"Interfering directed paths & the sign phase transition"
This event is part of the Condensed Matter Theory Seminar Series.
We consider the problem of interfering directed paths in disordered media, and discuss the physical contexts in which this problem arises. An important property of the path sum is the statistics of its sign. The average sign may tend to zero ("sign-disordered") or remain finite ("sign-ordered") at long distance, depending on dimensionality and the concentration of negative scattering sites x. We discuss the analogy with a dynamical out-of-equilibrium Ising field. We further show that the sign-ordered phase is always unstable for any non-zero x in 2D by identifying rare destabilizing events, and present numerical evidence that it is stable in 3D. These results have consequences for several different physical systems, which we conclude by describing.