Irreversible random and cooperative processes on lattices: Spatial correlations

Exactly solvable irreversible processes on Bethe lattices

We consider the kinetics of processes where the sites of a Bethe lattice are filled irreversibly and, in general, cooperatively by monomers, dimers, or polyatomics. For nearest neighbor and sometimes more general cooperative effects (including random filling as a special case), we show that the infinite hierarchy of rate equations for probabilities of empty subconfigurations can be exacty trunc...

Exactly solvable irreversible processes on one‐dimensional lattices

We consider the kinetics of a process where the sites of an infinite 1‐D lattice are filled irreversibly and, in general, cooperatively by N‐mers (taking Nconsecutive sites at a time). We extend the previously available exact solutionfor nearest neighbor cooperative effects to range N cooperative effects. Connection with the continuous ‘‘cooperative car parking problem’’ is indicated. Both unif...

Probability on Graphs Random Processes on Graphs and Lattices

Universal spatial correlations in random spinor fields.

We identify universal spatial fluctuations in systems with nontrivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations, and spin currents, both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction. We su...

Competing irreversible cooperative reactions on polymer chains

We analyze model processes involving competition between several irreversible reactions at the sites of a 1D, infinite, uniform polymer chain. These reactionscan be cooperative, i.e., the corresponding rates depend on the state of the surrounding sites. An infinite hierarchy of rate equations is readily derived for the probabilities of various subconfigurations. By exploiting a shielding proper...