Classical-quantum transition in terms of the order-disorder disjunction

Abstract

We attempt a statistical description of the quantum-classical transition (QCT) in terms of the order-disorder disjunction. Our protagonist is a notion called disequilibrium, advanced some 25 years ago. We discover that, in the simple case of the Harmonic Oscillator, the QCT can easily be visualized and described in terms of the ratio between the disequilibrium and the frequency. If the disorder–degree is large, the classical treatment works fine. For small disorder–degree, one needs quantum recipes. We encounter that for a quantal HO in an excited state containing just two phonons one already enters the transition semi classical zone.