Perfect fluid theory and its extensions

Jackiw, R.; Nair, V. P.; Pi, So‐Young; Polychronakos, Alexios P.

doi:10.1088/0305-4470/37/42/r01

Cited by 171 publications

(262 citation statements)

References 98 publications

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“…There is indeed a natural framework for discussing the dynamics of fluids using intrinsic variables which has been used over the years to describe ideal fluid dynamics [33][34][35][36][37][38][39]. This framework was re-examined recently in [40] who suggested that it could be useful beyond the ideal fluid level; by studying the corrections to the ideal fluid effective action [41] argued that the transport of non-dissipative neutral fluids could be systematically understood in this framework.…”

Section: Jhep03(2014)034mentioning

confidence: 99%

Effective actions for anomalous hydrodynamics

Haehl

Loganayagam

Rangamani

2014

J. High Energ. Phys.

111

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Abstract: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 thermofield double construction. In particular, we show that the anomalous Ward identities necessitate non-trivial interaction between the two parts of the Schwinger-Keldysh contour.

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Section: Jhep03(2014)034mentioning

confidence: 99%

Effective actions for anomalous hydrodynamics

Haehl

Loganayagam

Rangamani

2014

J. High Energ. Phys.

111

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“…This Hamiltonian supports two bands with the Bloch states |χ ± (k) , the nondegenerate energy eigenvalues 70) and the Berry curvatures…”

Section: Cmentioning

confidence: 69%

Noncommutative geometry for three-dimensional topological insulators

et al. 2012

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We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.

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“…There could be other instances where such an Abelian treatment might fail. Examples of more sophisticated non-Abelian fluids were considered in several recent excellent reviews [84,85]. These papers might serve as points of departure for the treatment of more elaborate hydrodynamical problems involving non-Abelian entanglements.…”

Section: Miscellaneousmentioning

confidence: 99%

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

Ballard¹,

Kholodenko²

2009

Physica A: Statistical Mechanics and its Applications

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Although in the case of polymer solutions the existence of hydrodynamic screening has been theoretically established some time ago, use of the same methods for suspensions of hard spheres thus far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological and London-style qualitative arguments we prove the existence of screening in hard sphere suspensions. Even though some of these arguments were employed initially for treatments of superconductivity and superfluidity, we find analogs of these phenomena in nontraditional settings such as in colloidal suspensions, turbulence, magnetohydrodynamics, etc. In particular, in suspensions we demonstrate that the hydrodynamic screening is an exact analog of Meissner effect in superconductors. The extent of screening depends on the volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind with such a state becoming fully "superconducting" at the critical volume fraction ϕ * for which the (zero frequency) relative viscosity η(relative) diverges. Brady and, independently, Bicerano et al using scaling-type arguments predicted that for ϕ close to ϕ * the viscosity η(relative) behaves as C(1−ϕ/ϕ * ) −2 with C being some constant. Their prediction is well supported by experimental data. In this work we explain such a behavior of viscosity in terms of a topological-type transition which mathematically can be made isomorphic to the more familiar Bose-Einstein condensation transition. Because of this, the results and methods of this work are not limited to suspensions. In the concluding section we describe other applications ranging from turbulence and magnetohydrodynamics to high temperature superconductors and QCD, etc.

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Perfect fluid theory and its extensions

Cited by 171 publications

References 98 publications

Effective actions for anomalous hydrodynamics

Effective actions for anomalous hydrodynamics

Noncommutative geometry for three-dimensional topological insulators

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

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