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Hamiltonian structure of 2D fluid dynamics with broken parity
by Gustavo Machado Monteiro, Alexander G. Abanov, Sriram Ganeshan
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Sriram Ganeshan · Gustavo Machado Monteiro |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2105.01655v4 (pdf) |
| Date accepted: | 2023-02-15 |
| Date submitted: | 2022-12-21 15:53 |
| Submitted by: | Machado Monteiro, Gustavo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
List of changes
We have replaced “constraints” by “sufficient conditions” and “only if” by “if” in the following paragraph on p. 03:
“For a hydrodynamic system whose energy is conserved, we derive sufficient conditions on the transport coefficients for the system to be Hamiltonian. As a consequence, we obtain that an energy-conserving hydrodynamic system is Hamiltonian if there exists a conserved quantity, ρvi + εi j∂jηH , which satisfies the diffeomorphism algebra”.
In addition to that, we have included the following paragraph on p.06:
"It is worth to note that the Hamiltonian function need not always be the total energy of
system, however we do not consider this possibility in this work. We aim to recover the ideal
fluid structure, in the limit of vanishing viscosity coefficients. In addition to that, we only consider
local deformations of the ideal fluid Poisson algebra here".
Published as SciPost Phys. 14, 103 (2023)