  Deposition and evaporation of infinitely thin hard rods (needles) is studied
in two dimensions using Monte Carlo simulations. The ratio of deposition to
evaporation rates controls the equilibrium density of rods, and increasing it
leads to an entropy-driven transition to a nematic phase in which both static
and dynamical orientational correlation functions decay as power laws, with
exponents varying continuously with deposition-evaporation rate ratio. Our
results for the onset of the power-law phase agree with those for a conserved
number of rods. At a coarse-grained level, the dynamics of the non-conserved
angle field is described by the Edwards-Wilkinson equation. Predicted relations
between the exponents of the quadrupolar and octupolar correlation functions
are borne out by our numerical results. We explore the effects of spatial
inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based
arguments and a study of the new terms introduced in the free energy. The
primary effect is that needles tend to align along the local spatial gradient
of the ratio. A uniform gradient thus induces a uniformly aligned state, as
does a gradient which varies randomly in magnitude and sign, but acts only in
one direction. Random variations of deposition-evaporation rates in both
directions induce frustration, resulting in a state with glassy
characteristics.
