arXiv subjects
Publications and source records attributed to Ph. Blanchard.
In the framework of Event Enhanced Quantum Theory (EEQT) a probabilistic construction of the piecewise deterministic process associated with a dynamical semigroup is presented. The process generates sample histories of individual systems quantums systems continuously coupled to classical measuring devices; it gives a unique algorithm generating time series of pointer readings in real experiments with quantum systems.
We review Event Enhanced Quantum Theory (EEQT). In Section 1 we address the question "Is Quantum Theory the Last Word". In particular we respond to some of recent challenging staments of H.P. Stapp. We also discuss a possible future of the quantum paradigm - see also Section 5. In Section 2 we give a short sketch of EEQT. Examples are given in Section 3. Section 3.3 discusses a completely new phenomenon - chaos and fractal-like phenomena caused by a simultaneous "measurement" of several non-commuting observables (we include picture of Barnsley's IFS on unit sphere of a Hilbert space). In Section 4 we answer "Frequently Asked Questions" concerning EEQT.
We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces decoherence and suppression of tunnelling. These features are widely accepted as definition of classicality, while we believe that classicality implies that quantum delocalized states spontaneously evolve into localized ones. We than show that this evolution take place only when both noise and non linearity in the equations are present.
The Schrödinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion. By choosing a reference Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential and the field of local accelerations it induces. We generate the family of affiliated diffusions with the same local dynamics, but different inaccessible boundaries on finite, semi-infinite and infinite domains. For each diffusion process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet boundary data) Wiener path integration.As a by-product of the discussion, we give an overview of the problem of inaccessible boundaries for the diffusion and bring together (sometimes viewed from unexpected angles) results which are little known, and dispersed in publications from scarcely communicating areas of mathematics and physics.
The new solution to the problem of time of arrival in quantum theory is presented herein. It allows for computer simulation of particle counters and it implies Born's interpretation. It also suggests new experiments that can answer the question: can a quantum particle detect a detector without being detected?
Time plays a special role in Standard Quantum Theory. The concept of time observable causes many controversies there. In Event Enhanced Quantum Theory (in short: EEQT) Schroedinger's differential equation is replaced by a em piecewise deterministic algorithm} that describes also the timing of events. This allows us to revisit the problem of time of arrival in quantum theory.
We extend the ideas of L.P. Horwitz and C. Piron and we propose a relativistic version of Event Enhanced Quantum Theory, with an event generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relativistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are non--negative.
We enhance elementary quantum mechanics with three simple postulates that enable us to define time observable. We discuss shortly justification of the new postulates and illustrate the concept with the detailed analysis of a delta function counter.
The existing formulations of the Schrödinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend the framework to encompass singular potentials and associated nonnegative Feynman-Kac-type kernels. It allows to deal with general nonnegative solutions of the Schrödinger boundary data problem. The resulting stochastic processes are capable of both developing and destroying nodes (zeros) of probability densities in the course of their evolution.
Event generating algorithm corresponding to a linear master equation of Lindblad's type is described and illustrated on two examples: that of a particle detector and of a fuzzy clock. Relation to other approaches to foundations of quantum theory and to description of quantum measurements is briefly discussed.
We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouville's equation that couples quantum system to a classical one. It implies a unique Markov process involving quantum jumps, classical events and describing sample histories of individual systems.
We review what we call "event-enhanced formalism" of quantum theory. In this approach we explicitly assume classical nature of events. Given a quantum system, that is coupled to a classical one by a suitable coupling, classical events are being triggered. The trigerring process is partly random and partly deterministic. Within this new approach one can modelize real experimental events, including pointer readings of measuring devices. Our theory gives, for the first time, a unique algorithm that can be used for computer generation of experimental runs with individual quantum objects.
The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment induced master equations are stressed. Questions: what is classical, what is time, and what are observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes'noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.
Model interactions between classical and quantum systems are briefly reviewed. These include: general measurement - like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, piecewise deterministic Markov processes and meaning of the wave function.
Model interactions between classical and quantum systems are briefly discussed. These include: general measurement-like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, SQUID-tank model.
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 k . A minimal piecewise deterministic random process compatible with the Liouville equation is described, and it is shown that 1/k can be interpreted as the jump frequency of the classical device