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

Abstract

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general coherence theory and its elementary results. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function $\Xi(t)$, but not from the entropy dynamics. Moreover, the concept of decoherence time is applicable in closed and finite systems. However, in most cases, the decay of off-diagonal elements differs from the usual $\exp(-t/\tau_{\rm d})$ behaviour. For concreteness, we report the form of decoherence time $\tau_{\rm d}$ in a finite Heisenberg model with respect to the number of particles $N$, density $n_{\rho}$, spatial dimension $D$ and $\epsilon$ in a $\eta/r^{\epsilon}$-type of potential.Comment: 31 pages, 5 figures, v2: major changes, accepted for publicatio

Quantum correlation via quantum coherence

“…The measurements on the observables that do not commute with A can reveal the interference. Based on different viewpoints, a lot of quantum coherence measure can be defined with respect to the basis [39,40]. Here we will present a new coherence measure by which we can classify the coherence.…”