Quantum brownian motion on a triangular lattice and c=2 boundary conformalfield theory

We study a single particle diffusing on a triangular lattice and interactin g with a heat bath. using boundary conformal field theory (CFT) and exact i ntegrability techniques. We derive a correspondence between the phase diagr am of this problem and that recently obtained for the 2-dimensional 3-state Potts model with a boundary. Exact results are obtained on phases with int ermediate mobilities. These correspond to nontrivial boundary states in a c onformal held theory with 2 free bosons which we explicitly construct for t he first time. These conformally invariant boundary conditions are nut simp ly products of Dirichlet and Neumann ones and unlike those trivial boundary conditions, are not invariant under a Heisenberg algebra. (C) 2001 Elsevie r Science B.V. All rights reserved.