Singlet growth - a universal dynamical model
Dietrich von Harrach (Institut für Kernphysik der Universität Mainz)

A dynamical model describing the evolution of physical systems based on a growing number of spins is presented. The growth process consists in recursively adding and entangling another pair of spins, preserving the norm and the overall singlet structure of the system. The amplitudes for the enlarged Hilbert space are fixed in an unbiased random process considered as spontaneous symmetry breaking. Fixing boundary conditions at each growth step M generates persisting relations and structures in the 2Mx2M index space. The description of the system is timeless. The emerging "spin crystal" bears fractal properties which can be read and analyzed in terms of observables based on index exchange operators. A positive definite and additive scalar quantity which is interpreted as the energy can be derived.
The total energy normalized to the number of index pairs is 1/4(1+O(1/M)). The energy flow at the growth boundary is naturally represented with a 3-vector quantity, which is interpreted as a momentum density. The system exhibits an interesting metric, charge structure and scaling.