Critical phenomena and scaling behavior in theories of activated barrier crossing

A novel critical scaling behavior is shown to be present in the theory of activated barrier crossing. The critical exponents and the scaling functions are calculated for a general memory friction kernel and for nonlinear potentials of the form V(x)=-1/2M${\mathrm{\omega }}_{\mathit{b}}^2$ ${\mathit{x}}^2$+(${\mathit{C}}_{\mathit{n}}$/2n)${\mathit{x}}^{2\mathit{n}}$, n=2,3,4,. . .. The critical exponents are found to depend only on the shape of the potential characterized by n and the form of the memory friction characterized by a certain parameter p.