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

Abanov, Alexander G.; Monteiro, Gustavo M.

doi:10.1103/PhysRevLett.122.154501

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

Abstract

We present variational and Hamiltonian formulations of incompressible fluid dynamics with a 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.

Authors:

Abanov, Alexander G. ^[1]; Monteiro, Gustavo M. ^[2]

Stony Brook Univ., NY (United States)
Univ. Estadual de Campinas (UNICAMP) (Brazil)

Publication Date:: Tue Apr 16 00:00:00 EDT 2019

Research Org.:: Stony Brook Univ., NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1596117

Grant/Contract Number:: SC0017662; DMR-1606591

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 122; Journal Issue: 15; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Hydrodynamic waves; Interfacial flows; Viscosit; Fluid Dynamics

Citation Formats


                    Abanov, Alexander G., and Monteiro, Gustavo M. Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevLett.122.154501.

Copy to clipboard


                    Abanov, Alexander G., & Monteiro, Gustavo M. Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity.  United States.  https://doi.org/10.1103/PhysRevLett.122.154501

Copy to clipboard


                    Abanov, Alexander G., and Monteiro, Gustavo M. Tue .  
"Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity".  United States.  https://doi.org/10.1103/PhysRevLett.122.154501.  https://www.osti.gov/servlets/purl/1596117.

Copy to clipboard


                    
@article{osti_1596117,

  title        = {Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity},

  author       = {Abanov, Alexander G. and Monteiro, Gustavo M.},

  abstractNote = {We present variational and Hamiltonian formulations of incompressible fluid dynamics with a 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.},

  doi          = {10.1103/PhysRevLett.122.154501},

  journal      = {Physical Review Letters},

  number       = 15,

  volume       = 122,

  place        = {United States},

  year         = {Tue Apr 16 00:00:00 EDT 2019},

  month        = {Tue Apr 16 00:00:00 EDT 2019}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1103/PhysRevLett.122.154501

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 6 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Hydrodynamic Electron Flow and Hall Viscosity
journal, June 2017

Scaffidi, Thomas; Nandi, Nabhanila; Schmidt, Burkhard
Physical Review Letters, Vol. 118, Issue 22
DOI: 10.1103/PhysRevLett.118.226601

Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions
journal, December 2014

Lucas, Andrew; Surówka, Piotr
Physical Review E, Vol. 90, Issue 6
DOI: 10.1103/PhysRevE.90.063005

Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states
journal, July 2013

Hughes, Taylor L.; Leigh, Robert G.; Parrikar, Onkar
Physical Review D, Vol. 88, Issue 2
DOI: 10.1103/PhysRevD.88.025040

Hall Viscosity and Electromagnetic Response
journal, February 2012

Hoyos, Carlos; Son, Dam Thanh
Physical Review Letters, Vol. 108, Issue 6
DOI: 10.1103/PhysRevLett.108.066805

Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and $p_{x} + i p_{y}$ paired superfluids
journal, January 2009

Read, N.
Physical Review B, Vol. 79, Issue 4
DOI: 10.1103/PhysRevB.79.045308

Transport Signatures of the Hall Viscosity
journal, November 2017

Delacrétaz, Luca V.; Gromov, Andrey
Physical Review Letters, Vol. 119, Issue 22
DOI: 10.1103/PhysRevLett.119.226602

Odd surface waves in two-dimensional incompressible fluids
journal, January 2018

Abanov, Alexander; Can, Tankut; Ganeshan, Sriram
SciPost Physics, Vol. 5, Issue 1
DOI: 10.21468/SciPostPhys.5.1.010

On Hadamard's variational formula
journal, June 1980

Peetre, Jaak
Journal of Differential Equations, Vol. 36, Issue 3
DOI: 10.1016/0022-0396(80)90053-4

Magnetoelasticity theory of incompressible quantum Hall liquids
journal, May 2006

Tokatly, I. V.
Physical Review B, Vol. 73, Issue 20
DOI: 10.1103/PhysRevB.73.205340

Hamiltonian formalism for nonlinear waves [Gamil'tonovskii formalizm dlya nelineinykh voln]
journal, January 1997

Zakharov, V. E.; Kuznetsov, Evgenii A.
Uspekhi Fizicheskih Nauk, Vol. 167, Issue 11
DOI: 10.3367/UFNr.0167.199711a.1137

Viscosity of Quantum Hall Fluids
journal, July 1995

Avron, J. E.; Seiler, R.; Zograf, P. G.
Physical Review Letters, Vol. 75, Issue 4
DOI: 10.1103/PhysRevLett.75.697

Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
journal, April 2012

Yang, Bo; Papić, Z.; Rezayi, E. H.
Physical Review B, Vol. 85, Issue 16
DOI: 10.1103/PhysRevB.85.165318

Odd viscosity in chiral active fluids
journal, November 2017

Banerjee, Debarghya; Souslov, Anton; Abanov, Alexander G.
Nature Communications, Vol. 8, Issue 1
DOI: 10.1038/s41467-017-01378-7

Swimming at low Reynolds number in fluids with odd, or Hall, viscosity
journal, April 2014

Lapa, Matthew F.; Hughes, Taylor L.
Physical Review E, Vol. 89, Issue 4
DOI: 10.1103/PhysRevE.89.043019

Hall viscosity, topological states and effective theories
journal, May 2014

Hoyos, Carlos
International Journal of Modern Physics B, Vol. 28, Issue 15
DOI: 10.1142/S0217979214300072

Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect
journal, January 2015

Gromov, Andrey; Cho, Gil Young; You, Yizhi
Physical Review Letters, Vol. 114, Issue 1
DOI: 10.1103/PhysRevLett.114.016805

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
journal, November 2015

Can, Tankut; Laskin, Michael; Wiegmann, Paul B.
Annals of Physics, Vol. 362
DOI: 10.1016/j.aop.2015.02.013

Erratum: Lorentz shear modulus of a two-dimensional electron gas at high magnetic field [Phys. Rev. B 76 , 161305(R) (2007)]
journal, May 2009

Tokatly, I. V.; Vignale, G.
Physical Review B, Vol. 79, Issue 19
DOI: 10.1103/PhysRevB.79.199903

Boundary Effective Action for Quantum Hall States
journal, March 2016

Gromov, Andrey; Jensen, Kristan; Abanov, Alexander G.
Physical Review Letters, Vol. 116, Issue 12
DOI: 10.1103/PhysRevLett.116.126802

Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids
journal, November 2017

Pellegrino, Francesco M. D.; Torre, Iacopo; Polini, Marco
Physical Review B, Vol. 96, Issue 19
DOI: 10.1103/PhysRevB.96.195401

�ber ein Minimumproblem f�r Potentialstr�mungen mit freiem Rande
journal, December 1934

Friedrichs, Kurt
Mathematische Annalen, Vol. 109, Issue 1
DOI: 10.1007/BF01449125

New Collective Mode in the Fractional Quantum Hall Liquid
journal, January 2007

Tokatly, I. V.; Vignale, G.
Physical Review Letters, Vol. 98, Issue 2
DOI: 10.1103/PhysRevLett.98.026805

Geometric Adiabatic Transport in Quantum Hall States
journal, August 2015

Klevtsov, S.; Wiegmann, P.
Physical Review Letters, Vol. 115, Issue 8
DOI: 10.1103/PhysRevLett.115.086801

Density-Curvature Response and Gravitational Anomaly
journal, December 2014

Gromov, Andrey; Abanov, Alexander G.
Physical Review Letters, Vol. 113, Issue 26
DOI: 10.1103/PhysRevLett.113.266802

Collective field theory for quantum Hall states
journal, December 2015

Laskin, M.; Can, T.; Wiegmann, P.
Physical Review B, Vol. 92, Issue 23
DOI: 10.1103/PhysRevB.92.235141

Geometrical Description of the Fractional Quantum Hall Effect
journal, September 2011

Haldane, F. D. M.
Physical Review Letters, Vol. 107, Issue 11
DOI: 10.1103/PhysRevLett.107.116801

Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
journal, July 2014

Can, T.; Laskin, M.; Wiegmann, P.
Physical Review Letters, Vol. 113, Issue 4
DOI: 10.1103/PhysRevLett.113.046803

A variational principle for a fluid with a free surface
journal, February 1967

Luke, J. C.
Journal of Fluid Mechanics, Vol. 27, Issue 2
DOI: 10.1017/S0022112067000412

Variational Principles for Water Waves
journal, January 2006

Kolev, B.; Sattinger, D. H.
SIAM Journal on Mathematical Analysis, Vol. 38, Issue 3
DOI: 10.1137/050647220

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
journal, October 2007

Tokatly, I. V.; Vignale, G.
Physical Review B, Vol. 76, Issue 16
DOI: 10.1103/PhysRevB.76.161305

On the effective hydrodynamics of the fractional quantum Hall effect
journal, June 2013

Abanov, Alexander G.
Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 29
DOI: 10.1088/1751-8113/46/29/292001

Quantum Hall Effect and Quillen Metric
journal, November 2016

Klevtsov, Semyon; Ma, Xiaonan; Marinescu, George
Communications in Mathematical Physics, Vol. 349, Issue 3
DOI: 10.1007/s00220-016-2789-2

Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons
journal, October 2016

Alekseev, P. S.
Physical Review Letters, Vol. 117, Issue 16
DOI: 10.1103/PhysRevLett.117.166601

Anomalous Hydrodynamics of Two-Dimensional Vortex Fluids
journal, July 2014

Wiegmann, Paul; Abanov, Alexander G.
Physical Review Letters, Vol. 113, Issue 3
DOI: 10.1103/PhysRevLett.113.034501

Stability of periodic waves of finite amplitude on the surface of a deep fluid
journal, January 1972

Zakharov, V. E.
Journal of Applied Mechanics and Technical Physics, Vol. 9, Issue 2
DOI: 10.1007/BF00913182

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
text, January 2007

Tokatly, I. V.; Vignale, G.
arXiv
DOI: 10.48550/arxiv.0706.2454

Variational Principles for Water Waves
text, January 2007

Kolev, Boris; Sattinger, David H.
arXiv
DOI: 10.48550/arxiv.0712.0054

Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
text, January 2012

Yang, Bo; Papić, Z.; Rezayi, E. H.
arXiv
DOI: 10.48550/arxiv.1202.5586

Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
text, January 2012

Bradlyn, Barry; Goldstein, Moshe; Read, N.
arXiv
DOI: 10.48550/arxiv.1207.7021

Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
text, January 2012

Hughes, Taylor L.; Leigh, Robert G.; Parrikar, Onkar
arXiv
DOI: 10.48550/arxiv.1211.6442

Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
text, January 2013

Lapa, Matthew F.; Hughes, Taylor L.
arXiv
DOI: 10.48550/arxiv.1310.6270

Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
text, January 2013

Wiegmann, Paul; Abanov, Alexander G.
arXiv
DOI: 10.48550/arxiv.1311.4479

Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
text, January 2014

Gromov, Andrey; Cho, Gil Young; You, Yizhi
arXiv
DOI: 10.48550/arxiv.1410.6812

Collective Field Theory for Quantum Hall States
text, January 2014

Laskin, M.; Can, T.; Wiegmann, P.
arXiv
DOI: 10.48550/arxiv.1412.8716

Geometric adiabatic transport in quantum Hall states
text, January 2015

Klevtsov, Semyon; Wiegmann, Paul
arXiv
DOI: 10.48550/arxiv.1504.07198

Quantum Hall effect and Quillen metric
text, January 2015

Klevtsov, Semyon; Ma, Xiaonan; Marinescu, George
arXiv
DOI: 10.48550/arxiv.1510.06720

Negative magnetoresistance in viscous flow of two-dimensional electrons
text, January 2016

Alekseev, P. S.
arXiv
DOI: 10.48550/arxiv.1603.04587

Magnetoelasticity theory of incompressible quantum Hall liquids
text, January 2005

Tokatly, I. V.
arXiv
DOI: 10.48550/arxiv.cond-mat/0505715

Viscosity of Quantum Hall Fluids
text, January 1995

Avron, J. E.; Seiler, R.; Zograf, P. G.
arXiv
DOI: 10.48550/arxiv.cond-mat/9502011

Similar Records in DOE PAGES and OSTI.GOV collections:

Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

Journal Article Abanov, Alexander G. ; Can, Tankut ; Ganeshan, Sriram ; ... - Physical Review Fluids (Online)

In this paper, we consider an isotropic compressible nondissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid and the free surface boundary conditions depend explicitly on the parity-breaking nondissipative odd viscosity term. We construct an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a 1+1D chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water casemore »« less
https://doi.org/10.1103/physrevfluids.5.104802

Full Text Available
Odd surface waves in two-dimensional incompressible fluids

Journal Article Abanov, Alexander ; Can, Tankut ; Ganeshan, Sriram - SciPost Physics

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit,more »« less
Cited by 40
https://doi.org/10.21468/SciPostPhys.5.1.010
The Hamiltonian description of incompressible fluid ellipsoids

Journal Article Morrison, P.J. ; Lebovitz, Norman R ; Biello, Joseph A - Annals of Physics (New York)

We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac's procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, andmore »« less
https://doi.org/10.1016/j.aop.2009.04.003
Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Journal Article Kaltsas, D. A. ; Throumoulopoulos, G. N. ; Morrison, P. J. - Journal of Plasma Physics

Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for the three-dimensional dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (Kaltsaset al.,Phys. Plasmas, vol. 24, 2017, 092504). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy–Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad–Shafranov–Bernoulli equilibrium equations. The axisymmetric and the translationally symmetric formulations can be retrieved as geometric reductions of the helicallymore »« less
https://doi.org/10.1017/s0022377818000338
Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics

Journal Article Morrison, P. J. ; Andreussi, T. ; Pegoraro, F. - Journal of Plasma Physics

The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac’s constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac’s method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian description, allowing for the advection of density. Both cases give the dynamics of infinite-dimensional geodesic flow onmore »« less
https://doi.org/10.1017/s0022377820000331

Full Text Available

Similar Records

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

Abstract

Citation Formats

Hydrodynamic Electron Flow and Hall Viscosity journal, June 2017

Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions journal, December 2014

Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states journal, July 2013

Hall Viscosity and Electromagnetic Response journal, February 2012

Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p x + i p y paired superfluids journal, January 2009

Transport Signatures of the Hall Viscosity journal, November 2017

Odd surface waves in two-dimensional incompressible fluids journal, January 2018

On Hadamard's variational formula journal, June 1980

Magnetoelasticity theory of incompressible quantum Hall liquids journal, May 2006

Hamiltonian formalism for nonlinear waves [Gamil'tonovskii formalizm dlya nelineinykh voln] journal, January 1997

Viscosity of Quantum Hall Fluids journal, July 1995

Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems journal, April 2012

Odd viscosity in chiral active fluids journal, November 2017

Swimming at low Reynolds number in fluids with odd, or Hall, viscosity journal, April 2014

Hall viscosity, topological states and effective theories journal, May 2014

Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect journal, January 2015

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients journal, November 2015

Erratum: Lorentz shear modulus of a two-dimensional electron gas at high magnetic field [Phys. Rev. B 76 , 161305(R) (2007)] journal, May 2009

Boundary Effective Action for Quantum Hall States journal, March 2016

Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids journal, November 2017

�ber ein Minimumproblem f�r Potentialstr�mungen mit freiem Rande journal, December 1934

New Collective Mode in the Fractional Quantum Hall Liquid journal, January 2007

Geometric Adiabatic Transport in Quantum Hall States journal, August 2015

Density-Curvature Response and Gravitational Anomaly journal, December 2014

Collective field theory for quantum Hall states journal, December 2015

Geometrical Description of the Fractional Quantum Hall Effect journal, September 2011

Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response journal, July 2014

A variational principle for a fluid with a free surface journal, February 1967

Variational Principles for Water Waves journal, January 2006

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field journal, October 2007

On the effective hydrodynamics of the fractional quantum Hall effect journal, June 2013

Quantum Hall Effect and Quillen Metric journal, November 2016

Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons journal, October 2016

Anomalous Hydrodynamics of Two-Dimensional Vortex Fluids journal, July 2014

Stability of periodic waves of finite amplitude on the surface of a deep fluid journal, January 1972

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field text, January 2007

Variational Principles for Water Waves text, January 2007

Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems text, January 2012

Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity text, January 2012

Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States text, January 2012

Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity text, January 2013

Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid text, January 2013

Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect text, January 2014

Collective Field Theory for Quantum Hall States text, January 2014

Geometric adiabatic transport in quantum Hall states text, January 2015

Quantum Hall effect and Quillen metric text, January 2015

Negative magnetoresistance in viscous flow of two-dimensional electrons text, January 2016

Magnetoelasticity theory of incompressible quantum Hall liquids text, January 2005

Viscosity of Quantum Hall Fluids text, January 1995

Hydrodynamic Electron Flow and Hall Viscosity
journal, June 2017

Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions
journal, December 2014

Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states
journal, July 2013

Hall Viscosity and Electromagnetic Response
journal, February 2012

Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and $p_{x} + i p_{y}$ paired superfluids
journal, January 2009

Transport Signatures of the Hall Viscosity
journal, November 2017

Odd surface waves in two-dimensional incompressible fluids
journal, January 2018

On Hadamard's variational formula
journal, June 1980

Magnetoelasticity theory of incompressible quantum Hall liquids
journal, May 2006

Hamiltonian formalism for nonlinear waves [Gamil'tonovskii formalizm dlya nelineinykh voln]
journal, January 1997

Viscosity of Quantum Hall Fluids
journal, July 1995

Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
journal, April 2012

Odd viscosity in chiral active fluids
journal, November 2017

Swimming at low Reynolds number in fluids with odd, or Hall, viscosity
journal, April 2014

Hall viscosity, topological states and effective theories
journal, May 2014

Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect
journal, January 2015

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
journal, November 2015

Erratum: Lorentz shear modulus of a two-dimensional electron gas at high magnetic field [Phys. Rev. B 76 , 161305(R) (2007)]
journal, May 2009

Boundary Effective Action for Quantum Hall States
journal, March 2016

Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids
journal, November 2017

�ber ein Minimumproblem f�r Potentialstr�mungen mit freiem Rande
journal, December 1934

New Collective Mode in the Fractional Quantum Hall Liquid
journal, January 2007

Geometric Adiabatic Transport in Quantum Hall States
journal, August 2015

Density-Curvature Response and Gravitational Anomaly
journal, December 2014

Collective field theory for quantum Hall states
journal, December 2015

Geometrical Description of the Fractional Quantum Hall Effect
journal, September 2011

Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
journal, July 2014

A variational principle for a fluid with a free surface
journal, February 1967

Variational Principles for Water Waves
journal, January 2006

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
journal, October 2007

On the effective hydrodynamics of the fractional quantum Hall effect
journal, June 2013

Quantum Hall Effect and Quillen Metric
journal, November 2016

Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons
journal, October 2016

Anomalous Hydrodynamics of Two-Dimensional Vortex Fluids
journal, July 2014

Stability of periodic waves of finite amplitude on the surface of a deep fluid
journal, January 1972

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
text, January 2007

Variational Principles for Water Waves
text, January 2007

Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
text, January 2012

Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
text, January 2012

Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
text, January 2012

Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
text, January 2013

Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
text, January 2013

Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
text, January 2014

Collective Field Theory for Quantum Hall States
text, January 2014

Geometric adiabatic transport in quantum Hall states
text, January 2015

Quantum Hall effect and Quillen metric
text, January 2015

Negative magnetoresistance in viscous flow of two-dimensional electrons
text, January 2016

Magnetoelasticity theory of incompressible quantum Hall liquids
text, January 2005

Viscosity of Quantum Hall Fluids
text, January 1995