Hamiltonian structure of 2D fluid dynamics with broken parity

Journal Article · 09 May 2023 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.14.5.103 · OSTI ID:1973167

Machado Monteiro, Gustavo ^[1]; Abanov, Alexander G. ^[2]; Ganeshan, Sriram ^[3]

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1. City University of New York
2. Simons Center for Geometry and Physics, Stony Brook University
3. City University of New York, The Graduate Center, CUNY

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

• Research Organization: State Univ. of New York (SUNY), Albany, NY (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0017662
• OSTI ID: 1973167
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 5 Vol. 14; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English