Cyclic metric Lie groups

Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and solvable cases are studied. We extend to the general case, Kowalski-Tricerri's and Bieszk's classifications of connected and simply-connected unimodular cyclic metric Lie groups for dimensions less than or equal to five

Relaxation in open one-dimensional systems

A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file system); and the total number of walkers in the lattice can fluctuate because of exchange with a bath.In addition, the movement of the random walkers is biased by an external perturbation. Two models for the latter are considered: (1) an inverse potential (V $\propto$ 1/r), where r is the distance between the center of the perturbation and the random walker and (2) an inverse of sixth power potential ($V \propto 1/r^6$). The calculated density of the walkers and the total energy show interesting dynamics. When the size of the system is comparable to the range of the perturbing field, the energy relaxation is found to be highly non-exponential. In this range, the system can show stretched exponential ($e^{-{(t/\tau_s)}^{\beta}}$) and even logarithmic time dependence of energy relaxation over a limited range of time. Introduction of density exchange in the lattice markedly weakens this non-exponentiality of the relaxation function, irrespective of the nature of perturbation