Decoherence within the concept of consistent histories

Claus Kiefer

Claus Kiefer

Lajos Diósi

The theory of decoherent histories is checked for the requirement of statistical independence of subsystems. Strikingly, this is satisfied only when the decoherence functional is diagonal in both its real and imaginary parts. Although the weakened condition of consistency (or weak decoherence), allowing a nondiagonal imaginary part, is sufficient for the assignment of probabilities, it may easily violate the statistical independence of subsystems. Therefore, weakened consistency conditions and various related generalizations of the concept of decoherent histories appear to be ruled out. The same conclusion is obtained independently, by claiming a plausible dynamical robustness of decoherent histories.

Nistico', Giuseppe, Roberto Beneduci

We introduce a new notion of consistency for 2-events quantum histories, based on the concept of mirror projection. Contrary to all notions of consistency so far introduced, our consistency, named self-decoherence, is an individual property, i.e., it can be attributed to every single sample of the physical system. Furthermore, self-decoherence forbids contrary inferences.

Angelo Bassi, G. C. Ghirardi

Esteban Calzetta, B. L. Hu

We use a λΦ 4 scalar quantum field theory to illustrate a new approach to the study of quantum to classical transition. In this approach, the decoherence functional is employed to assign probabilities to consistent histories defined in terms of correlations among the fields at separate points, rather than the field itself. We present expressions for the quantum amplitudes associated with such histories, as well as for the decoherence functional between two of them. The dynamics of an individual consistent history may be described by a Langevintype equation, which we derive. Dedicated to Professor Brill on the occasion of his sixtieth birthday, August 1993 Introduction Interpretations of Quantum Mechanics and Paradigms of Statistical Mechanics This paper attempts to bring together two basic concepts, one from the foundations of statistical mechanics and the other from the foundations of quantum mechanics, for the purpose of addressing two basic issues in physics: the quantum to classical transition, and the quantum origin of stochastic dynamics. Both issues draw in the interlaced effects of dissipation, decoherence, noise, and fluctuation. A central concern is the role played by coarse-graining —the naturalness of its choice, the effectiveness of its implementation and the relevance of its consequences.