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Nassar A.B., Miret-Artes S. Bohmian Mechanics, Open Quantum Systems and Continuous Measurements

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Nassar A.B., Miret-Artes S. Bohmian Mechanics, Open Quantum Systems and Continuous Measurements
Springer International Publishing AG, 2017. — 255 p. — ISBN: 9783319536514
In standard quantum mechanics, the collapse of the wave function resulting of the interaction of a given system with a measuring apparatus is a clear unsatisfactory assumption. As is well known, this assumption, due to von Neumann, was established around 1932 by means of the so-called reduction (or collapse or projection) postulate. A unitary Schrödinger evolution can never lead to such a collapse and, therefore, at some point, the time evolution of a quantum system undergoing a
measurement has to be suspended and replaced by a discontinuous, noncausal, nonlineal, nonunitary (but norm-preserving) and stochastic one. The collapse is postulated to happen in accordance with the well-known Born probability rule, with no dynamical theory behind such a mechanism. It is also very well known that the absence of macroscopic superpositions is at the heart of the measurement problem in quantum mechanics. Another aspect worth mentioning is the emergence of the classical features from the quantum world; in other words, the conversion of a coherent superposition into a mixture. The resulting decoherence process leads to the selection of one of the components of this mixture. This selection of one out of many alternatives still remains obscure. Thus, we still do not understand why the measurement process destroys the linear superposition of the initial states and why macroscopic objects are not found in superposed states. Even more, as asked by Bell, where is the quantum-classical dividing line? Mesoscopic systems are also ideal to address this fundamental question. In brief, too many open questions are even today waiting for some sort of satisfactory response.
Contents
Historical and Introductory Account of Bohmian Mechanics
Some Selected Applications of Bohmian Mechanics
Bohmian Stochastic Trajectories
Continuous Quantum Measurements in the Bohmian Framework
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