A Jadczyk

ON THE INTERACTION BETWEEN CLASSICAL AND QUANTUM-SYSTEMS

Abstract We propose a mathematically consistent model of interaction between classical and quantum systems.

Strongly coupled quantum and classical systems and Zeno's effect

Abstract A model interaction between a two-state quantum system and a classical switching device is analysed and shown to lead to the quantum Zeno effect for large values of the coupling constant ϰ. A minimal piecewise deterministic random process compatible with the Liouville equation is described, and it is shown that ϰ -1 can be interpreted as the jump frequency of the classical device.

On quantum jumps, events, and spontaneous localization models

We propose a precise meaning to the concepts of “experiment,” “measurement,” and “event” in the event-enhanced formalism of quantum theory. A minimal piecewise deterministic process is given that can be used for a computer simulation of real time series of experiments on single quantum objects. As an example a generalized cloud chamber is described, including the multiparticle case. Relation to the GRW spontaneous localization model is discussed.

EVENTS AND PIECEWISE DETERMINISTIC DYNAMICS IN EVENT-ENHANCED QUANTUM-THEORY

We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouvilles equation that couples a quantum system to a classical one. It implies a unique Markov process involving quantum jumps, classical events and describing sample histories of individual systems.

Relativistic quantum events

AbstractStandard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓ Today it is customary to try to explain emergence of the classical world through a decoherence mechanism due to “environment.≓ But, we believe, as it was with the concept of measurement, “environment≓ itself cannot be defined within the standard quantum theory. We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call “event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an “experiment≓ and of a “measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory. In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative.

Barrier traversal times using a phenomenological track formation model

Abstract A phenomenological model for a measurement of “barrier traversal times” for particles is proposed. Two idealized detectors for passage and arrival provide entrance and exit times for the barrier traversal. The averaged traversal time is computed over the ensemble of particles detected twice, before and after the barrier. The “Hartman effect” can still be found when passage detectors that conserve the momentum distribution of the incident packet are used.

Completely mixing quantum open systems and quantum fractals

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the mixing behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting spin components is shown to lead to a chaotic jumps on the quantum spin sphere and to generate specific fractal images of a nonlinear iterated function system.

Some Comments on the Formal Structure of Spontaneous Localization Theories

We propose a mathematical and a conceptual framework that encompasses and generalizes the “flash” ontology discussed in a recent paper by R. Tumulka.

EEQT A Way Out of the Quantum Trap

We review Event Enhanced Quantum Theory (EEQT). In Sect. 1 we address the question ‘Is quantum theory the last word’. In particular we respond to some of the challenging statements of H. P. Stapp. We also discuss a possible future of the quantum paradigm — see also Sect. 5. In Sect. 2 we give a short sketch of EEQT. Examples are given in Sect. 3. Section 3.3 discusses a completely new phenomenon — chaos and fractal-like phenomena caused by a simultaneous ‘measurement’ of several non-commuting observables. In Sect. 4 we answer ‘frequently asked questions’ concerning EEQT — mostly coming from referees of our publications. Summary and conclusions are in Sect. 6.

How events come into being: EEQT, particle tracks, quantum chaos and tunnelling time

Abstract We review Event Enhanced Quantum Theory (EEQT), discuss applications of EEQT to tunnelling time, and compare its quantitative predictions with other approaches, in particular with phase time and the Büttiker-Larmor approach. We discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, nonlinear, iterated function system type, patterns arising from quantum jumps and from the associated Markov operator.