Non-Markovian dynamics in a spin star system: The failure of thermalization

In most cases, a small system weakly interacting with a thermal bath will finally reach the thermal state with the temperature of the bath. We show that this intuitive picture is not always true by a spin star model where non-Markov effect predominates in the whole dynamical process. The spin star system consists a central spin homogeneously interacting with an ensemble of identical noninteracting spins. We find that the correlation time of the bath is infinite, which implies that the bath has a perfect memory, and that the dynamical evolution of the central spin must be non- Markovian. A direct consequence is that the final state of the central spin is not the thermal state equilibrium with the bath, but a steady state which depends on its initial state.Comment: 8 page

Partial possibilistic regression path modeling

This paper introduces structural equation modeling for imprecise data, which enables evaluations with different types of uncertainty. Coming under the framework of variance-based analysis, the proposed method called Partial Possibilistic Regression Path Modeling (PPRPM) combines the principles of PLS path modeling to model the network of relations among the latent concepts, and the principles of possibilistic regression to model the vagueness of the human perception. Possibilistic regression defines the relation between variables through possibilistic linear functions and considers the error due to the vagueness of human perception as reflected in the model via interval-valued parameters. PPRPM transforms the modeling process into minimizing components of uncertainty, namely randomness and vagueness. A case study on the motivational and emotional aspects of teaching is used to illustrate the method