Quantum spin chains arising as the 1-dimensional quantum version of classical 2-dimensional statistical mechanical models exhibit the same Hilbert spaces as those arising by iterating correspondences in the sense of Connes. This will be explained and the highly speculative possibility of a continuum limit conformal field theory proposed.

We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multichannel quantum defect theory. The resulting classical map is analyzed at energies above the threshold for the Rydberg electron. At energies very near to this threshold we find the possibility of bounded motion for positive energy due ...

The new techniques in seismic design of structures are usually attributed to high damping ratios. In such systems, the assumption of classical (i.e. proportional) damping is not valid and in most cases they should be considered as Non-classical systems. Since the analytical tools for studying the behavior of such structures are not easily available, the present work attempts to find the limits,...

The phonon dispersion relations calculated by atomic model: shell model and ab initio, and by microcontinuum theory are introduced in this paper. It is found that both atomic models and microcontinuum theory can describe the common feature of phonon dispersion relation for the crystal having more than one atom per primitive cell and can give a good fit to the experimentally measured data. The o...

In this paper, transfinite element method is used to analyze the two dimensional thermoelasticity problems. A comparison is made between the thermoelastic analysis results of the classical theory and theories with one or two relaxation times (i.e. L-S and G-L theories), for the half space problem. Governing equations are transformed to Laplace domain and then, node variables are calculated by t...

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces. We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classi...

We propose a new method which analyzes the dynamical triangulation from the viewpoint of the non-critical string field theory. By using the transfer matrix formalism, we construct the non-critical string field theory (including c > 1 cases) at the discrete level. For pure quantum gravity, we succeed in taking the continuum limit and obtain the c = 0 non-critical string field theory at the conti...