this work we explore the possibility that anomalies can induce a chiral magnetic effect in non-anomalous currents as well. This effect is implemented through an explicit breaking of the symmetries.
Anomalous Transport and Explicit Symmetry Breaking in Holography
本文研究了五维共形场论中纯规范和混合规范-引力Chern-Simons项对反常传输的影响，发现显式对称破缺可扩展至非反常部分，运输系数依赖于对称破缺质量参数。
We study the holographic flow of anomalous conductivities induced by gauge and gravitational Chern-Simons terms. We find that the contribution from the gauge Chern-Simons term gives rise to a flow that can be interpreted in terms of an effective, cutoff dependent chemical potential. In contrast the contribution of the gauge-gravitational Chern-Simons term is just the temperature squared and does not flow.
We compute, in the framework of the fluid/gravity correspondence, the transport coefficients of a relativistic fluid affected by chiral and gauge-gravitational anomalies, including external electromagnetic fields. The computation is performed at first and second order in the hydrodynamical expansion. We use a 5-dim holographic model with pure gauge and mixed gauge-gravitational Chern-Simons terms in the action. We reproduce at first order previous results on the anomaly induced current of a magnetic field and a vortex in a relativistic fluid, and compute at second order the anomalous and non a…
We study anomalous conductivities in Chiral Superfluids in the framework of two different holographic models, by means of Kubo formulae. In addition, we point out the existence of an anomalous transport phenomenon that consists in the presence of a charge density when the superfluid velocity is aligned with a magnetic field. It has been pointed out recently that certain chiral conductivities in holographic superfluids exhibit universal behavior at zero temperature. We show that anomalous conductivities always stabilize at low temperatures in our setup. Even though the particular value they acq…
We construct the kinetic theory in ($1+2d$)-dimensional phase space and time when all abelian and nonabelian phase-space Berry curvatures are nonzero. Then we calculate anomalous transports induced by the Berry curvatures on the basis of the kinetic theory. As an example, we study anomalous charge and spin transports induced by the SU($2$) Berry curvatures. We also derive the topological effective theory to reproduce the transports in insulators calculated from the kinetic theory. Such an effective theory is given by the nonabelian phase space Chern-Simons theory.
Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of non-hydrodynamic modes. We review non-hydrodynamic modes in kinetic theory and gauge/gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data, we find hints of non-hydrodynamic modes in cold Fermi gases in two and three dimensions.
The exact expression for the entropy current of a fluid in presence of two dimensional gravitational anomalies is given. To make it compatible with the second law of thermodynamics; i.e. positivity of the entropy production rate of a system (which is considered to be fundamental), we find a bound on the sum of the two response parameters ($\bar{C}_1$ and $\bar{C}_2$), in terms of the trace and diffeomorphism anomaly coefficients ($c_w$ and $c_g$). The precise expression, we obtain here, is $\bar{C}_1 + \bar{C}_2\leq 4π^2c_w + 8π^2 c_g$. Interestingly, when the bound is saturated corresponding …
We find the hydrodynamic equations of a system of particles constrained to be in the lowest Landau level. We interpret the hydrodynamic theory as a Hamiltonian system with the Poisson brackets between the hydrodynamic variables determined from the noncommutativity of space. We argue that the most general hydrodynamic theory can be obtained from this Hamiltonian system by allowing the Righi-Leduc coefficient to be an arbitrary function of thermodynamic variables. We compute the Righi-Leduc coefficients at high temperatures and show that it satisfies the requirements of particle-hole symmetry, w…
In this paper we study the dynamical properties of charged systems immersed in an external magnetic field and perturbed by a set of scalar operators breaking translations either spontaneously or pseudo-spontaneously. By combining hydrodynamic and quantum field theory arguments we provide analytic expressions for all the hydrodynamic transport coefficients relevant for the diffusive regime in terms of thermodynamic quantities and DC thermo-electric conductivities. This includes the momentum dissipation rate. We shed light on the role of the momentum dissipation rate in the transition between th…
We derive a set of nontrivial relations between second-order transport coefficients which follow from the second law of thermodynamics upon considering a regime close to uniform rotation of the fluid. We demonstrate that extension of hydrodynamics by spin variable is equivalent to modifying conventional hydrodynamics by a set of second-order terms satisfying the relations we derived. We point out that a novel contribution to the heat current orthogonal to vorticity and temperature gradient reminiscent of the thermal Hall effect is constrained by the second law.
We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasi-relativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the underlying lattice. In the hydrodynamic limit, we find that the thermal and electrical conductivities are dominated by viscous effects, and that the thermal conductivity is most sensitive to this disorder. We compare the effects of inhomogeneity in the spatial metric to inhomogeneity in the chemical potential, and discuss the extent to which our hydrodynamic theor…
The spectrum of collective excitations in Weyl materials is studied by using consistent hydrodynamics. The corresponding framework includes the vortical and chiral anomaly effects, as well as the dependence on the separations between the Weyl nodes in energy $b_0$ and momentum $\mathbf{b}$. The latter are introduced via the Chern-Simons contributions to the electric current and charge densities in Maxwell's equations. It is found that, even in the absence of a background magnetic field, certain collective excitations (e.g. the helicon-like modes and the anomalous Hall waves) are strongly affec…
Hydrodynamic magneto-transport in holographic charge density wave states
通过流体动力学与规范/引力对偶研究平移对称性（伪）自发破缺相中的磁输运，推导出输运系数解析式并验证了全息模型作为磁声子研究的有效代表。
We show that generic U(1) superfluids with a U(1)^3 anomaly feature universal anomalous transport at low temperature. This universal behavior had been encountered before for a class holographic models by performing explicit computations: anomalous conductivities were found to either vanish or to be 1/3 of the value they present for ordinary fluids. In this note we argue in favor of the fact that at zero temperature chiral conductivities are fully determined by anomaly coefficients. We also compute them and show explicitly where their particular value arises from. The proof is based on Ward Ide…
Anomalous transport from geometry
本文通过黑洞几何中的反常方程，推导出热气体的手性输运系数，并扩展至规范反常和弱磁场，得到手性磁效应和涡旋效应的完整系数集。
Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
本文研究了Weyl半金属中反常流体力学输运的弛豫项，发现满足守恒和热力学约束的弛豫必然使系统开放并违反热力学第二定律，这些弛豫可从动理论推导，并得出与文献不同的DC电导率。
The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab of finite thickness is studied by using the consistent hydrodynamic theory. The latter includes viscous, anomalous, and vortical effects, as well as accounts for dynamical electromagnetism. The energy and momentum separations between the Weyl nodes are taken into account via the topological Chern-Simons contributions in the electric current and charge densities in Maxwell's equations. When an external electric field is applied parallel to the slab, it is found that the electron fluid velocity has a nonuniform profile d…
We show that the scale (conformal) anomaly in field theories leads to new anomalous transport effects that emerge in an external electromagnetic field in an inhomogeneous gravitational background. In inflating geometry the QED scale anomaly locally generates an electric current that flows in opposite direction with respect to background electric field (the scale electric effect). In a static spatially inhomogeneous gravitational background the dissipationless electric current flows transversely both to the magnetic field axis and to the gradient of the inhomogeneity (the scale magnetic effect)…
Following the previous work 1103.3773, we give a more general and systematic discussion on the Chern-Simons effect in the 5-dimensional Maxwell-Gauss-Bonnet gravity. After constructing the first order perturbative black brane solution, we extract the stress tensor and charge current of dual fluid. From these results, we find out the dependence of some transport coefficients on the Gauss-Bonnet coupling $α$ and Chern-Simons coupling $κ_{cs}$. We also show that the new anomalous term can provide an additional contribution to the anomalous chiral magnetic conductivity.
We present a theory of thermoelectric transport in weakly disordered Weyl semimetals where the electron-electron scattering time is faster than the electron-impurity scattering time. Our hydrodynamic theory consists of relativistic fluids at each Weyl node, coupled together by perturbatively small inter-valley scattering, and long-range Coulomb interactions. The conductivity matrix of our theory is Onsager reciprocal and positive-semidefinite. In addition to the usual axial anomaly, we account for the effects of a distinct, axial-gravitational anomaly expected to be present in Weyl semimetals.…
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