A Trajectory Description of Quantum Processes. II. Applications
A Trajectory Description of Quantum Processes. II. Applications

Author: Ángel S. Sanz

Publisher: Springer

Published: 2013-09-13

Total Pages: 345

ISBN-13: 3642179746

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Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.

Emergent Quantum Mechanics
Emergent Quantum Mechanics

Author: Jan Walleczek

Publisher: MDPI

Published: 2019-04-02

Total Pages: 544

ISBN-13: 3038976164

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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in "deeper-level" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.

Bohmian Mechanics, Open Quantum Systems and Continuous Measurements
Bohmian Mechanics, Open Quantum Systems and Continuous Measurements

Author: Antonio B. Nassar

Publisher: Springer

Published: 2017-03-14

Total Pages: 255

ISBN-13: 3319536532

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This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories.

Applied Bohmian Mechanics
Applied Bohmian Mechanics

Author: Xavier Oriols Pladevall

Publisher: CRC Press

Published: 2019-05-24

Total Pages: 389

ISBN-13: 1000650561

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Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schrödinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schrödinger equation, can be developed from it.

Quantum Foundations
Quantum Foundations

Author: Pedro W. Lamberti

Publisher: MDPI

Published: 2019-04-02

Total Pages: 188

ISBN-13: 3038977543

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Since its conception 90 years ago, the quantum uncertainty principle introduced by Werner Heisenberg lies behind most important features of quantum physics, and its implications have an impact that goes far beyond the physics community. This book focuses on the quantum uncertainty principle, providing an up-to-date examination of recent developments of its applications in quantum information theory. The book brings together several renowned experts working in the foundations of quantum mechanics and quantum information theory. The authors provide different approaches to the study of uncertainty relations and other fundamental aspects of the quantum formalism. Topics addressed include entanglement and Bell inequalities, the application of entropic information measures to the study of uncertainty inequalities, the characterization of deep learning networks in the context of adiabatic quantum computation, and the study of general properties of the set of quantum states. The content of this book will surely benefit both experienced and new researchers specializing in quantum information theory and the foundations of quantum mechanics.

A Trajectory Description of Quantum Processes. I. Fundamentals
A Trajectory Description of Quantum Processes. I. Fundamentals

Author: Ángel S. Sanz

Publisher: Springer

Published: 2012-03-27

Total Pages: 309

ISBN-13: 3642180922

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Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning at an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This first volume is focussed on the classical and quantum background necessary to understand the fundamentals of Bohmian mechanics, which can be considered the main topic of this work. Extensions of the formalism to the fields of open quantum systems and to optics are also proposed and discussed.

Advances in Neutron Optics
Advances in Neutron Optics

Author: Maria L. Calvo

Publisher: CRC Press

Published: 2019-12-05

Total Pages: 373

ISBN-13: 1000727602

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Neutron optics studies the interactions of a beam of slow neutrons with matter. This book updates various advances on neutron optics. There will be a focus on the very active topics of neutron imaging (NI) and neutron spin optics (NSO). The book will also present applications of neutron beams in biomedicine, such as Boron Neutron Capture Therapy (BNCT) and related techniques. Features: Discusses diffraction and interference of slow neutrons, including computational approaches Reviews neutron imaging (NI) and neutron spin optics (NSO) Treats two major sources of slow neutron beams: (1) fission reactions at nuclear reactors and (2) collisions in particle accelerators (small ones, spallation sources) of charged particle beams with targets of heavy atoms Selects subjects on fundamental quantum aspects of slow neutrons and on confined propagation and waveguiding thereof Updates slow neutron beams and BNCT

Chemical Reactivity
Chemical Reactivity

Author: Savaş Kaya

Publisher: Elsevier

Published: 2023-05-15

Total Pages: 502

ISBN-13: 0323906281

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The growth of technology for chemical assessment has led to great developments in the investigation of chemical reactivity in recent years, but key information is often dispersed across many different research fields. Exploring both traditional and advanced methods, Chemical Reactivity, Volume 2: Approaches and Applications present the latest approaches and strategies for the computational assessment of chemical reactivity.Following an insightful introduction, the book begins with an overview of conformer searching techniques before progressing to explore numerous different techniques and methods, including confined environments, quantum similarity descriptors, volume-based thermodynamics and polarizability. A unified approach to the rules of aromaticity is followed by methods for assessing interaction energies and the role of electron density for varied different analyses. Algorithms for confirmer searching, partitioning and a whole range of quantum chemical methods are also discussed.Consolidating the knowledge of a global team of experts in the field, Chemical Reactivity, Volume 2: Approaches and Applications is a useful resource for both students and researchers interested in applying and refining their use of the latest approaches for assessing chemical reactivity in their own work. - Compiles a broad range of contemporary methods and approaches for reactivity and structure prediction - Highlights the application of chemical reactivity strategies for the investigation of such areas as aromaticity, halogen bonds, and electronic materials - Includes discussion of computational tools for exploring molecular spaces from different angles, including interaction energies, quantum similarity, and electron density

Generated Dynamics of Markov and Quantum Processes
Generated Dynamics of Markov and Quantum Processes

Author: Martin Janßen

Publisher: Springer

Published: 2016-04-28

Total Pages: 236

ISBN-13: 3662496968

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This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put into the context of generated stochastic processes. Classical mechanics and classical field theory are deterministic processes which emerge when fluctuations in relevant variables are negligible. Quantum mechanics and quantum field theory consider genuine quantum processes. Equilibrium and non-equilibrium statistics apply to the regime where relaxing Markov processes emerge from quantum processes by omission of a large number of uncontrollable variables. Systems with many variables often self-organize in such a way that only a few slow variables can serve as relevant variables. Symmetries and topological classes are essential in identifying such relevant variables. The third aim of this book is to provide conceptually general methods of solutions which can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generating functionals. The potential reader is a graduate student who has heard already a course in quantum theory and equilibrium statistical physics including the mathematics of spectral analysis (eigenvalues, eigenvectors, Fourier and Laplace transformation). The reader should be open for a unifying look on several topics.