Kardar-Parisi-Zhang equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall.

We present an exact solution for the height distribution of the KPZ equation at any time t in a half space with flat initial condition. This is equivalent to obtaining the free-energy distribution of a polymer of length t pinned at a wall at a single point. In the large t limit a binding transition takes place upon increasing the attractiveness of the wall.

Half-Space Stationary Kardar-Parisi-Zhang Equation.

We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height (, ) on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a wall at . The boundary condition corresponds to an attractive wall for , and leads to the binding of the polymer to the wall below the critical value . Here we choose the initial condition (, 0) to be a Brownian motion in with drift .

Stochastic growth in time-dependent environments.

We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance c(t) depending on time. We find that for c(t)∝t^{-α} there is a transition at α=1/2. When α>1/2, the solution saturates at large times towards a nonuniversal limiting distribution.