Summary: Journal of Statistical Physics, Vol. 92, Nos. 3/4. 1998
J. E. Avron1
Received December 8, 1997
When time reversal is broken, the viscosity tensor can have a nonvanishing odd
part. In two dimensions, and only then, such odd viscosity is compatible with
isotropy. Elementary and basic features of odd viscosity are examined by
considering solutions of the wave and Navier-Stokes equations forhypothetical
fluids where the stress is dominated by odd viscosity.
1. INTRODUCTION AND OVERVIEW
Normally, one associates viscosity with dissipation. However, as the viscosity
is, in general, a tensor, this need not be the case since the antisymmetric
part of a tensor is not associated with dissipation. We call the antisym-
metric part odd. It must vanish, by Onsager relation, if time reversal holds.
It must also vanish in three dimensions if the tensor is isotropic. But, in
two dimensions odd viscosity is compatible with isotropy.
It is conceivable that that odd viscosity does not vanish for many
system where time reversal is broken either spontaneously or by external
fields.But, I know of only two systems for which there are theoretical studies
of the odd viscosity and none for which it has been studied experimentally.