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This book provides a state-of-the-art review of Pilot Wave Theory at the beginning of the XXI century. It contains the best contributions of the first International Conference on Advances in Pilot Wave Theory, held in Lisbon in 2021. The event brought together physicists from the new emerging field of Hydrodynamic Quantum Analogs (HQA) and philosophers of science. Three main themes were discussed: 1. Hydrodynamic quantum analogs, 2. Theoretical advances in pilot wave physics and, 3. Philosophical foundations of pilot wave theory. Recent experimental work in HQA has provided impetus to develop the pilot-wave approach into a realistic basis of quantum mechanics, specifically a dynamical completion of the existing theory of quantum statistics. To that end, the meeting featured theoretical work that advanced Louis de Broglie original pilot wave theory. This collection shows how several aspects of quantum systems have been reproduced in the hydrodynamic environment, and how the power of analogy suggests the possibility of a relatively intelligible quantum realm. Most notably, the notion of memory, as engendered in the pilot-wave-hydrodynamic system, suggests a profitable direction to explore in developing a more complete description of quantum phenomena. This book is expected to be of great interest to physicists, computer scientists and philosophers of science interested in the foundations of Quantum Mechanics. Chapter 1 and Chapter 12 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory.Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.

This book gathers selected contributions presented at the Enzo Levi and XX Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2014. The individual papers explore recent advances in experimental and theoretical fluid dynamics and are suitable for use in both teaching and research. The fluid dynamics applications covered include multiphase flows, convection, diffusion, heat transfer, rheology, granular materials, viscous flows, porous media flows, geophysics and astrophysics.The contributions, some of which are introductory and avoid the use of complicated mathematics, are suitable for fourth-year undergraduate and graduate students. Accordingly, the book is of immense benefit to these students, as well as to scientists in the fields of physics, chemistry and engineering with an interest in fluid dynamics from experimental and theoretical points of view.