VALLEYS IN NONCRITICAL STRING FOAM SUPPRESS QUANTUM COHERENCE

As an example of our noncritical string approach to microscopic black hole dynamics, we exhibit some string contributions to the [Formula: see text] matrix relating in- and out-state density matrices that do not factorize as a product of S and S† matrices. They are associated with valley trajectories between topological defects on the string worldsheet, that appear as quantum fluctuations in the space-time foam. Through their uv renormalization scale dependences these valleys cause non-Hamiltonian time evolution and suppress off-diagonal entries in the density matrix at large times. Our approach is a realization of previous formulations of nonequilibrium quantum statistical mechanics with an arrow of time.