Properties of noninteger moments in a first passage time problem

We calculate the moments t^q, whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t_q ~L(q) asL, then we show that there is a phase transition atq=q_csuch that whenq<q_c,(g)=0, and forq>q_c, (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.