On the space-time curvature experienced by quasiparticle excitations in the Painleve-Gullstrand effective geometry
arXiv:cond-mat/0205139 · doi:10.1016/S0003-4916(03)00011-3
Abstract
We consider quasiparticle propagation in constant-speed-of-sound (iso-tachic) and almost incompressible (iso-pycnal) hydrodynamic flows, using the technical machinery of general relativity to investigate the ``effective space-time geometry'' that is probed by the quasiparticles. This effective geometry, described for the quasiparticles of condensed matter systems by the Painleve-Gullstrand metric, generally exhibits curvature (in the sense of Riemann), and many features of quasiparticle propagation can be re-phrased in terms of null geodesics, Killing vectors, and Jacobi fields. As particular examples of hydrodynamic flow we consider shear flow, a constant-circulation vortex, flow past an impenetrable cylinder, and rigid rotation.
arXiv comment9 RevTex4 pages, 1 figure, minor modifications, to appear in Annals of Physics (N.Y.)
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