Non-hermitian integrable quantum chains and their applications to equilibrium crystal shapes and reaction-diffusion problems

Abstract

In the first part of this work the free energy of the asymmetric six-vertex model is computed analytically. Using the correspondence between this model and the surface shape of an fcc crystal, it is shown how the non-analytical behavior of the free energy leads to the appearance of singularities (edges) in the crystal facet. A new exponent describing such singularities is found, and its possible experimental measurement is discussed. In the second part, a list of reaction-diffusion processes for two species of molecules on a one-dimensional lattice is presented. The markovian evolution of such systems is shown to be governed by a Master Equation whose Hamiltonian is that of the U_qSU(P/M)-invariant Perk-Schultz chain. (orig.)Available from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman