Everyday fluids such as water and air move far slower than light and are described by non-relativistic hydrodynamics. Much of my early work built non-relativistic and Galilean hydrodynamics from first principles: equilibrium partition functions, entropy currents, the effects of anomalies, and a systematic way to obtain non-relativistic fluids from relativistic ones through null (light-cone) reduction.
Later, I developed effective field theories for non-relativistic hydrodynamics and, with Jay Armas, for hydrodynamics that assumes no boost symmetry at all. This treats relativistic fluids, Galilean fluids and systems with neither symmetry in one framework.
Papers
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Effective field theory for hydrodynamics without boosts
Most theories of fluids assume that physics looks the same to an observer moving at constant speed, a symmetry called boost invariance. Many systems break it, such as fluids flowing through a medium, electrons in some quantum materials, or very cold liquid helium-3. We build the effective field theory of hydrodynamics without boost symmetry, including random fluctuations, and find 29 independent transport coefficients at first order. Sound then travels at different speeds with and against the flow. The framework treats relativistic, non-relativistic and exotic fluids alike.
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Effective field theory for non-relativistic hydrodynamics
Everyday fluids such as water and air move far slower than light and obey non-relativistic physics. A modern effective field theory of hydrodynamics, which also accounts for random thermal fluctuations, existed for relativistic fluids, but not for these ordinary ones. I construct it using a geometric trick: a non-relativistic fluid can be viewed as a relativistic one in a spacetime with one extra dimension, along a special lightlike direction. The relativistic tools then carry over, and I use them to work out how fluctuations of energy, momentum and density interact.
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Second order Galilean fluids and Stokes’ law
Everyday fluids are described by the Navier–Stokes equations, which capture viscosity but are only the first step in an expansion in how rapidly the flow varies. We work out the next step, the second-order corrections for an uncharged non-relativistic fluid, using “null fluids”: a description of such fluids as relativistic ones in one extra dimension, which makes their symmetries easy to handle. The method yields an algorithm for any order. We then ask how the new terms affect Stokes’ law for the drag on a small sphere moving slowly through a fluid, and find which leave it unchanged.
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First Order Galilean Superfluid Dynamics
Superfluids, first seen in liquid helium in 1938, flow without friction and form vortices when rotated. We work out the general theory of how non-relativistic superfluids flow and dissipate at first order in gradients, including effects that break mirror symmetry or come from quantum anomalies. To do so, we construct “null superfluids”: relativistic superfluids in one extra dimension that are exactly equivalent to non-relativistic ones, so that the powerful tools of relativistic hydrodynamics can be applied.
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Galilean Anomalies and Their Effect on Hydrodynamics
Quantum anomalies are symmetries of a classical theory that are broken by quantum effects. In relativistic fluids, such as the quark-gluon plasma, they make currents flow along magnetic fields and rotation axes. I study anomalies in non-relativistic theories by viewing them as relativistic theories in one extra dimension, now also allowing for spin and the torsion of spacetime. As in the relativistic case, they only occur in even dimensions, and they leave Galilean boosts untouched. I also work out how they modify the flow of non-relativistic fluids.
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Null Fluids - A New Viewpoint of Galilean Fluids
Non-relativistic physics can be seen as a corner of relativistic physics: the symmetries of everyday, slow-moving systems sit inside those of special relativity in one extra dimension. We use this to define “null fluids”, relativistic fluids in one higher dimension that are exactly equivalent to ordinary non-relativistic fluids, with the same symmetries, thermodynamics and equations to all orders. This makes their symmetries manifest and lets relativistic results carry over. We also use it to include quantum anomalies, which add new effects that break mirror symmetry.
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Equilibrium partition function for nonrelativistic fluids
For relativistic fluids, the equilibrium behaviour in any external field follows from a single object, the equilibrium partition function, which strongly constrains its flow. We construct the analogous partition function for non-relativistic fluids, obtaining them from relativistic fluids in one extra dimension through a light-cone reduction. The resulting “null fluid” matches the non-relativistic fluid exactly, with the same symmetries, thermodynamics, equations and partition function to all orders. This short paper introduced null fluids, developed fully in our follow-up work.
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Entropy current for non-relativistic fluid
The second law of thermodynamics, that entropy never decreases, strongly constrains how fluids can dissipate energy. We apply it to non-relativistic charged fluids in electric and magnetic fields, including fluids whose microscopic physics breaks mirror symmetry, by obtaining them from relativistic fluids in one extra dimension. For ordinary fluids, it simply requires viscosity and the conductivities to be positive. For mirror-asymmetric fluids, the entropy current needs two extra terms, which the second law fixes exactly, and such effects survive only if the fluid is incompressible.
Talks
Non-relativistic Schwinger-Keldysh hydrodynamics
Offshell framework of hydrodynamics
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Durham University, UK (HEP Student Seminar)
Non-relativistic hydrodynamics and null reduction
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International Centre for Theoretical Physics, Italy
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LACES 2015 Workshop, Galileo Galilei Institute for Theoretical Physics, Italy
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Durham University, UK (HEP Student Seminar)
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Poster
STRINGS 2015 Conference, ICTS Bangalore, India
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Conference talk
Young Theorists Forum Conference, Durham University, UK
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Conference talk
Inter-IISER and NISER Physics Meet, IISER Pune, India
