Coherence theory and coherence phenomena in a closed spin 1/2 system

We study a simplified Heisenberg spin model in order to clarify the idea of decoherence in closed quantum systems. For this purpose, we define a new concept: the coherence function Ξ(t), which describes the dynamics of coherence in the whole system, and which is linked with the total coarsegrained (von Neumann) entropy of all particles. We discuss in some detail a general coherence theory and its elementary results. For example, in the particular setup, decoherence diagonalises reduced density matrices in all possible basis sets. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to entropy. Moreover, the concept of decoherence time is applicable in closed systems. However, in most cases, the decay of off-diagonal elements differs from the usual exp(−t/τd) behaviour. We have solved the form of decoherence time τd in an infinite Heisenberg model with respect to density ρ, spatial dimension D and ǫ in a 1/r ǫ -type of potential.