  We consider the the intersections of the complex nodal set of the analytic
continuation of an eigenfunction of the Laplacian on a real analytic surface
with the complexification of a geodesic. We prove that if the geodesic flow is
ergodic and if the geodesic is periodic and satisfies a generic asymmetry
condition, then the intersection points condense along the real geodesic and
become uniformly distributed with respect to its arc-length. We prove an
analogous result for non-periodic geodesics except that the `origin' is allowed
to move with $\lambda_j$. The proof uses the quantum ergodic restriction
theorem due to J. Toth and the author (see also Dyatlov-Zworski).
