Abstract
We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. This system has topological semimetal-like crossing nodes in the spectrum of hydrodynamic modes that require the protection of a special combination of translational and boost symmetries in two spatial directions. We confirm the nontrivial topology from the existence of an undetermined Berry phase. These energy momentum non-conservation terms could naturally be produced by an external gravitational field that comes from a reference frame change from the original inertial frame, i.e. by fictitious forces in a non-inertial reference frame. This non-inertial frame is the rest frame of an accelerating observer moving along a trajectory of a helix. This suggests that topologically trivial modes could become nontrivial by being observed in a special non-inertial reference frame, and this fact could be verified in laboratories, in principle. Finally, we propose a holographic realization of this system.
Highlights
Hydrodynamics is the universal low energy theory for systems close to local thermal equilibrium at a long distance and time
We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way
We confirm the nontrivial topology from the existence of an undetermined Berry phase. These energy momentum nonconservation terms could naturally be produced by an external gravitational field that comes from a reference frame change from the original inertial frame, i.e., by fictitious forces in a noninertial reference frame
Summary
Hydrodynamics is the universal low energy theory for systems close to local thermal equilibrium at a long distance and time It could describe a variety of physical systems ranging from matter at large scales in the Universe, the quarkgluon plasma [1], to Weyl semimetals [2,3] and graphenes [4] in the laboratory. It has been found that many classical systems have nontrivial topological states too, including topological optical/sound systems (see, e.g., [8,9,10] and references therein), which have been observed experimentally It raises the question if the gapless modes in relativistic hydrodynamics could become topologically nontrivial under certain conditions. We start from the relativistic hydrodynamics and show that after weakly breaking conservation of energy momentum, hydrodynamic modes could become topological semimetal-like nontrivial states that require the protection of a special spacetime symmetry, and interestingly, these nonconservation terms for the energy momentum tensor could come from a noninertial reference frame of an accelerating observer moving along a helix
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