Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions

Lucas, Andrew; Surówka, Piotr

doi:10.1103/physreve.90.063005

Cited by 42 publications

(47 citation statements)

References 86 publications

(121 reference statements)

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“…The function P also determines the ground state density n 0 = P (µ), and the leading dispersion of the Goldstone mode ω 2 = c 2 s q 2 , where c 2 s = ∂ n0 P 0 /m = P /P m is the speed of sound, squared. For = 0, the spin connection appears in each ∇θ (6), and so L 0 includes O (p) contributions, which produce the leading odd viscosity and conductivity, discussed below. There are no additional terms at O (p), so that L 1 = 0 [21].…”

Section: Effective Field Theorymentioning

confidence: 99%

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Boundary central charge from bulk odd viscosity: Chiral superfluids

2019

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We derive a low energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave-vector, contains a dependence on the chiral central charge c of the boundary degrees of freedom, as well as additional non-universal contributions. We identify related bulk observables which allow for a bulk measurement of c. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model. < l a t e x i t s h a 1 _ b a s e 6 4 = " r L w / X U c T o a 2 Z e K G I 9 H 4 s i a p 2 4 C g = " > A A A B 6 n i c b V B N S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I ...

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Section: Effective Field Theorymentioning

confidence: 99%

“…The combination P T of parity and time-reversal is a symmetry in any system in which T is broken (perhaps spontaneously) due to some kind of angular momentum, as in QH states, -wave SFs, and active chiral fluids [6]. Here we consider the implications of P T symmetry on (B19).…”

Section: P T Symmetrymentioning

confidence: 99%

Boundary central charge from bulk odd viscosity: Chiral superfluids

2019

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“…The odd viscosity effects have been studied extensively in the context of QH fluids (where it is dubbed as Hall viscosity) . However, realistic odd viscosity effects measurable in laboratory for general classical fluids with broken time reversal symmetries [29][30][31] have received less attention. The closest attempt to this end was made recently in Ref.…”

Section: Introductionmentioning

confidence: 99%

Odd viscosity in two-dimensional incompressible fluids

2017

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In this work, we present observable consequences of parity violating odd viscosity term in incompressible 2+1D hydrodynamics. For boundary conditions depending on the velocity field (flow) alone we show that: (i) The fluid flow quantified by the velocity field is independent of odd viscosity, (ii) The force acting on a closed contour is independent of odd viscosity, and (iii) The odd viscosity part of torque on a closed contour is proportional to the rate of change of area enclosed by the contour with the proportionality constant being twice the odd viscosity. The last statement allows us to define a measurement protocol of odd viscostance in analogy to Hall resistance measurements. We also consider no-stress boundary conditions which explicitly depend on odd viscosity. A classic hydrodynamics problem with no-stress boundary conditions is that of a bubble in a planar Stokes flow. We solve this problem exactly for shear and hyperbolic flows and show that the steady-state shape of the bubble in the shear flow depends explicitly on the value of odd viscosity.

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“…These effects are subtle in the case when the classical twodimensional fluid is incompressible. Recent works have outlined some of observable consequences of the odd viscosity for incompressible flows [33][34][35][36][37][38]. In particular, in Ref.[38] the equations governing the Hamiltonian dynamics of surface waves were derived in the case where bulk vorticity is absent.Let us start by summarizing the main equations of an incompressible fluid dynamics with odd viscosity.…”

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confidence: 99%

Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity

Abanov

Monteiro

2019

Phys. Rev. Lett.

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We present variational and Hamiltonian formulations of incompressible fluid dynamics with free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric boundary terms. These boundary terms modify Zakharov's Poisson brackets and lead to a new type of boundary dynamics. The modified boundary conditions have a natural geometric interpretation describing an additional pressure at the free surface proportional to the angular velocity of the surface itself. These boundary conditions are believed to be universal since the proposed hydrodynamic action is fully determined by the symmetries of the system.Introduction. Variational principle in hydrodynamics have a long history. We refer to Ref.[1] and references therein for an introduction to the topic. In particular, the Luke's variational principle (LVP) is a variational principle of an inviscid and incompressible fluid with a free surface [2,3]. LVP provides both bulk hydrodynamic equations for an irrotational flow as well as kinematic and dynamic boundary conditions at the free surface boundary [3]. Such principle was later extended to include surface tension and bulk vorticity (for a recent summary see [4]). In this letter, we present a further extension of LVP which accounts for the presence of odd viscosity in isotropic two-dimensional fluids with broken parity.In three dimensions, parity odd terms in the viscosity tensor were known for a long time in the context of plasma in a magnetic field [5] and in hydrodynamic theories of superfluid He-3A [6], where the fluid anisotropy plays a major role. In two dimensions however the odd viscosity is compatible with isotropy of the fluid [7]. The odd viscosity is the parity violating non-dissipative part of the stress-strain rate response of a two-dimensional fluid. The recent interest in odd viscosity is motivated by the seminal paper by Avron, Seiler, and Zograf [8] where it was shown that, in general, quantum Hall states have non-vanishing odd viscosity. The role of odd viscosity (a.k.a. Hall viscosity) in the context of quantum Hall effect has been an active area of research [9-32], but is out of the scope of this work.In the Ref.[7], Avron has initiated the search for odd viscosity effects in classical 2D hydrodynamics. These effects are subtle in the case when the classical twodimensional fluid is incompressible. Recent works have outlined some of observable consequences of the odd viscosity for incompressible flows [33][34][35][36][37][38]. In particular, in Ref.[38] the equations governing the Hamiltonian dynamics of surface waves were derived in the case where bulk vorticity is absent.Let us start by summarizing the main equations of an incompressible fluid dynamics with odd viscosity. In the following we assume that the fluid density is constant and take it as unity. We also neglect all thermal effects. Then, the hydrodynamic equations are the incompressibility condition and the Euler equationHere, v(x, t) is a two-component veloc...

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Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions

Cited by 42 publications

References 86 publications

Boundary central charge from bulk odd viscosity: Chiral superfluids

Boundary central charge from bulk odd viscosity: Chiral superfluids

Odd viscosity in two-dimensional incompressible fluids

Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity

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