Fundamental phenomena of quantum mechanics explored with neutron interferometers
Klepp, J.; Sponar, S.; Hasegawa, Y.
2014-01-01
Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years.
On the quantum mechanics of consciousness, with application to anomalous phenomena
Jahn, Robert G.; Dunne, Brenda J.
1986-08-01
Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrödinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantum mechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent
On the quantum mechanics of consciousness, with application to anomalous phenomena
Energy Technology Data Exchange (ETDEWEB)
Jahn, R.G.; Dunne, B.J.
1986-08-01
Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrodinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition.
Interference Phenomena in Quantum Information
Stefanak, Martin
2010-01-01
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the description of quantum systems. In terms of physics we usually talk about the superposition principle valid for individual and composed quantum objects. So, while the source of interference is understandable it leads in fact to many counter-intuitive physical phenomena which puzzle physicists for almost hundred years. The present thesis studies interference in two seemingly disjoint fields of physics. However, both have strong links to quantum information processing and hence are related. In the first part we study the intriguing properties of quantum walks. In the second part we analyze a sophisticated application of wave packet dynamics in atoms and molecules for factorization of integers. The main body of the thesis is based on the original contributions listed separately...
Diósi, Lajos; Elze, Hans-Thomas; Fronzoni, Leone; Halliwell, Jonathan; Prati, Enrico; Vitiello, Giuseppe; Yearsley, James
2013-06-01
Presented in this volume are the Invited Lectures and the Contributed Papers of the Sixth International Workshop on Decoherence, Information, Complexity and Entropy - DICE 2012, held at Castello Pasquini, Castiglioncello (Tuscany), 17-21 September 2012. These proceedings may document to the interested public and to the wider scientific community the stimulating exchange of ideas at the meeting. The number of participants has been steadily growing over the years, reflecting an increasing attraction, if not need, of such conference. Our very intention has always been to bring together leading researchers, advanced students, and renowned scholars from various areas, in order to stimulate new ideas and their exchange across the borders of specialization. In this way, the series of meetings successfully continued from the beginning with DICE 20021, followed by DICE 20042, DICE 20063, DICE 20084, and DICE 20105, Most recently, DICE 2012 brought together more than 120 participants representing more than 30 countries worldwide. It has been a great honour and inspiration to have Professor Yakir Aharonov (Tel Aviv) with us, who presented the opening Keynote Lecture 'The two-vector quantum formalism'. With the overarching theme 'Spacetime - Matter - Quantum Mechanics - from the Planck scale to emergent phenomena', the conference took place in the very pleasant and inspiring atmosphere of Castello Pasquini - in beautiful surroundings, overlooking a piece of Tuscany's coast. The 5-day program covered these major topics: Quantum Mechanics, Foundations and Quantum-Classical Border Quantum-Classical Hybrids and Many-Body Systems Spectral Geometry, Path Integrals and Experiments Quantum -/- Gravity -/- Spacetime Quantum Mechanics on all Scales? A Roundtable Discussion under the theme 'Nuovi orizzonti nella ricerca scientifica. Ci troviamo di fronte ad una rivoluzione scientifica?' formed an integral part of the program. With participation of E Del Giudice (INFN & Università di
EDITORIAL: Quantum phenomena in Nanotechnology Quantum phenomena in Nanotechnology
Loss, Daniel
2009-10-01
Twenty years ago the Institute of Physics launched the journal Nanotechnology from its publishing house based in the home town of Paul Dirac, a legendary figure in the development of quantum mechanics at the turn of the last century. At the beginning of the 20th century, the adoption of quantum mechanical descriptions of events transformed the existing deterministic world view. But in many ways it also revolutionised the progress of research itself. For the first time since the 17th century when Francis Bacon established inductive reasoning as the means of advancing science from fact to axiom to law, theory was progressing ahead of experiments instead of providing explanations for observations that had already been made. Dirac's postulation of antimatter through purely theoretical investigation before its observation is the archetypal example of theory leading the way for experiment. The progress of nanotechnology and the development of tools and techniques that enabled the investigation of systems at the nanoscale brought with them many fascinating observations of phenomena that could only be explained through quantum mechanics, first theoretically deduced decades previously. At the nanoscale, quantum confinement effects dominate the electrical and optical properties of systems. They also render new opportunities for manipulating the response of systems. For example, a better understanding of these systems has enabled the rapid development of quantum dots with precisely determined properties, which can be exploited in a range of applications from medical imaging and photovoltaic solar cells to quantum computation, a radically new information technology being currently developed in many labs worldwide. As the first ever academic journal in nanotechnology, {\\it Nanotechnology} has been the forum for papers detailing progress of the science through extremely exciting times. In the early years of the journal, the investigation of electron spin led to the formulation
Khrennikov, A Yu
1999-01-01
We use the system of p-adic numbers for the description of informationprocesses. Basic objects of our models are so called transformers ofinformation, basic processes are information processes, the statistics areinformation statistics (thus we present a model of information reality). Theclassical and quantum mechanical formalisms on information p-adic spaces aredeveloped. It seems that classical and quantum mechanical models on p-adicinformation spaces can be applied for the investigation of flows of informationin cognitive and social systems, since a p-adic metric gives quite naturaldescription of the ability to form associations.
Quantum theory of collective phenomena
Sewell, G L
2014-01-01
""An excellent and competent introduction to the field … [and] … a source of information for the expert."" - Physics Today""This a book of major importance…. I trust that this book will be used as a basis for the teaching of a balanced, modern and rigorous course on statistical mechanics in all universities."" - Bulletin of the London Mathematical Society""This is one of the best introductions to the subject, and it is strongly recommended to anyone interested in collective phenomena."" - Physics Bulletin ""The book may be recommended for students as a well-balanced introduction to this rich s
Quantum field theory and critical phenomena
Zinn-Justin, Jean
1996-01-01
Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics. This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and the renormalization group are examined, as are critical phenomena and the role of instantons. Changes for this edition 1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing. 2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic li...
Quantum Non-Objectivity from Performativity of Quantum Phenomena
Khrennikov, Andrei
2014-01-01
We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables and the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenter's performances are not self-consistent. This self-inconsistency is an effect of that the language of QM differs much from the language of human performances. The first is the language of a mathematical theory which uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The second language consists of performative propositions which are self-consistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic which is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: from a mathematical theory to a logic of pe...
Rae, Alastair I M
2016-01-01
A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...
Parity-time symmetric quantum critical phenomena
Ashida, Yuto; Ueda, Masahito
2016-01-01
Symmetry plays a central role in the theory of phase transitions. Parity-time (PT) symmetry is an emergent notion in synthetic nonconservative systems, where the gain-loss balance creates a threshold for spontaneous symmetry breaking across which spectral singularity emerges. Considerable studies on PT symmetry have been conducted in optics and weakly interacting open quantum systems. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we discover unconventional quantum critical phenomena, where spectral singularity and quantum criticality conspire to yield an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find that superfluid correlation is anomalously enhanced owing to winding renormalization group flows in a PT-symmetry-broken quantum critical phase. Our findings can experimentally be tested in ultracold atoms.
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
Mandl, F.
1992-07-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.
Simulating Physical Phenomena by Quantum Networks
Somma, R D; Gubernatis, J E; Knill, E H; Laflamme, R
2002-01-01
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by means of the algebra generated by the usual fermionic creation and annihilation operators, or by using the algebra of Pauli (spin-1/2) operators. The correspondence between the two algebras is given by the Jordan-Wigner isomorphism. As we previously noted similar one-to-one mappings enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental concept in quantum information processing to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g, spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian $H$.
Fitzpatrick, Richard
2015-01-01
Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.
Ghosh, P K
2014-01-01
Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.
Quantum phenomena in magnetic nano clusters
Indian Academy of Sciences (India)
C Raghu; Indranil Rudra; Diptiman Sen; S Ramasesha
2001-10-01
One of the fascinating fields of study in magnetism in recent years has been the study of quantum phenomena in nanosystems. While semiconductor structures have provided paradigms of nanosystems from the stand point of electronic phenomena, the synthesis of high nuclearity transition metal complexes have provided examples of nano magnets. The range and diversity of the properties exhibited by these systems rivals its electronic counterparts. Qualitative understanding of these phenomena requires only a knowledge of basic physics, but quantitative study throws up many challenges that are similar to those encountered in the study of correlated electronic systems. In this article, a brief overview of the current trends in this area are highlighted and some of the efforts of our group in developing a quantitative understanding of this field are outlined.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
Zagoskin, Alexandre
2015-01-01
Written by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, ra
Retrocausality in Quantum Phenomena and Chemical Evolution
Directory of Open Access Journals (Sweden)
Koichiro Matsuno
2016-10-01
Full Text Available The interplay between retrocausality and the time-reversal symmetry of the dynamical law of quantum mechanics underscores the significance of the measurement dynamics with the use of indivisible and discrete quantum particles to be mediated. One example of empirical evidence demonstrating the significance of retrocausality going along with time-reversal symmetry is seen in the operation of a reaction cycle to be expected in chemical evolution. A reaction cycle can hold itself when the causative operation of the cycle remains robust, even when facing frequent retrocausal interventions of a quantum-mechanical origin. Quantum mechanics in and of itself has potential in raising a reaction cycle in the prebiotic phase of chemical evolution, even without any help of artefactual scaffoldings of an external origin.
Dolev, S; Kolenda, N
2005-01-01
For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Quantum mechanics of molecular structures
Yamanouchi, Kaoru
2012-01-01
At a level accessible to advanced undergraduates, this textbook explains the fundamental role of quantum mechanics in determining the structure, dynamics, and other properties of molecules. Readers will come to understand the quantum-mechanical basis for harmonic oscillators, angular momenta and scattering processes. Exercises are provided to help readers deepen their grasp of the essential phenomena.
Macroscopic quantum phenomena from the large N perspective
Chou, C. H.; Hu, B. L.; Subaşi, Y.
2011-07-01
Macroscopic quantum phenomena (MQP) is a relatively new research venue, with exciting ongoing experiments and bright prospects, yet with surprisingly little theoretical activity. What makes MQP intellectually stimulating is because it is counterpoised against the traditional view that macroscopic means classical. This simplistic and hitherto rarely challenged view need be scrutinized anew, perhaps with much of the conventional wisdoms repealed. In this series of papers we report on a systematic investigation into some key foundational issues of MQP, with the hope of constructing a viable theoretical framework for this new endeavour. The three major themes discussed in these three essays are the large N expansion, the correlation hierarchy and quantum entanglement for systems of 'large' sizes, with many components or degrees of freedom. In this paper we use different theories in a variety of contexts to examine the conditions or criteria whereby a macroscopic quantum system may take on classical attributes, and, more interestingly, that it keeps some of its quantum features. The theories we consider here are, the O(N) quantum mechanical model, semiclassical stochastic gravity and gauge / string theories; the contexts include that of a 'quantum roll' in inflationary cosmology, entropy generation in quantum Vlasov equation for plasmas, the leading order and next-to-leading order large N behaviour, and hydrodynamic / thermodynamic limits. The criteria for classicality in our consideration include the use of uncertainty relations, the correlation between classical canonical variables, randomization of quantum phase, environment-induced decoherence, decoherent history of hydrodynamic variables, etc. All this exercise is to ask only one simple question: Is it really so surprising that quantum features can appear in macroscopic objects? By examining different representative systems where detailed theoretical analysis has been carried out, we find that there is no a priori
Macroscopic quantum phenomena from the large N perspective
Energy Technology Data Exchange (ETDEWEB)
Chou, C H [department of Physics, National Cheng Kung University, Tainan, Taiwan 701 (China) and National Center for Theoretical Sciences (South), Tainan, Taiwan 701 (China); Hu, B L; Subasi, Y, E-mail: hubeilok@gmail.com [Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742 (United States)
2011-07-08
Macroscopic quantum phenomena (MQP) is a relatively new research venue, with exciting ongoing experiments and bright prospects, yet with surprisingly little theoretical activity. What makes MQP intellectually stimulating is because it is counterpoised against the traditional view that macroscopic means classical. This simplistic and hitherto rarely challenged view need be scrutinized anew, perhaps with much of the conventional wisdoms repealed. In this series of papers we report on a systematic investigation into some key foundational issues of MQP, with the hope of constructing a viable theoretical framework for this new endeavour. The three major themes discussed in these three essays are the large N expansion, the correlation hierarchy and quantum entanglement for systems of 'large' sizes, with many components or degrees of freedom. In this paper we use different theories in a variety of contexts to examine the conditions or criteria whereby a macroscopic quantum system may take on classical attributes, and, more interestingly, that it keeps some of its quantum features. The theories we consider here are, the O(N) quantum mechanical model, semiclassical stochastic gravity and gauge / string theories; the contexts include that of a 'quantum roll' in inflationary cosmology, entropy generation in quantum Vlasov equation for plasmas, the leading order and next-to-leading order large N behaviour, and hydrodynamic / thermodynamic limits. The criteria for classicality in our consideration include the use of uncertainty relations, the correlation between classical canonical variables, randomization of quantum phase, environment-induced decoherence, decoherent history of hydrodynamic variables, etc. All this exercise is to ask only one simple question: Is it really so surprising that quantum features can appear in macroscopic objects? By examining different representative systems where detailed theoretical analysis has been carried out, we find that
Mandl, Franz
1992-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient
Studies of Novel Quantum Phenomena in Ruthenates
Energy Technology Data Exchange (ETDEWEB)
Mao, Zhiqiang
2011-04-08
Strongly correlated oxides have been the subject of intense study in contemporary condensed matter physics, and perovskite ruthenates (Sr,Ca)n+1RunO3n+1 have become a new focus in this field. One of important characteristics of ruthenates is that both lattice and orbital degrees of freedom are active and are strongly coupled to charge and spin degrees of freedom. Such a complex interplay of multiple degrees of freedom causes the properties of ruthenates to exhibit a gigantic response to external stimuli under certain circumstances. Magnetic field, pressure, and chemical composition all have been demonstrated to be effective in inducing electronic/magnetic phase transitions in ruthenates. Therefore, ruthenates are ideal candidates for searching for novel quantum phenomena through controlling external parameters. The objective of this project is to search for novel quantum phenomena in ruthenate materials using high-quality single crystals grown by the floating-zone technique, and investigate the underlying physics. The following summarizes our accomplishments. We have focused on trilayered Sr4Ru3O10 and bilayered (Ca1-xSrx)3Ru2O7. We have succeeded in growing high-quality single crystals of these materials using the floating-zone technique and performed systematic studies on their electronic and magnetic properties through a variety of measurements, including resistivity, Hall coefficient, angle-resolved magnetoresistivity, Hall probe microscopy, and specific heat. We have also studied microscopic magnetic properties for some of these materials using neutron scattering in collaboration with Los Alamos National Laboratory. We have observed a number of unusual exotic quantum phenomena through these studies, such as an orbital selective metamagnetic transition, bulk spin valve effect, and a heavy-mass nearly ferromagnetic state with a surprisingly large Wilson ratio. Our work has also revealed underlying physics of these exotic phenomena. Exotic phenomena of correlated
Novel nuclear phenomena in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J.
1987-08-01
Many of the key issues in understanding quantum chromodynamics involve processes in nuclear targets at intermediate energies. A range of hadronic and nuclear phenomena-exclusive processes, color transparency, hidden color degrees of freedom in nuclei, reduced nuclear amplitudes, jet coalescence, formation zone effects, hadron helicity selection rules, spin correlations, higher twist effects, and nuclear diffraction were discussed as tools for probing hadron structure and the propagation of quark and gluon jets in nuclei. Several areas were also reviewed where there has been significant theoretical progress determining the form of hadron and nuclear wave functions, including QCD sum rules, lattice gauge theory, and discretized light-cone quantization. A possible interpretation was also discussed of the large spin correlation A/sub NN/ in proton-proton scattering, and how relate this effect to an energy and angular dependence of color transparency in nuclei. 76 refs., 24 figs.
Hadronic and nuclear phenomena in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J.
1987-06-01
Many of the key issues in understanding quantum chromodynamics involves processes at intermediate energies. We discuss a range of hadronic and nuclear phenomena - exclusive processes, color transparency, hidden color degrees of freedom in nuclei, reduced nuclear amplitudes, jet coalescence, formation zone effects, hadron helicity selection rules, spin correlations, higher twist effects, and nuclear diffraction - as tools for probing hadron structure and the propagation of quark and gluon jets in nuclei. Many of these processes can be studied in electroproduction, utilizing internal targets in storage rings. We also review several areas where there has been significant theoretical progress in determining the form of hadron and nuclear wavefunctions, including QCD sum rules, lattice gauge theory, and discretized light-cone quantization. 98 refs., 40 figs., 2 tabs.
Quantum Simulator for Transport Phenomena in Fluid Flows.
Mezzacapo, A; Sanz, M; Lamata, L; Egusquiza, I L; Succi, S; Solano, E
2015-08-17
Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics transport phenomena within a lattice kinetic formalism. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes. The proposed simulator is amenable to realization in controlled quantum platforms, such as ion-trap quantum computers or circuit quantum electrodynamics processors.
Bulk Rashba Semiconductors and Related Quantum Phenomena.
Bahramy, Mohammad Saeed; Ogawa, Naoki
2017-03-29
Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.
Quantum Simulator for Transport Phenomena in Fluid Flows
Mezzacapo, A; Lamata, L; Egusquiza, I L; Succi, S; Solano, E
2015-01-01
Transport phenomena are one of the most challenging problems in computational physics. We present a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics problems within a lattice kinetic formalism. This quantum simulator is obtained by exploiting the analogies between Dirac and lattice Boltzmann equations. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes. The proposed simulator is amenable to realization in controlled quantum platforms, such as ion-trap quantum computers or circuit quantum electrodynamics processors.
Quantum mechanics II advanced topics
Rajasekar, S
2015-01-01
Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.
Bohmian Mechanics and the Quantum Revolution
Goldstein, Sheldon
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena--...
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Emergent quantum mechanics and emergent symmetries
Hooft, G. 't
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such
Superluminal Phenomena and the Quantum Preferred Frame
Rembielinski, J
2000-01-01
Motivated by a number of recent experiments, we discuss in this paper a speculative but physically admissible form and solutions of effective Maxwell-like equations describing propagation of electromagnetic field in a medium which ``feels'' a quantum preferred frame.
Stable Quantum Filters with Scattering Phenomena
Institute of Scientific and Technical Information of China (English)
W. U. Ahamed; C. Kambhampati
2008-01-01
Quantum neural network filters for signal processing have received a lot of interest in the recent past. The implementations of these filters had a number of design parameters that led to numerical inefficiencies. At the same time the solution procedures employed were explicit in that the evolution of the time-varying functions had to be controlled. This often led to numerical instabilities. This paper outlines a procedure for improving the stability, numerical efficiency, and the accuracy of quantum neural network filters. Two examples are used to illustrate the principles employed.
Greiner, Walter
1989-01-01
"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...
Quantum mechanics of leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Mendizabal Cofre, Sebastian
2010-08-15
Leptogenesis is an attractive mechanism that simultaneously explains the matterantimatter asymmetry of the universe as well as the small masses of the standard model neutrinos. This is performed by naturally extending the standard model with the insertion of right handed neutrinos. Leptogenesis is usually studied via the semi-classical Boltzmann equations. However, these equations suffer from basic conceptual problems and they lack to include many quantum phenomena, such as memory effects and coherence oscillations. In order to fully describe leptogenesis, a full quantum treatment is required. In this work we show how to address leptogenesis systematically in a purely quantum way. We start by studying scalar and fermionic excitations in a plasma by solving the Kadanoff-Baym equations of motion for Green's functions, with significant emphasis on the initial and boundary conditions of the solutions. We compute analytically the asymmetry generated from the departure of equilibrium of a particle in a thermal bath. The comparison with the semi-classical Boltzmann approach is also analysed, leading to a qualitative difference between both methods. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry, effects that cannot be studied with the Boltzmann equations. The insertion of standard model interactions like the decay widths for the particles of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes, i.e. we regain the Boltzmann equations. (orig.)
Introduction to quantum mechanics
Villaseñor, Eduardo J. S.
2008-01-01
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
Quantum inertia stops superposition: Scan Quantum Mechanics
Gato-Rivera, Beatriz
2017-08-01
Scan Quantum Mechanics is a novel interpretation of some aspects of quantum mechanics in which the superposition of states is only an approximate effective concept. Quantum systems scan all possible states in the superposition and switch randomly and very rapidly among them. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia Iq reaches a critical value Icr for an observable, the switching among its different eigenvalues stops and the corresponding superposition comes to an end, leaving behind a system with a well defined value of that observable. Consequently, increasing the mass, temperature, gravitational strength, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. Moreover, the process could be reversible. Entanglement can only occur between quantum systems because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia Icr corresponding to different observables, which translates into a critical mass Mcr for fixed environmental conditions as well as critical temperatures, critical electric and magnetic fields, etc. In addition, this proposal implies a new radiation mechanism from astrophysical objects with strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
Testing Nonassociative Quantum Mechanics.
Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut
2015-11-27
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Submicroscopic Deterministic Quantum Mechanics
Krasnoholovets, V
2002-01-01
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10^{-28} cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons". The further study has disclosed that inertons are a substructure of the matter waves which are described by the orthodox wave \\psi-function formalism. The c...
Ahn, Doyeol
2011-01-01
A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...
Quantum Phenomena in High Energy Density Plasmas
Energy Technology Data Exchange (ETDEWEB)
Murnane, Margaret [Univ. of Colorado, Boulder, CO (United States); Kapteyn, Henry [Univ. of Colorado, Boulder, CO (United States)
2017-05-10
The possibility of implementing efficient (phase matched) HHG upconversion of deep- UV lasers in multiply-ionized plasmas, with potentially unprecedented conversion efficiency is a fascinating prospect. HHG results from the extreme nonlinear response of matter to intense laser light:high harmonics are radiated as a result of a quantum coherent electron recollision process that occurs during laser field ionization of an atom. Under current support from this grant in work published in Science in 2015, we discovered a new regime of bright HHG in highly-ionized plasmas driven by intense UV lasers, that generates bright harmonics to photon energies >280eV
Coherence In Quantum Chaos, Stochastic Spacetime, And Collective Phenomena
Shiokawa, K
1998-01-01
Various manifestations of coherence properties in quantum and classical dynamics in open and closed systems are studied. Among many different issues and phenomena related to coherence, particular aspects are expounded by models chosen from quantum chaos, quantum optics, mesoscopic and high energy physics, and semiclassical relativity. I show how coherence in quantum and classical systems manifests itself in different forms and is enhanced, altered, and suppressed in the presence of chaos, randomness, boundary, and environment. Author's contributions start from the first time discussion of decoherence in quantum cat map and quantum kicked rotor. Wave propagation in stochastic spacetime is considered as that in random media by extending the analogy of spacetime metric with the refractive index of media...
Nonlinear phenomena in quantum thermoelectrics and heat
Sánchez, David; López, Rosa
2016-12-01
We review recent developments in nonlinear quantum transport through nanostructures and mesoscopic systems driven by thermal gradients or in combination with voltage biases. Low-dimensional conductors are excellent platforms for analyzing both the thermoelectric and heat dynamics beyond the linear response because, due to their small size, a small temperature difference applied across regions gives rise to large thermal biases. We offer a theoretical discussion based on the scattering approach to highlight the differences between the linear and the nonlinear regimes of transport. We discuss recent experiments on quantum dots and molecular junctions subjected to strong temperature differences. Theoretical predictions concerning the Kondo effect and heat rectification proposals are briefly examined. An important issue is the calculation of thermoelectric efficiencies including nonlinearities. Cross Seebeck effects and nonlinear spin filtering arise in superconductors and topological insulators, while mixed noises between charge and heat currents are also considered. Finally, we provide an outlook on the possible future directions of the field. xml:lang="fr"
Advanced Visual Quantum Mechanics
Thaller, Bernd
2005-01-01
Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.
Macroscopic Quantum Phenomena from the Correlation, Coupling and Criticality Perspectives
Chou, C. H.; Hu, B. L.; Subaşi, Y.
2011-12-01
In this sequel paper we explore how macroscopic quantum phenomena can be measured or understood from the behavior of quantum correlations which exist in a quantum system of many particles or components and how the interaction strengths change with energy or scale, under ordinary situations and when the system is near its critical point. We use the nPI (master) effective action related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a tool for systemizing the contributions of higher order correlation functions to the dynamics of lower order correlation functions. Together with the large N expansion discussed in our first paper [1] we explore 1) the conditions whereby an H-theorem is obtained, which can be viewed as a signifier of the emergence of macroscopic behavior in the system. We give two more examples from past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice under the large Script N (field components), 2PI and second order perturbative expansions, illustrating how N and Script N enter in these three aspects of quantum correlations, coherence and coupling strength. 3) the behavior of an interacting quantum system near its critical point, the effects of quantum and thermal fluctuations and the conditions under which the system manifests infrared dimensional reduction. We also discuss how the effective field theory concept bears on macroscopic quantum phenomena: the running of the coupling parameters with energy or scale imparts a dynamical-dependent and an interaction-sensitive definition of 'macroscopia'.
Quantum mechanics in chemistry
Schatz, George C
2002-01-01
Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matt
Bohmian mechanics and the quantum revolution
Goldstein, S
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.
Quantum mechanics for pedestrians
Pade, Jochen
2014-01-01
This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix coll...
Control of quantum phenomena: Past, present, and future
Brif, Constantin; Rabitz, Herschel
2009-01-01
Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. The current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. The two most critical theoretical insights were (1) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (2) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control, which is a laboratory procedure employing measurement-driven, closed-loop o...
Discrete computational mechanics for stiff phenomena
Michels, Dominik L.
2016-11-28
Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.
Dirac, Paul A M
2001-01-01
The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.The four lectures in this book were delivered
Facing quantum mechanical reality.
Rohrlich, F
1983-09-23
Two recent precision experiments provide conclusive evidence against any local hidden variables theory and in favor of standard quantum mechanics. Therefore the epistemology and the ontology of quantum mechanics must now be taken more seriously than ever before. The consequences of the standard interpretation of quantum mechanics are summarized in nontechnical language. The implications of the finiteness of Planck's constant (h > 0) for the quantum world are as strange as the implications of the finiteness of the speed of light (c < infinity for space and time in relativity theory. Both lead to realities beyond our common experience that cannot be rejected.
Holography and Quantum Mechanics
Wang, X J
2002-01-01
It is illustrated that quantum mechanics can be interpreted as holographic projection of higher dimension classical gravity. In this explanation every quantum path in D-dimension is dual to a classical path of (D+1)-dimension gravity under definite holographic projection. I consider 2-dimension non-relativitic free particle and harmonic oscillator as two examples, and find their gravity dual. I conjecture that every quantum mechanics system has their dual gravity description.
Elementary Nonrelativistic Quantum Mechanics
Rosu, H C
2000-01-01
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Gol'dman, I I
2010-01-01
A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. Among the topics: one-dimensional motion, transmission through a potential barrier, commutation relations, angular momentum and spin, and motion of a particle in a magnetic field. An ideal adjunct to any textbook in quantum mechanics, useful in courses in atomic and nuclear physics, mathematical methods in physics, quantum statistics and applied differential equations. 1961 edition.
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Directory of Open Access Journals (Sweden)
Tadashi Okazaki
2015-01-01
Full Text Available We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N=16 and N=12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2 and SU(1,1|6 quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi–Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N=8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Why Quantum Mechanics is Hard to Understand
Bilodeau, D
1998-01-01
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena are favored because of their clarity. Quantum phenomena, however, do not permit them. Instead, the historical and dynamical aspects of description diverge and must be expressed in different but complementary languages. Objective historical facts are recorded in terms of objects, which necessarily have an imprecise, empirical quality. Dynamics is based on quantitative abstraction from recurring patterns. The "quantum of action" is the discontinuity between these two ways of looking at the physical world.
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
Quasi-quantum phenomena: the key to understanding homeopathy.
Molski, Marcin
2010-04-01
On the basis of the first- and second-order Gompertzian kinetics it has been proved that the crystallization and its reciprocal process of dissolution belong to the class of quasi-quantum non-local coherent phenomena. Hence, there exists a direct link to homeopathy: molecules of the remedy prepared in the process of dilution of the active substance are non-locally interconnected at-a-distance. The results obtained provide strong arguments justifying formulated ad hoc macroscopic versions of quantum non-locality, entanglement and coherence employed in interpretation of the homeopathic remedies activity and effectiveness. In particular they are consistent with the predictions of the weak quantum theory developed by Atmanspacher and coworkers.
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Quantum mechanics for mathematicians
Takhtajan, Leon A
2008-01-01
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks ...
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Could quantum decoherence and measurement be deterministic phenomena?
Directory of Open Access Journals (Sweden)
Sparenberg Jean-Marc
2013-09-01
Full Text Available The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in contrast with variables characterizing the measured microscopic system, is shown to lead to a violation of Bell’s inequalities and to agree with standard quantum mechanics. An explicit realization of this interpretation is explored (for details, see [1] for a primitive model of cloud chamber inspired by Mott [2]. Being highly non local, this interpretation of quantum mechanics is argued to open the way to faster-than-light information transfer.
Quantum mechanical Carnot engine
Bender, C M; Meister, B K
2000-01-01
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Rosu, H C
2000-01-01
This is the first graduate course on elementary quantum mechanics in Internet written in Romanian for the benefit of Romanian speaking students (Romania and Moldova). It is a translation (with corrections) of the Spanish version of the course (physics/9808031, English translation is under consideration), which I did at the request of students of physics in Bucharest. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Effectively Emergent Quantum Mechanics
Exirifard, Qasem
2008-01-01
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently flat. In other words, quantum mechanics might play no role when and where the space-time geometry is highly curved. We study the first two simple models of Effectively Emergent Quantum Mechanics(EEQM): R-dependent EEQM and G-dependent EEQM where R is the Ricci scalar and G is the Gauss-Bonnet Lagrangian density. We discuss that these EEQM theories might be fine tuned to remain consistent with all the implemented experiments and performed observations. In particular, we observe that G-dependent EEQM softens the problem of quantum gravity.
Natural Phenomena in the Mechanism of Legal Regulation
Directory of Open Access Journals (Sweden)
Alexander V. Malyshkin
2012-09-01
Full Text Available The article examines the interaction of nature phenomena and law in the regulation of social relations. The author proves that natural phenomena should be considered when legal acts are worked out. The analysis of the place and role of natural phenomena in the mechanism of legal regulation is analysed.
Quantum mechanics and the psyche
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Mayato, R; Egusquiza, I
2002-01-01
The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.
Probability in quantum mechanics
Directory of Open Access Journals (Sweden)
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Effectively calculable quantum mechanics
Bolotin, Arkady
2015-01-01
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if...
Mechanics classical and quantum
Taylor, T T
2015-01-01
Mechanics: Classical and Quantum explains the principles of quantum mechanics via the medium of analytical mechanics. The book describes Schrodinger's formulation, the Hamilton-Jacobi equation, and the Lagrangian formulation. The author discusses the Harmonic Oscillator, the generalized coordinates, velocities, as well as the application of the Lagrangian formulation to systems that are partially or entirely electromagnetic in character under certain conditions. The book examines waves on a string under tension, the isothermal cavity radiation, and the Rayleigh-Jeans result pertaining to the e
Are quantum-mechanical-like models possible, or necessary, outside quantum physics?
Plotnitsky, Arkady
2014-12-01
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
The quantum mechanics of cosmology.
Hartle, James B.
The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation
Fundamentals of quantum mechanics
House, J E
2017-01-01
Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models-including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom-are clearly and completely presented. Applications of these models to selected “real world” topics are also included. This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.
Macroscopic Quantum Phenomena from the Correlation, Coupling and Criticality Perspectives
Chou, C H; Subasi, Y
2011-01-01
In this sequel paper we explore how macroscopic quantum phenomena can be measured or understood from the behavior of quantum correlations which exist in a quantum system of many particles or components and how the interaction strengths change with energy or scale, under ordinary situations and when the system is near its critical point. We use the nPI (master) effective action related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a tool for systemizing the contributions of higher order correlation functions to the dynamics of lower order correlation functions. Together with the large N expansion discussed in our first paper(MQP1) we explore 1) the conditions whereby an H-theorem is obtained, which can be viewed as a signifier of the emergence of macroscopic behavior in the system. We give two more examples from past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice under the large $\\cal N$ (field components), 2PI and second order perturbative expansions, illustrating h...
Quantization and Quantum-Like Phenomena: A Number Amplitude Approach
Robinson, T. R.; Haven, E.
2015-12-01
Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.
Quantum Mechanics with Applications
Afnan, Iraj R
2011-01-01
The ebook introduces undergraduate students to the basic skills required to use non-relativistic quantum mechanics for bound and scattering problems in atomic, molecular and nuclear physics. Initial emphasis is on problems that admit analytic solutions. These results are then used in conjunction with symmetry to develop approximation methods for both bound and scattering problems. The text concentrates on the application of computational problems to introduce the basic concepts of quantum mechanics. These are then used to study more complex problems that can be reduced to one-body problems.
Kogan, VI; Gersch, Harold
2011-01-01
Written by a pair of distinguished Soviet mathematicians, this compilation presents 160 lucidly expressed problems in nonrelativistic quantum mechanics plus completely worked-out solutions. Some were drawn from the authors' courses at the Moscow Institute of Engineering, but most were prepared especially for this book. A high-level supplement rather than a primary text, it constitutes a masterful complement to advanced undergraduate and graduate texts and courses in quantum mechanics.The mathematics employed in the proofs of the problems-asymptotic expansions of functions, Green's functions, u
Saxon, David S
2012-01-01
Based on lectures for an undergraduate UCLA course in quantum mechanics, this volume focuses on the formulas of quantum mechanics rather than applications. Widely used in both upper-level undergraduate and graduate courses, it offers a broad self-contained survey rather than in-depth treatments.Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, m
Noncommutative quantum mechanics
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
Hollowood, Timothy J.
2016-07-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
Time Asymmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Arno R. Bohm
2011-09-01
Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Determinism beneath Quantum Mechanics
Hooft, G
2002-01-01
Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is difficult however is to obtain a Hamiltonian that is bounded from below, and whose ground state is a vacuum that exhibits complicated vacuum fluctuations, as in the real world. Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Institute of Scientific and Technical Information of China (English)
吴宁; 阮图南
1996-01-01
A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.
Quantum entanglement phenomena in photosynthetic light harvesting complexes
Whaley, K Birgitta; Ishizaki, Akihito
2010-01-01
We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomo...
Beyond relativity and quantum mechanics: space physics
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
Uncertainty in quantum mechanics: faith or fantasy?
Penrose, Roger
2011-12-13
The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.
Hollowood, Timothy J
2013-01-01
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
Quantum mechanics with applications
Beard, David B
2014-01-01
This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.
Epigenetics: Biology's Quantum Mechanics.
Jorgensen, Richard A
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Epigenetics: Biology's Quantum Mechanics
Directory of Open Access Journals (Sweden)
Richard A Jorgensen
2011-04-01
Full Text Available The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920's and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Advanced concepts in quantum mechanics
Esposito, Giampiero; Miele, Gennaro; Sudarshan, George
2015-01-01
Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.
Oss, Stefano; Rosi, Tommaso
2015-04-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Quantum Phenomena in Ignition and Detonation at Elevated Density
Drakon, A. V.; Emelianov, A. V.; Eremin, A. V.; Gurentsov, E. V.; Petrushevich, Yu. V.; Starostin, A. N.; Taran, M. D.; Fortov, V. E.
2012-11-01
The influence of quantum effects on the processes of initiation of combustion and detonation of hydrogen and acetylene near the low-temperature limits at elevated pressures is analyzed. A theoretical consideration which allows quantification of the quantum corrections to the rate constants of endothermic reactions associated with an increase in the high-energy tail of the equilibrium momentum distribution function at high pressures is presented. This quantum effect is caused by a manifestation of the principle of uncertainty for the energy of the colliding particles at a high frequency of collisions. It is shown that significant deviations of experimentally observed ignition and detonation delay time from the predictions of kinetic calculations are quite well described by the proposed quantum corrections. This general mechanism should be considered in the safety problem with emergency emissions of hydrogen at nuclear power stations, as well as problems of the safe production and storage of hydrogen and acetylene, which have a fundamental importance for industry and power engineering.
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Nonrelativistic Quantum Mechanics with Fundamental Environment
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Graduate Quantum Mechanics Reform
Carr, L D
2008-01-01
We address four main areas in which graduate quantum mechanics education in the U.S. can be improved: course content; textbook; teaching methods; and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all four of these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, use modern textbooks that include such content, incorporate a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey (QMCS). We find that graduate students respond well to research-based techniques that have previously been tested mainly in introductory courses, and that they learn a great deal of the new content introduced in each ve...
Quantum Mechanics in the Infrared
Radicevic, Djordje
2016-01-01
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not a different effective quantum mechanics. Each energy eigenstate of the UV Hamiltonian flows to a probability distribution whose entropy is a natural diagnostic of quantum ergodicity of the original state. These conclusions are supported by various examples worked out in detail.
Potentiality, Actuality, and Quantum Mechanics
Directory of Open Access Journals (Sweden)
Boris Koznjak
2007-12-01
Full Text Available In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality (δύναµις and actuality (ἐνέργεια is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings (δυνάµει ὄντα actualized by the measurement process in appropriate experimental arrangement, and the problem of actual beings (ἐνεργείᾳ ὄντα of the atomic world (better known as the measurement problem in quantum mechanics is considered in the context of Aristotle’s threefold requirement for the priority of actuality over potentiality – in time (χρόνος, definition or knowledge (λόγος, and substantiality (οὐσία.
The Picture Book of Quantum Mechanics
Brandt, Siegmund
2012-01-01
The aim of this book is to explain the basic concepts and phenomena of quantum mechanics by means of visualization. Computer-generated illustrations in color are used extensively throughout the text, helping to establish the relation between quantum mechanics—wave functions, interference, atomic structure, and so forth—and classical physics—point mechanics, statistical mechanics, and wave optics. Even more important, by studying the pictures in parallel with the text, readers develop an intuition for such notoriously abstract phenomena as • the tunnel effect • excitation and decay of metastable states • wave-packet motion within a well • systems of distinguishable and indistinguishable particles • free wave packets and scattering in 3 dimensions • angular-momentum decomposition • stationary bound states in various 3-dimensional potentials • hybrid states • Kepler motion of wave packets in the Coulomb field • spin and magnetic resonance Illustrations from experiments in a variety of f...
Basdevant, Jean-Louis
2007-01-01
Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc2'. Nevertheless, the formula 'E=hV' which was written in the same year 1905 by the same Albert Einstein, and which started quantum theory, concerns their daily life considerably more. In fact, of the three watershed years for physics toward the beginning of the 20th century - 1905: the Special Relativity of Einstein, Lorentz and Poincaré; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the full development of Quantum Mechanics - it is surely the last which has the mos...
Hollowood, Timothy J
2015-01-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generat...
Sakurai, Jun John
2011-01-01
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text’s usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. You will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. The style and treatment of topics is now more consistent across chapters.
Quantum phenomena in transport measurements of topological insulator nanostructures (Review Article)
Energy Technology Data Exchange (ETDEWEB)
Fang, Lei; Kwok, Wai-Kwong
2014-04-01
We review the recent experimental advances on quantum phenomena in transport measurements of topological insulators with emphasis on quantum oscillation, weak antilocalization and Aharonov-Bohm effect and Altshuler-Aronov-Spivak effect. Following a brief introduction on the topic, we discuss the identification of the topological surface state based on quantum phenomena. Research prospect of topological insulators is described at the end of this article.
Quantum phenomena in transport measurements of topological insulator nanostructures (Review Article)
Fang, Lei; Kwok, Wai-Kwong
2014-04-01
We review the recent experimental advances on quantum phenomena in transport measurements of topological insulators with emphasis on quantum oscillation, weak antilocalization and Aharonov-Bohm effect and Altshuler-Aronov-Spivak effect. Following a brief introduction on the topic, we discuss the identification of the topological surface state based on quantum phenomena. Research prospect of topological insulators is described at the end of this article.
Bananaworld quantum mechanics for primates
Bub, Jeffrey
2016-01-01
What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro?dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered...
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
Gato-Rivera, Beatriz
2015-01-01
A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. leading to...
Statistical mechanics of stochastic growth phenomena
Alekseev, Oleg
2016-01-01
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasi-static) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with planar domains. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with the free-particle propagator on the infinite dimensional complex manifold with the K\\"ahler metric.
Exactly Solvable Quantum Mechanics
Sasaki, Ryu
2014-01-01
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Pykacz, Jarosław
2015-01-01
This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special Łukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.
Non-locality beyond quantum mechanics
Popescu, Sandu
2010-01-01
Quantum mechanics is, without any doubt, a tremendously successful theory: it started by explaining black-body radiation and the photoelectric effect, it explained the spectra of atoms, and then went on to explain chemical bonds, the structure of atoms and of the atomic nucleus, the properties of crystals and the elementary particles, and a myriad of other phenomena. Yet it is safe to say that we still lack a deep understanding of quantum mechanics – surprising and even puzzling new effects continue to be discovered with regularity. That we are surprised and puzzled is the best sign that we still don't understand; however, the veil over the mysteries of quantum mechanics is starting to lift a little.
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Vargas, David L.
Emerging quantum simulator technologies provide a new challenge to quantum many body theory. Quantifying the emergent order in and predicting the dynamics of such complex quantum systems requires a new approach. We develop such an approach based on complex network analysis of quantum mutual information. First, we establish the usefulness of quantum mutual information complex networks by reproducing the phase diagrams of transverse Ising and Bose-Hubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to non-equilibrium quantum dynamics. We conclude with a study of student collaboration networks, correlating a student's role in a collaboration network with their grades. This work thus initiates a quantitative theory of quantum complexity and provides a new tool for physics education research. (Abstract shortened by ProQuest.).
Sanz, A S
2015-01-01
To date, quantum mechanics has proven to be our most successful theoretical model. However, it is still surrounded by a "mysterious halo" that can be summarized in a simple but challenging question: Why quantum phenomena are not understood under the same logic as classical ones? Although this is an open question (probably without an answer), from a pragmatist's point of view there is still room enough to further explore the quantum world, marveling ourselves with new physical insights. We just need to look back in the historical evolution of the quantum theory and thoroughly reconsider three key issues: (1) how this has developed since its early stages at a conceptual level, (2) what kind of experiments can be performed at present in a laboratory, and (3) what nonstandard conceptual models are available to extract some extra information. This contribution is aimed at providing some answers (and, perhaps, also raising some issues) to these questions through one of such models, namely Bohmian mechanics, a hydro...
Quantum mechanics of materials
Energy Technology Data Exchange (ETDEWEB)
Cohen, M.L.; Heine, V.; Phillips, J.C.
1982-06-01
In the past 25 years, new quantum-mechanical methods have been developed for predicting the configuration of the valence electrons in an atom or an aggregate of many atoms, within the range of energy excitations in which the atoms form interatomic bonds. A theory specifying the configuration of the valence electrons has much to say about the bulk properties of matter that depends on the nature of the interatomic bonds. The new method regards the core electrons and the atomic nucleus as if they constituted a single particle without internal structure. The method is called the pseudopotential theory. A general quantum-mechanical prediction of the properties of a substance in terms of the additive properties of separate chemical bonds is not yet feasible for molecules. However, there is one realm where prediction is now practical: crystalline solids. The regularity of the lattice into which the atoms are organized in a crystal makes it possible to calculate the properties of a macroscopic solid. In other words, many properties of an elemental solid such as lead or a simple binary solid such as gallium arsenide can not be deduced from energy considerations alone. (SC)
Quantum mechanics using Fradkin's representation
Shajesh, K V; Milton, Kimball A.
2005-01-01
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Quantum mechanics, strong emergence and ontological non-reducibility
Gambini, Rodolfo; Pullin, Jorge
2015-01-01
We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the Copenhagen interpretation, it does not resort to elements of a classical ontology. The quantum ontology in turn allows us to recognize that a typical behavior of quantum systems exhibits strong emergence and ontological non-reducibility. Such phenomena are not exceptional but natural, and are rooted in the basic mathematical structure of quantum mechanics.
Quantum Mechanics for Electrical Engineers
Sullivan, Dennis M
2011-01-01
The main topic of this book is quantum mechanics, as the title indicates. It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at
A Quantum Space behind Simple Quantum Mechanics
Directory of Open Access Journals (Sweden)
Chuan Sheng Chew
2017-01-01
Full Text Available In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles. This configuration space (as well as phase space can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.
Event-by-event simulation of quantum phenomena
Raedt, H. De; Raedt, K. De; Michielsen, K.; Landau, DP; Lewis, SP; Schuttler, HB
2006-01-01
In various basic experiments in quantum physics, observations are recorded event-by-event. The final outcome of such experiments can be computed according to the rules of quantum theory but quantum theory does not describe single events. In this paper, we describe a stimulation approach that does
Quantum mechanics the theoretical minimum
Susskind, Leonard
2014-01-01
From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Factorization Method in Quantum Mechanics
Dong, Shi-Hai
2007-01-01
This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into ...
Bohmian mechanics and quantum theory an appraisal
Goldstein, Sheldon; Cushing, James T
1996-01-01
We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's vers...
Decoherence in quantum mechanics and quantum cosmology
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Nanowires:inter-connection between newton mechanics and quantum mechanics
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Nanowires have been proved to be excellent candidates for future nanodevices for their advantages of being the smallest charge carrier,enabling abundant choice of materials,and related size,surface and quantum effects.Nanowires thus play important role to understand the physical phenomena between macro-scale Newton world and the micro-scale quantum mechanical world. Our group is among the few pioneers in early 1998's in developing methods for synthesis of silicon nanowires,and extending the nanowire synt...
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Exotic Phenomena in Quantum limit in nodal-line semimetal ZrSiS
Energy Technology Data Exchange (ETDEWEB)
Hu, Jin [Tulane Univ., New Orleans, LA (United States); Liu, Jinyu [Tulane Univ., New Orleans, LA (United States); Mao, Zhiqiang [Tulane Univ., New Orleans, LA (United States); Jaime, Marcelo [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Weickert, Dagmar Franziska [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-03-01
In quantum limit, all carriers condense to the lowest Landau level, leading to possible exotic quantum phenomena such as Lifshitz transition and density waves. Usually, quantum limit is not easily achieved due to relatively large Fermi surface in metals. Fortunately, the nodal-line semimetal ZrSiS possesses a very small Fermi pocket with a characteristic quantum oscillation frequency of 8.4T, which represents the 2D Dirac states protected by non-symmorphic symmetry. The quantum limit of such Dirac bands can be reached in moderate magnetic field ~25T, indicating that ZrSiS could be a nice platform to explore the novel quantum phenomena of Dirac fermions in quantum limit.
Popper's test of Quantum Mechanics
Bramon, A
2005-01-01
A test of quantum mechanics proposed by K. Popper and dealing with two-particle entangled states emitted from a fixed source has been criticized by several authors. Some of them claim that the test becomes inconclusive once all the quantum aspects of the source are considered. Moreover, another criticism states that the predictions attributed to quantum mechanics in Popper's analysis are untenable. We reconsider these criticisms and show that, to a large extend, the `falsifiability' potential of the test remains unaffected.
The theoretical foundations of quantum mechanics
Baaquie, Belal E
2013-01-01
The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and a...
Noncommutative Quantum Mechanics and Quantum Cosmology
Bastos, Catarina; Dias, Nuno; Prata, Joao Nuno
2009-01-01
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, $\\theta$ and $\\eta$. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Principles of Quantum Mechanics
Landé, Alfred
2013-10-01
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Energy Technology Data Exchange (ETDEWEB)
Bouchard, A.M.
1994-07-27
This report discusses the following topics: Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices; solvable dynamical model of an electron in a one-dimensional aperiodic lattice subject to a uniform electric field; and quantum dynamical phenomena of electrons in aperiodic semiconductor superlattices.
Discovering Quantum Mechanics Once Again
Duck, Ian M
2003-01-01
We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who seeks to construct a dynamical theory of probabilities and is lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.
On Finite $J$-Hermitian Quantum Mechanics
Lee, Sungwook
2014-01-01
In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.
Modern Approach to Quantum Mechanics
Townsend, John S.
Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.
Consolidation mechanisms and interfacial phenomena in thermoplastic powder impregnated composites
1995-01-01
Thermoplastic powder impregnation of continuous reinforcement filaments is studied in this work, focusing on impregnation mechanisms and interfacial phenomena. Various existing techniques to mingle powdered resins to continuous filaments are reviewed; a powder impregnation line designed at the Laboratoire de Technologie des Composites et Polymères (LTC) is presented. Two important types of powder coated towpregs are addressed: FIT bundles (Fibre...
Event-by-event simulation of quantum phenomena
De Raedt, H.; Zhao, S.; Yuan, S.; Jin, F.; Michielsen, K.; Miyashita, S.
2010-01-01
We discuss recent progress in the development of simulation algorithms that do not rely on any concept of quantum theory but are nevertheless capable of reproducing the averages computed from quantum theory through an event-by-event simulation. The simulation approach is illustrated by applications
Mathematical foundation of quantum mechanics
Parthasarathy, K R
2005-01-01
This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...
Quantum mechanics a modern development
Ballentine, Leslie E
2015-01-01
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory. In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions ...
Communication: quantum mechanics without wavefunctions.
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.
Coherent states in quantum mechanics
Rodrigues, R D L; Fernandes, D
2001-01-01
We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.
Quantum Mechanics of Extended Objects
Sastry, R R
2000-01-01
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example the phenomenological coupling constant of the $\\omega$ meson which mediates the short range and repulsive nucleon force as well as the repulsive core radius are theoretically predicted.
Quantum mechanics in Hilbert space
Prugovecki, Eduard
2006-01-01
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the
Linear operators for quantum mechanics
Jordan, Thomas F
2006-01-01
This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators.Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear fun
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Quantum mechanical irreversibility and measurement
Grigolini, P
1993-01-01
This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will
Time Asymmetric Quantum Mechanics
National Research Council Canada - National Science Library
Arno R Bohm; Manuel Gadella; Piotr Kielanowski
2011-01-01
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1...
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Analytical mechanics for relativity and quantum mechanics
Johns, Oliver Davis
2011-01-01
Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...
Hilbert space and quantum mechanics
Gallone, Franco
2015-01-01
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...
Quantum mechanics principles and formalism
McWeeny, Roy
2012-01-01
Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.
Quantum mechanical description of waveguides
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong; He Bing
2008-01-01
Applying the spinor representation of the electromagnetic field,this paper present a quantum-mechanical description of waveguides.As an example of application,a potential qubit generated by photon tunnelling is discussed.
Quantum Mechanics and Common Sense
Gantsevich, S V
2016-01-01
A physical picture for Quantum Mechanics which permits to conciliate it with the usual common sense is proposed. The picture agrees with the canonical Copenhagen interpretation making more clear its statements.
Quantum mechanics I the fundamentals
Rajasekar, S
2015-01-01
Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.
On Macroscopic Quantum Phenomena in Biomolecules and Cells: From Levinthal to Hopfield
Directory of Open Access Journals (Sweden)
Dejan Raković
2014-01-01
Full Text Available In the context of the macroscopic quantum phenomena of the second kind, we hereby seek for a solution-in-principle of the long standing problem of the polymer folding, which was considered by Levinthal as (semiclassically intractable. To illuminate it, we applied quantum-chemical and quantum decoherence approaches to conformational transitions. Our analyses imply the existence of novel macroscopic quantum biomolecular phenomena, with biomolecular chain folding in an open environment considered as a subtle interplay between energy and conformation eigenstates of this biomolecule, governed by quantum-chemical and quantum decoherence laws. On the other hand, within an open biological cell, a system of all identical (noninteracting and dynamically noncoupled biomolecular proteins might be considered as corresponding spatial quantum ensemble of these identical biomolecular processors, providing spatially distributed quantum solution to a single corresponding biomolecular chain folding, whose density of conformational states might be represented as Hopfield-like quantum-holographic associative neural network too (providing an equivalent global quantum-informational alternative to standard molecular-biology local biochemical approach in biomolecules and cells and higher hierarchical levels of organism, as well.
On Macroscopic Quantum Phenomena in Biomolecules and Cells: From Levinthal to Hopfield
Raković, Dejan; Dugić, Miroljub; Jeknić-Dugić, Jasmina; Plavšić, Milenko; Jaćimovski, Stevo; Šetrajčić, Jovan
2014-01-01
In the context of the macroscopic quantum phenomena of the second kind, we hereby seek for a solution-in-principle of the long standing problem of the polymer folding, which was considered by Levinthal as (semi)classically intractable. To illuminate it, we applied quantum-chemical and quantum decoherence approaches to conformational transitions. Our analyses imply the existence of novel macroscopic quantum biomolecular phenomena, with biomolecular chain folding in an open environment considered as a subtle interplay between energy and conformation eigenstates of this biomolecule, governed by quantum-chemical and quantum decoherence laws. On the other hand, within an open biological cell, a system of all identical (noninteracting and dynamically noncoupled) biomolecular proteins might be considered as corresponding spatial quantum ensemble of these identical biomolecular processors, providing spatially distributed quantum solution to a single corresponding biomolecular chain folding, whose density of conformational states might be represented as Hopfield-like quantum-holographic associative neural network too (providing an equivalent global quantum-informational alternative to standard molecular-biology local biochemical approach in biomolecules and cells and higher hierarchical levels of organism, as well). PMID:25028662
Consciousness and quantum mechanics life in parallel worlds
Mensky, Michael B
2010-01-01
The phenomenon of consciousness includes mysterious aspects providing a basis for many spiritual doctrines (including religions) and psychological practices. These directions of human knowledge are usually considered to contradict the laws of science. However, quantum mechanics - in a sense, the mysterious direction of science - allows us to include the phenomena of consciousness and life as well as the relevant phenomena in the sphere of science. Wolfgang Pauli, one of the pioneers of quantum mechanics, together with great psychologist Carl Gustav Jung, guessed about the relation between quan
Infrared phenomena in quantum electrodynamics : II. Bremsstrahlung and compton scattering
Haeringen, W. van
1960-01-01
The infrared aspects of quantum electrodynamics are discussed by treating two examples of scattering processes, bremsstrahlung and Compton scattering. As in the previous paper one uses a non-covariant diagram technique which gives very clear insight in the cancelling of infrared divergences between
Random matrix theory and critical phenomena in quantum spin chains
Hutchinson, J.; Keating, J. P.; Mezzadri, F.
2015-09-01
We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and $Sp(2N)$. In particular we calculate critical exponents $s$, $\
The physics of quantum mechanics
Binney, James
2014-01-01
The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be
Quantum mechanics in a nutshell
Mahan, Gerald D
2009-01-01
Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original
Mathematical foundations of quantum mechanics
Mackey, George W
2004-01-01
Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University.Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum
Quantum Mechanics and determinism
Hooft, G. 't
2001-01-01
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied to free Maxwell fields. Lorentz invariance is demonstrated.
Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions
Hattori, Koichi
2016-01-01
The relativistic heavy-ion collisions create both hot quark-gluon matter and strong magnetic fields, and provide an arena to study the interplay between quantum chromodynamics (QCD) and quantum electrodynamics (QED). In recent years, it has been shown that such an interplay can generate a number of interesting quantum phenomena in hadronic and quark-gluon matter. In this short review, we first discuss some properties of the magnetic fields in heavy-ion collisions and then give an overview of the magnetic-field induced novel quantum effects. In particular, we focus on the magnetic effect on the heavy-flavor mesons, and the heavy quark transports, and also the phenomena closely related to chiral anomaly.
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Chaotic phenomena in Josephson circuits coupled quantum cellular neural networks
Institute of Scientific and Technical Information of China (English)
Wang Sen; Cai Li; Li Qin; Wu Gang
2007-01-01
In this paper the nonlinear dynamical behaviour of a quantum cellular neural network (QCNN) by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset of chaotic oscillation. The theoretical analysis and simulation for the two Josephson-circuits-coupled QCNN have been done by using the amplitude and phase as state variables. The complex chaotic behaviours can be observed and then proved by calculating Lyapunov exponents. The study provides valuable information about QCNNs for future application in high-parallel signal processing and novel chaotic generators.
Can many-valued logic help to comprehend quantum phenomena?
Pykacz, Jarosław
2014-01-01
Following {\\L}ukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger-Horne-Zeilinger `paradox' is shown to be an artifact caused by unjustified use of 2-valued logic while considering results of future non-certain events. Description of properties of quantum objects before they are measured should be performed with the use of propositional functions that form a particular model of infinitely-valued {\\L}ukasiewicz logic. This model is distinguished by specific operations of negation, conjunction, and disjunction that are used in it.
Teaching Quantum Mechanical Commutation Relations via an Optical Experiment
Billur, A Alper; Bursal, Murat
2015-01-01
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the operator formalisms are generally given theoretically and it is documented that these abstract formalisms are usually misunderstood by the students. Based on the idea that quantum mechanical phenomena can be investigated via geometric optical tools, this study aims to introduce an experiment, where the quantum mechanical commutation relations are represented in a concrete way to provide students an easy and permanent learning. The experimental tools are chosen to be easily accessible and economic. The experiment introduced in this paper can be done with students or used as a demonstrative experiment in laboratory based or theory based courses requiring quantum physics content; particularly in physics, physics education and science education programs.
Quantum Mechanics and Narratability
Myrvold, Wayne C.
2016-07-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
Quantum Mechanics: Harbinger of a Non-Commutative Probability Theory?
Hiley, Basil J.
2014-01-01
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to see the structure of quantum processes in terms of non-commutative probability theory, a non-Boolean structure of the implicate order which contains Boolean sub-structures which accommodates the explicate classical world. We move away from mechanical `wave...
Random matrix theory and critical phenomena in quantum spin chains.
Hutchinson, J; Keating, J P; Mezzadri, F
2015-09-01
We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators 〈σ_{i}^{x}σ_{i+n}^{x}〉_{g},〈σ_{i}^{y}σ_{i+n}^{y}〉_{g}, and 〈∏_{i=1}^{n}σ_{i}^{z}〉_{g}, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.
Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C
2015-08-28
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.
Framing difficulties in quantum mechanics
Modir, Bahar; Sayre, Eleanor C
2016-01-01
Students' difficulties in quantum mechanics may be the result of unproductive framing and not fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of the epistemological framing, we investigated four frames in our observational data: algorithmic math, conceptual math, algorithmic physics, and conceptual physics. We then used our framework to seek an underlying structure to the long lists of published difficulties that span many topics in quantum mechanics. We mapped descriptions of published difficulties into errors in epistemological framing and resource use. We analyzed descriptions of students' problem solving to find their frames, and compared students' framing to framing (and frame shifting) required by problem statements. We found three categories of error: mismatches between students' framing and problem statement framing; inappropriate or absent transiti...
Algebraic Quantum Mechanics and Pregeometry
Hiley, D J B P G D B J
2006-01-01
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Coupled Mechanical and Electrochemical Phenomena in Lithium-Ion Batteries
Cannarella, John
Lithium-ion batteries are complee electro-chemo-mechanical systems owing to a number of coupled mechanical and electrochemical phenomena that occur during operation. In this thesis we explore these phenomena in the context of battery degradation, monitoring/diagnostics, and their application to novel energy systems. We begin by establishing the importance of bulk stress in lithium-ion batteries through the presentation of a two-year exploratory aging study which shows that bulk mechanical stress can significantly accelerate capacity fade. We then investigate the origins of this coupling between stress and performance by investigating the effects of stress in idealized systems. Mechanical stress is found to increase internal battery resistance through separator deformation, which we model by considering how deformation affects certain transport properties. When this deformation occurs in a spatially heterogeneous manner, local hot spots form, which accelerate aging and in some cases lead to local lithium plating. Because of the importance of separator deformation with respect to mechanically-coupled aging, we characterize the mechanical properties of battery separators in detail. We also demonstrate that the stress state of a lithium-ion battery cell can be used to measure the cell's state of health (SOH) and state of charge (SOC)--important operating parameters that are traditionally difficult to measure outside of a laboratory setting. The SOH is shown to be related to irreversible expansion that occurs with degradation and the SOC to the reversible strains characteristic of the cell's electrode materials. The expansion characteristics and mechanical properties of the constituent cell materials are characterized, and a phenomenological model for the relationship between stress and SOH/SOC is developed. This work forms the basis for the development of on-board monitoring of SOH/SOC based on mechanical measurements. Finally we study the coupling between mechanical
Time Symmetric Quantum Mechanics and Causal Classical Physics ?
Bopp, Fritz W.
2017-02-01
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.
Time Symmetric Quantum Mechanics and Causal Classical Physics
Bopp, Fritz W
2016-01-01
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.
Comments on New Ontology of Quantum Mechanics called CSM
Kupczynski, Marian
2016-01-01
A new quantum ontology of quantum mechanics has been proposed recently. This ontology is based on impossible to realize measurements which need to be performed repeatedly on the same single physical system or on the same pair of physical systems. We agree that quantum mechanics is a contextual theory and that the experimental contexts have to be a part of any description of quantum phenomena but in our opinion this new ontology is neither convincing nor useful. In particular the authors claim that their ontology explains the peaceful coexistence between quantum mechanics and relativity in spin polarization correlation experiments. We show that, contrary to their claim, the authors are unable to explain why strong correlations, between the outcomes of distant local measurements, do exist and why they preserve a condition of parameter independence (non-signaling). Strangely enough the authors ignore that these strong but imperfect correlations can be explained in a local and causal way using statistical context...
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Reality without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics
Plotnitsky, Arkady
2015-01-01
First, the article considers the nature of quantum reality (the reality responsible for quantum phenomena) and the concept of realism (our ability to represent this reality) in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different (from quantum mechanics) theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, "the statistical Copenhagen interpretation," is non-realist, insofar as the description or even conception of the nature of quantum objects and processes is precluded. The second, by A. Khrennikov, is ultimately realist, because it assumes that the quantum-mechanical level of reality is underlain by a deeper level of reality, described, in a realist fashion, by a model based on the pre-quantum classical statistical field theory (PCSFT), the predict...
Black holes and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, G. ' t, E-mail: g.thooft@uu.n [Institute for Theoretical Physics, Utrecht University and Spinoza Institute, P.O. Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-15
After a brief review of quantum black hole physics, it is shown how the dynamical properties of a quantum black hole may be deduced to a large extent from Standard Model Physics, extended to scales near the Planck length, and combined with results from perturbative quantum gravity. Together, these interactions generate a Hilbert space of states on the black hole horizon, which can be investigated, displaying interesting systematics by themselves. To make such approaches more powerful, a study is made of the black hole complementarity principle, from which one may deduce the existence of a hidden form of local conformal invariance. Finally, the question is raised whether the principles underlying Quantum Mechanics are to be sharpened in this domain of physics as well. There are intriguing possibilities.
Quantum mechanics foundations and applications
Swanson, Donald Gary
2006-01-01
Progressing from the fundamentals of quantum mechanics (QM) to more complicated topics, Quantum Mechanics: Foundations and Applications provides advanced undergraduate and graduate students with a comprehensive examination of many applications that pertain to modern physics and engineering.Based on courses taught by the author, this textbook begins with an introductory chapter that reviews historical landmarks, discusses classical theory, and establishes a set of postulates. The next chapter demonstrates how to find the appropriate wave functions for a variety of physical systems in one dimens
Spin-related transport phenomena in HgTe-based quantum well structures
Energy Technology Data Exchange (ETDEWEB)
Koenig, Markus
2007-12-15
Within the scope of this thesis, spin related transport phenomena have been investigated in HgTe/Hg{sub 0.3}Cd{sub 0.7}Te quantum well structures. In our experiments, the existence of the quantum spin Hall (QSH) state was successfully demonstrated for the first time and the presented results provide clear evidence for the charge transport properties of the QSH state. Our experiments provide the first direct observation of the Aharonov-Casher (AC) effect in semiconductor structures. In conclusion, HgTe quantum well structures have proven to be an excellent template for studying spin-related transport phenomena: The QSH relies on the peculiar band structure of the material and the existence of both the spin Hall effect and the AC effect is a consequence of the substantial spin-orbit interaction. (orig.)
Effective equations for the quantum pendulum from momentous quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Hernández-Tenorio, C.; Serkin, V. N.; Belyaeva, T. L.; Peña-Moreno, R.; Morales-Lara, L.
2015-01-01
The nonlinear Schrödinger equation (NLSE) model with an external harmonic potential is one of the most important in modern science. This model makes it possible to analyze a variety of nonlinear phenomena, in nonlinear optics and laser physics, biophysics and in the theory of Bose-Einstein condensation of atoms. It is shown that the main specific feature of the dynamics of dark GP matter wave solitons in a parabolic trap is the formation of solitons with dynamically changing form-factors producing the periodic variation in the modulation depth (the degree of "blackness") of dark solitons. In general, the period of dark soliton oscillations in trapping potential depends on the specific conditions of the experiment and does not coincide with the oscillation period of a linear quantum-mechanical oscillator. In the case of an immobile pedestal in the trap, the oscillation period of the black soliton considerably increases because of the periodic transformation of the black soliton to the gray one and vice versa. Surprisingly, that if the dark soliton is superimposed on the base pedestal oscillating in the trap and displaced from the trap center, the oscillation period of the dark soliton coincides with the period of oscillations of the linear harmonic oscillator, while the dynamics of the dark soliton is similar to that of a classical particle obeying the Newton mechanics laws.
Quantum Mechanics, is it magic
Ferrero, M; Sánchez-Gómez, J L
2008-01-01
We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of knowledge could be, what could be called its magic precisely resides in this violation.
Mind, matter and quantum mechanics
Stapp, Henry P
2009-01-01
"Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questi...
Philosophic foundations of quantum mechanics
Reichenbach, Hans
1998-01-01
Physics concerns direct analysis of the physical world, while philosophy analyzes knowledge about the physical world. This volume combines both disciplines for a philosophical interpretation of quantum physics - an interpretation free from the imprecision of metaphysics, offering a view of the atomic world and its quantum mechanical results as concrete as the visible everyday world.Written by an internationally renowned philosopher who specialized in symbolic logic and the theory of relativity, this approach consists of three parts. The first section, which requires no background in math or p
Memetics of Quantum Mechanical Interpretations
Chakrabarty, I
2006-01-01
Memes, self reproducing mental information and cognitive structures analogous to genes in biology, can be seen as the basis for an explanatory model of cultural and psychological behavior. Their properties and effects are evolutionary conditioned and ultimately seeks to promote their replication. To survive in a context the memes must meet certain conditions. We here propose a Memetics of Quantum Mechanical Interpretations, which have eluded mankind for a century now. We also see how the ideas of memes best fit the way scientific theories in general and Quantum Theory in particular propagates in the scientific brains and finds its expressions in the scientific community and effects the way we perceive Nature.
Operator methods in quantum mechanics
Schechter, Martin
2003-01-01
This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q
Wigner distributions in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ercolessi, E; Marmo, G; Morandi, G; Mukunda, N [Physics Department, University of Bologna, INFN and CNISM. 46 v.Irnerio. I-40126, Bologna (Italy); Dip. di Scienze Fisiche. University di Napoli ' Federico II' and INFN. v.Cinzia. I-80100 Naples (Italy); Physics Department, University of Bologna, INFN and CNISM. 6/2 v.le Berti Pichat. I-40127, Bologna (Italy); Centre for High-Energy Physics. Indian Institute of Science. Bamgalore 560012 (India)
2007-11-15
The Weyl-Wigner description of quantum mechanical operators and states in classical phase-space language is well known for Cartesian systems. We describe a new approach based on ideas of Dirac which leads to the same results but with interesting additional insights. A way to set up Wigner distributions in an interesting non-Cartesian case, when the configuration space is a compact connected Lie group, is outlined. Both these methods are adapted to quantum systems with finite-dimensional Hilbert spaces, and the results are contrasted.
Paradoxical reflection in quantum mechanics
Pedro L. Garrido; Goldstein, Sheldon; Lukkarinen, Jani; Tumulka, Roderich
2011-01-01
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This p...
Making sense of quantum mechanics
Bricmont, Jean
2016-01-01
This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why correlations between simultaneous events occurring far apart cannot be explained by local mechanisms, and why, nevertheless, the quantum theory can be understood in terms of matter in motion. No need to worry, as some people do, whether a cat can be both dead and alive, whether the moon is there when nobody looks at it, or whether quantum systems need an observer to acquire definite properties. The author’s inimitable and even humorous style makes the book a pleasure to read while bringing a new clarity to many of the longstanding puzzles of quantum physics.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Star Products for Relativistic Quantum Mechanics
Henselder, P.
2007-01-01
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition
Del Re, Lorenzo; Fabrizio, Michele; Tosatti, Erio
2016-03-01
We consider nonequilibrium phenomena in a very simple model that displays a zero-temperature first-order phase transition. The quantum Ising model with a four-spin exchange is adopted as a general representative of first-order quantum phase transitions that belong to the Ising universality class, such as for instance the order-disorder ferroelectric transitions, and possibly first-order T =0 Mott transitions. In particular, we address quantum quenches in the exactly solvable limit of infinite connectivity and show that, within the coexistence region around the transition, the system can remain trapped in a metastable phase, as long as it is spatially homogeneous so that nucleation can be ignored. Motivated by the physics of nucleation, we then study in the same model static but inhomogeneous phenomena that take place at surfaces and interfaces. The first-order nature implies that both phases remain locally stable across the transition, and with that the possibility of a metastable wetting layer showing up at the surface of the stable phase, even at T =0 . We use mean-field theory plus quantum fluctuations in the harmonic approximation to study quantum surface wetting.
Quantum mechanics of black holes.
Witten, Edward
2012-08-03
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Quantum communication between remote mechanical resonators
Felicetti, S.; Fedortchenko, S.; Rossi, R.; Ducci, S.; Favero, I.; Coudreau, T.; Milman, P.
2017-02-01
Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. Here, we introduce an interferometric scheme where the interaction of a mechanical resonator with input-output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as a building block for the implementation of long-distance quantum networks of mechanical resonators.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Helping Students Learn Quantum Mechanics for Quantum Computing
Singh, Chandralekha
2016-01-01
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Transition Decomposition of Quantum Mechanical Evolution
Strauss, Y; Machnes, S; Horwitz, L P
2011-01-01
We show that the existence of the family of self-adjoint Lyapunov operators introduced in [J. Math. Phys. 51, 022104 (2010)] allows for the decomposition of the state of a quantum mechanical system into two parts: A past time asymptote, which is asymptotic to the state of the system at t goes to minus infinity and vanishes at t goes to plus infinity, and a future time asymptote, which is asymptotic to the state of the system at t goes to plus infinity and vanishes at t goes to minus infinity. We demonstrate the usefulness of this decomposition for the description of resonance phenomena by considering the resonance scattering of a particle off a square barrier potential. We show that the past time asymptote captures the behavior of the resonance. In particular, it exhibits the expected exponential decay law and spatial probability distribution.
Supersymmetric quantum mechanics with reflections
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128 (QC) H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-10-28
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q {yields} -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented. (paper)
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
The Hamiltonian and path integral approaches to supersymmetric quantum mechanics were reviewed. The related path integrals for the Witten Index and for stochastic processes were discussed and shown to be indications for supersymmetry breakdown. A system where in the superpotential W(x) has assymetrical values at + or - infinity was considered. Nonperturbative strategies for studying supersymmetry breakdown were described. These strategies are based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed.
The formalisms of quantum mechanics an introduction
David, Francois
2015-01-01
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...
Geometrical Lorentz Violation and Quantum Mechanical Physics
Mignani, R; Cardone, F
2013-01-01
On the basis of the results of some experiments dealing with the violation of Local Lorentz Invariance (LLI) and on the formalism of the Deformed Special Relativity (DSR), we examine the connections between the local geometrical structure of space-time and the foundation of Quantum Mechanics. We show that Quantum Mechanics, beside being an axiomatic theory, can be considered also a deductive physical theory, deducted from the primary physical principle of Relativistic Correlation. This principle is synonym of LLI and of a rigid and at minkowskian space-time. The results of the experiments mentioned above show the breakdown of LLI and hence the violation of the principle of Relativistic Correlation. The formalism of DSR allows to highlight the deep meaning of LLI breakdown in terms of the geometrical structure of local space-time which, far from being rigid and at, is deformed by the energy of the physical phenomena that take place and in this sense it has an active part in the dynamics of the whole physical p...
An introduction to the tomographic picture of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ibort, A [Departamento de Matematicas, Universidad Carlos III de Madrid, Avda de la Universidad 30, 28911 Leganes, Madrid (Spain); Man' ko, V I [P N Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G; Simoni, A; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S Angelo, via Cintia, 80126 Naples (Italy)], E-mail: albertoi@math.uc3m.es, E-mail: manko@na.infn.it, E-mail: marmo@na.infn.it, E-mail: simoni@na.infn.it, E-mail: ventriglia@na.infn.it
2009-06-15
Starting from the famous Pauli problem on the possibility of associating quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference between those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to non-negativity of probability density on phase space in the classical domain. The intersection of such sets is studied. The mathematical mechanism that allows us to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc is clarified and a connection with abstract Hilbert space properties is established. The superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equations like quantum evolution and energy spectra equations are given in an explicit form. A method to check experimentally the uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two-qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.
Applying quantum mechanics to macroscopic and mesoscopic systems
T., N Poveda
2012-01-01
There exists a paradigm in which Quantum Mechanics is an exclusively developed theory to explain phenomena on a microscopic scale. As the Planck's constant is extremely small, $h\\sim10^{-34}{J.s}$, and as in the relation of de Broglie the wavelength is inversely proportional to the momentum; for a mesoscopic or macroscopic object the Broglie wavelength is very small, and consequently the undulatory behavior of this object is undetectable. In this paper we show that with a particle oscillating around its classical trajectory, the action is an integer multiple of a quantum of action, $S = nh_{o}$. The quantum of action, $h_{o}$, which plays a role equivalent to Planck's constant, is a free parameter that must be determined and depends on the physical system considered. For a mesoscopic and macroscopic system: $h_{o}\\gg h$, this allows us to describe these systems with the formalism of quantum mechanics.
Trace anomalies from quantum mechanics
Bastianelli, F; Bastianelli, Fiorenzo; Nieuwenhuizen, Peter van
1993-01-01
The 1-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the regulated path integral jacobian matrix, as shown by Fujikawa. In 1983, Alvarez-Gaum\\'e and Witten observed that one can simplify this evaluation by replacing the operators which appear in the regulator and in the jacobian by quantum mechanical operators with the same (anti)commutation relations. By rewriting this quantum mechanical trace as a path integral with periodic boundary conditions for a one-dimensional supersymmetric nonlinear sigma model, they obtained the chiral anomalies for spin 1/2 and 3/2 fields and selfdual antisymmetric tensors in d dimensions. In this article, we treat the case of trace anomalies for spin 0, 1/2 and 1 fields in a gravitational and Yang-Mills background. We do not introduce a supersymmetric sigma model, but keep the original Dirac matrices $\\g^\\m$ and internal symmetry generators $T^a$ in the path integral. As a result, we get a matrix-valued action. Gauge covariance o...
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Negative entropy and information in quantum mechanics
Cerf, N. J.; Adami, C.
1995-01-01
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles sug...
The quantum mechanics of materials
Cohen, M. L.; Heine, V.; Phillips, J. C.
1982-06-01
The prediction of the properties of materials from fundamental principles, i.e., quantum mechanics, by the use of pseudopotential theory is discussed. Following a review of previous difficulties encountered in the application of quantum theory to complex aggregates of matter, and the failures of early theories to resolve differences corresponding to important phase transitions in solids, the idea first proposed by Herring concerning the energy cancellation of valence electrons and the possibility of neglecting core electron effects is examined as the basis of pseudopotential theory. The application of the electron pseudopotential, representing the scattering strength of one atomic core with respect to a single Fourier component of one valence-electron wave, to the calculation of the scattering of an electron wave in crystalline solids is examined, and the derivation of structural properties from the pseudopotentials is discussed. Recent advances in pseudopotential theory explaining the properties of surface and interface structures, and the total energy of semiconducting materials are indicated.
Hidden scale in quantum mechanics
Giri, Pulak Ranjan
2007-01-01
We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three dimensional space can have unusual localized wave-packet.
Quantum mechanics: Myths and facts
Nikolic, H
2006-01-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Matrix Quantum Mechanics from Qubits
Hartnoll, Sean A; Mazenc, Edward A
2016-01-01
We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O(N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1+1 dimensional spacetime.
Quantum Mechanics: Myths and Facts
Nikolić, Hrvoje
2007-11-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Deformation of noncommutative quantum mechanics
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
A quantum mechanical model of "dark matter"
Belokurov, V V
2014-01-01
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
Bohmian mechanics. The physics and mathematics of quantum theory
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.
2009-07-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang-Bong
1993-09-01
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
Fun with supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
Correspondence Truth and Quantum Mechanics
Karakostas, Vassilios
2015-01-01
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state...
Transfer of Learning in Quantum Mechanics
Singh, Chandralekha
2016-01-01
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.
Quantum localization of Classical Mechanics
Batalin, Igor A
2016-01-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum localization of classical mechanics
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Supersymmetric Quantum Mechanics and Topology
Directory of Open Access Journals (Sweden)
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Finkelstein, Noah; Hoehn, Jessica
2017-01-01
Learning quantum mechanics requires students to develop not only new mathematical skills and conceptual understanding, but also has students reason about what these mean and how to organize understanding of quantum mechanical principles, tools and concepts. Towards this instructional goal, we present current research that examines how students make interpretations, probes understanding of student ontologies, and curricula that explicitly addresses interpretation of quantum phenomena and student reasoning structures (ontologies).
Quantum Interference Phenomena and Novel Switching in Split Gate High Electron Mobility Transistors.
Wu, Jong-Ching
Nanometer scales electronic channels with and without a discontinuity were made in modulation-doped AlGaAs/GaAs heterojunctions using a split-gate technique. Quantum interference phenomena in an electron cavity, and fast switching behavior due to hot electron effects in a lateral double potential barrier structure were explored. First, one-dimensional channels with a double bend discontinuity were examined in the mK temperature range. Low-field ac-conductance measurements have evidenced quantum wave guide effects: resonant features were observed in the one-dimensional conductance plateaus in which the number of peaks was directly related to the geometry of the double bend. Temperature and magnetic field studies, along with a standing wave model have provided a better understanding of quantum interference phenomena in electron wave guide and cavity structures. Secondly, a structure containing two cascaded double bend discontinuities was studied. The structure behaves as a constricted cavity coupling two point-contacts, in which the depletion by the split gate was used to form and control the lateral double potential barriers. The low temperature source-drain characteristics exhibited a pronounced S-shaped negative differential conductance that can be attributed to a nonlinear electron temperature effect along the conducting path. The data presented show two types of conducting state: electron tunneling in the off state and hot electron conduction (thermionic emission) in the on state. The estimated switching speed of the device could be as fast as 5 ps due to short transit time.
Macroscopic Quantum Phenomena and Topological Phase Interference Effects in Single-Domain Magnets
Institute of Scientific and Technical Information of China (English)
L(U) Rong; ZHU Jialin
2001-01-01
The tunneling of macroscopic object is one of the most fascinating phenomena in condensed matter physics.During the last decade,the problem of quantum tunneling of magnetization in nanometer-scale magnets has attracted a great deal of theoretical and experimental interest.A review of recent theoretical research of the macroscopic quantum phenomena in nanometer-scale single-domain magnets is presented in this paper.It includes macroscopic quantum tunneling (MQT) and coherence (MQC) in single-domain magnetic particles,the topological phase interference or spin-parity effects,and tunneling of magnetization in an arbitrarily directed magnetic field.The general formulas are shown to evaluate the tunneling rate and the tunneling level splitting for single-domain AFM particles.A nontrivial generalization of Kramers degeneracy for double-well system is provided to coherently spin tunneling for spin systems with m-fold rotational symmetry.The effects induced by the external magnetic field have been studied,where the field is along the easy,medium,hard axis,or arbitrary direction.
Quantum mechanics for applied physics and engineering
Fromhold, Albert T
2011-01-01
This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Ch
A Quantum Space Behind Simple Quantum Mechanics
Chew, Chuan Sheng; Payne, Jason
2016-01-01
In physics, we are supposed to learn from experiments what constitutes a good/correct theoretical/mathematical model of any physical concept, the physical space should not be an exception. The best picture of the physical space, in Newtonian physics, is given by the configuration space of a free particle. The space, as well as the phase space, can be constructed as a representation space of the relativity symmetry. Starting with the corresponding quantum symmetry, we illustrate the construction of a quantum space along the lines of the quantum phase space and demonstrate the retrieval of the classical picture as an approximation through the contraction of the (relativity) symmetry and the representations of it. The result suggests a picture of the physical space beyond that of a finite dimensional manifold.
Are there fundamental limits for observing quantum phenomena from within quantum theory?
Kofler, Johannes
2010-01-01
Does there exist a limit for the applicability of quantum theory for objects of large mass or size, or objects whose states are of large complexity or dimension of the Hilbert space? The possible answers range from practical limitations due to decoherence within quantum theory to fundamental limits due to collapse models that modify quantum theory. Here, we suggest the viewpoint that there might be also fundamental limits without altering the quantum laws. We first demonstrate that for two quantum spins systems of a given spin length, no violation of local realism can be observed, if the measurements are sufficiently coarse-grained. Then we show that there exists a fundamental limit for the precision of measurements due to (i) the Heisenberg uncertainty relation which has to be applied to the measuring apparatus, (ii) relativistic causality, and (iii) the finiteness of resources in any laboratory including the whole universe. This suggests that there might exist a limit for the size of the systems (dimension ...
The emerging quantum the physics behind quantum mechanics
Pena, Luis de la; Valdes-Hernandez, Andrea
2014-01-01
This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physi...
Simulating quantum-optical phenomena with cold atoms in optical lattices
Energy Technology Data Exchange (ETDEWEB)
Navarrete-Benlloch, Carlos [Departament d' Optica, Universitat de Valencia, Dr Moliner 50, 46100 Burjassot (Spain); Vega, Ines de [Institut fuer Theoretische Physik, Albert-Einstein-Allee 11, Universitaet Ulm, D-89069 Ulm (Germany); Porras, Diego [Departamento de Fisica Teorica I, Universidad Complutense, 28040 Madrid (Spain); Ignacio Cirac, J, E-mail: carlos.navarrete@uv.es, E-mail: ines.devega@uni-ulm.de, E-mail: diego.porras@fis.ucm.es, E-mail: ignacio.cirac@mpq.mpg.de [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching (Germany)
2011-02-15
We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state through a Raman scheme. The coupling between these two types of atoms (trapped and free) turns out to be similar to that describing light-matter interaction within the rotating-wave approximation, the role of matter and photons being played by the trapped and free atoms, respectively. We explain in particular how to observe phenomena arising from the collective spontaneous emission of atomic and harmonic oscillator samples, such as superradiance and directional emission. We also show how the same setup can simulate Bose-Hubbard Hamiltonians with extended hopping as well as Ising models with long-range interactions. We believe that this system can be realized with state of the art technology.
Quantum theory as a tool for the description of simple psychological phenomena
Vol, E D
2011-01-01
We propose the consistent statistical approach for the quantitative description of simple psychological phenomena using the methods of quantum theory of open systems (QTOS). Taking as the starting point the K. Lewin's psychological field theory we show that basic concepts of this theory can be naturally represented in the language of QTOS. In particular provided that all stimuli acting on psychological system (that is individual or group of interest) are known one can associate with these stimuli corresponding operators and after that to write down the equation for evolution of density matrix of the relevant open system which allows one to find probabilities of all possible behavior alternatives. Using the method proposed we consider in detail simple model describing such interesting psychological phenomena as cognitive dissonance and the impact of competition among group members on its unity.
Quantum mechanics in complex systems
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Bridging classical and quantum mechanics
Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.
2016-10-01
Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.
A Process Model of Quantum Mechanics
Sulis, William
2014-01-01
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has th...
On the Use of a Virtual Mach-Zehnder Interferometer in the Teaching of Quantum Mechanics
Pereira, Alexsandro; Ostermann, Fernanda; Cavalcanti, Claudio
2009-01-01
For many students, the conceptual learning of quantum mechanics can be rather painful owing to the counter-intuitive nature of quantum phenomena. In order to enhance students' understanding of the odd behaviour of photons and electrons, we introduce a computational simulation of the Mach-Zehnder interferometer, developed by our research group. An…
On the Use of a Virtual Mach-Zehnder Interferometer in the Teaching of Quantum Mechanics
Pereira, Alexsandro; Ostermann, Fernanda; Cavalcanti, Claudio
2009-01-01
For many students, the conceptual learning of quantum mechanics can be rather painful owing to the counter-intuitive nature of quantum phenomena. In order to enhance students' understanding of the odd behaviour of photons and electrons, we introduce a computational simulation of the Mach-Zehnder interferometer, developed by our research group. An…
Dielectric Anomaly in Ice near 20 K; Evidence of Macroscopic Quantum Phenomena
Yen, Fei
2015-01-01
H2O is one of the most important substances needed in sustaining life; but yet not much is known about its ground state. Here, a previously unidentified anomaly is identified in the form of a minimum in the imaginary part of the dielectric constant with respect to temperature near 20 K while the real part remains monotonic. Isothermal dispersion and absorption measurements show coinciding results. For the case of heavy ice (D2O), no anomaly was identified confirming an apparent isotope effect. Concerted quantum tunneling of protons is believed to be the main cause behind the reported anomaly. Our findings identify another system that exhibits macroscopic quantum phenomena of which rarely occur in nature.
Energy Technology Data Exchange (ETDEWEB)
Whitaker, A [Department of Physics, Queen' s University, Belfast (United Kingdom)
2004-02-27
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding
Schwinger Algebra for Quaternionic Quantum Mechanics
Horwitz, L P
1997-01-01
It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \\to \\infty$.
Quantum mechanics and computation; Quanta y Computacion
Energy Technology Data Exchange (ETDEWEB)
Cirac Sasturain, J. I.
2000-07-01
We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs.
Interactive learning tutorials on quantum mechanics
Singh, Chandralekha
2016-01-01
We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs) which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as a self-study tool.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Towards a Constructive Foundation of Quantum Mechanics
Smilga, Walter
2016-11-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Towards a Constructive Foundation of Quantum Mechanics
Smilga, Walter
2017-01-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Quantum Mechanics As A Limiting Case of Classical Mechanics
Ghose, Partha
2000-01-01
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which quantum mechanics emerges as a limiting case of classical mechanics in which the classical system is decoupled from its environment.
BOOK REVIEWS: Quantum Mechanics: Fundamentals
Whitaker, A.
2004-02-01
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a
Quantum mechanics without potential function
Energy Technology Data Exchange (ETDEWEB)
Alhaidari, A. D., E-mail: haidari@sctp.org.sa [Saudi Center for Theoretical Physics, P.O. Box 32741, Jeddah 21438 (Saudi Arabia); Ismail, M. E. H. [Department of Mathematics, University of Central Florida, Orlando, Florida 32816 (United States)
2015-07-15
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
Quantum mechanics of Proca fields
Zamani, Farhad; Mostafazadeh, Ali
2009-05-01
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
A modern approach to quantum mechanics
Townsend, John S
2012-01-01
Using an innovative approach that students find both accessible and exciting, A Modern Approach to Quantum Mechanics, Second Edition lays out the foundations of quantum mechanics through the physics of intrinsic spin. Written to serve as the primary textbook for an upper-division course in quantum mechanics, Townsend's text gives professors and students a refreshing alternative to the old style of teaching, by allowing the basic physics of spin systems to drive the introduction of concepts such as Dirac notation, operators, eigenstates and eigenvalues, time evolution in quantum mechanics, and entanglement. Chapters 6 through 10 cover the more traditional subjects in wave mechanics-the Schrodinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials-but they are motivated by the foundations developed in the earlier chapters. Students using this text will perceive wave mechanics as an important aspect of quantum mechanics, but not necessarily the core of the subj...
Quantum mechanics II a second course in quantum theory
Landau, Rubin H
2004-01-01
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature.As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists
Quantum Mechanics: Bell and Quantum Entropy for the Classroom
Pluch, Philipp
2014-01-01
In this article we are willing to give some first steps to quantum mechanics and a motivation of quantum mechanics and its interpretation for undergraduate students not from physics. After a short historical review in the development we discuss philosophical, physical and mathematical interpretation. We define local realism, locality and hidden variable theory which ends up in the EPR paradox, a place where questions on completeness and reality comes into play. The fundamental result of the last century was maybe Bell's that states that local realism is false if quantum mechanics is true. From this fact we can obtain the so called Bell inequalities. After a didactic example of the fact what these inequalities means we describe the key concept of quantum entanglement motivated here by quantum information theory. Also classical entropy and von Neuman entropy is discussed.
Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...
Pragmatic Information in Quantum Mechanics
Roederer, Juan G
2015-01-01
An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism ...
Morlet Wavelets in Quantum Mechanics
Directory of Open Access Journals (Sweden)
John Ashmead
2012-11-01
Full Text Available Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or δ function decomposition. Morlet wavelets in particular are well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. But to take full advantage of Morlet wavelets we need to supply an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We construct both here.Quanta 2012; 1: 58–70.
Kindergarten Quantum Mechanics lectures notes
Coecke, B
2005-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.
Quantum Tunneling In Deformed Quantum Mechanics with Minimal Length
Guo, Xiaobo; Tao, Jun; Wang, Peng
2016-01-01
In the deformed quantum mechanics with a minimal length, one WKB connection formula through a turning point is derived. We then use it to calculate tunnelling rates through potential barriers under the WKB approximation. Finally, the minimal length effects on two examples of quantum tunneling in nuclear and atomic physics are discussed
Testing non-associative quantum mechanics
Bojowald, Martin; Buyukcam, Umut
2015-01-01
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Thermodynamic integration from classical to quantum mechanics.
Habershon, Scott; Manolopoulos, David E
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
Algebraic-statistical approach to quantum mechanics
Slavnov, D A
2001-01-01
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative algebra (observables) and the nonlinear functionals on this algebra (physical states) are used as the primary constituents. The functionals associate with results of a particular measurement. It is suggested to consider certain ensembles of the physical states as quantum states of the standart quantum mechanics. It is shown that in such scheme the mathematical formalism of the standart quantum mechanics can be reproduced completely.
Random Matrix theory approach to Quantum mechanics
Chaitanya, K. V. S. Shiv
2015-01-01
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional ...
Review of student difficulties in upper-level quantum mechanics
National Research Council Canada - National Science Library
Chandralekha Singh; Emily Marshman
2015-01-01
... at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different...
Elucidating reaction mechanisms on quantum computers.
Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias
2017-07-18
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
The transactional interpretation of quantum mechanics
Cramer, John G.
2001-06-01
The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."
Critique of Conventional Relativistic Quantum Mechanics.
Fanchi, John R.
1981-01-01
Following an historical sketch of the development of relativistic quantum mechanics, a discussion of the still unresolved difficulties of the currently accepted theories is presented. This review is designed to complement and update the discussion of relativistic quantum mechanics presented in many texts used in college physics courses. (Author/SK)
Third emission mechanism in solid-state nanocavity quantum electrodynamics.
Yamaguchi, Makoto; Asano, Takashi; Noda, Susumu
2012-09-01
Photonic crystal (PC) nanocavities have been receiving a great deal of attention recently because of their ability to strongly confine photons in a tiny space with a high quality factor. According to cavity quantum electrodynamics (cavity QED), such confined photons can achieve efficient interactions with excitons in semiconductors, leading to the Purcell effect in the weak coupling regime and vacuum Rabi splitting (VRS) in the strong coupling regime. These features are promising for applications such as quantum information processing, highly efficient single photon sources and ultra-low threshold lasers. In this context, the coupled system of a semiconductor quantum dot (QD) and a PC nanocavity has been intensively investigated in recent years.Although experimental reports have demonstrated such fundamental features, two anomalous phenomena have also been observed. First, photon emission from the cavity occurs even when it is significantly detuned from the QD. Second, spectral triplets are formed by additional bare-cavity lines between the VRS lines. These features cannot be explained by standard cavity QED theories and have prompted controversy regarding their physical mechanisms. In this review we describe the recent experimental and theoretical progress made in the investigation of these phenomena. Similar mechanisms will also occur in many other coupled quantum systems, and thus the findings are applicable to a wide range of fields.
On the Classical Limit of Quantum Mechanics
Allori, V; Allori, Valia; Zangh\\`{\\i}, Nino
2001-01-01
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\\h \\to 0$ asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
Conference on Mathematical Results in Quantum Mechanics
Exner, Pavel; Tater, Miloš; QMath-7
1999-01-01
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.
Propagators in Polymer Quantum Mechanics
Flores-González, Ernesto; Reyes, Juan D
2013-01-01
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green's function character. Furthermore they are also shown to reduce to the usual Schr\\"odinger propagators in the limit of sm...
Quantum Semiotics: A Sign Language for Quantum Mechanics
Prashant
2006-01-01
Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.
Dorit Aharonov; Umesh Vazirani
2012-01-01
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Bibliographic guide to the foundations of quantum mechanics and quantum information
Cabello, A
2000-01-01
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.
Molecular Beam Epitaxial Growth of Heterostructures to Study Quantum Interference Phenomena
1990-01-01
MBE growth and regrowth of heterostructures for quantum interference transistors and a detailed study of the physical mechanisms and the limitations imposed by them in such devices. We have investigated in detail the suitability of the MBE regrowth process for such applications. Very encouraging progress has been made. The performance characteristics of dual-channel quantum interference devices grown in our laboratory and defined by e-beam lithography have been measured and reported. From this work it is clear that to achieve enhanced performance and to demonstrate a large
Prologue to super quantum mechanics something is rotten in the state of quantum mechanics
Vaguine, Victor
2012-01-01
Since its foundation more than eight decades ago, quantum mechanics has been plagued by enigmas, mysteries and paradoxes and held hostage by quantum positivism. This fact strongly suggests that something is fundamentally wrong with the quantum mechanics paradigm. The best scientific minds, such as Albert Einstein, Louis de Broglie, David Bohm, Richard Feynman and others have spent years of their professional lives attempting to find resolution to the quantum mechanics predicament, with not much success. A shift of the quantum mechanics paradigm toward a deeper physics theory is long overdue.
How Does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?
Solé, A.; Oriols, X.; Marian, D.; Zanghì, N.
2016-10-01
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state — the positions of the particles — must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.
Feshbach Prize: New Phenomena and New Physics from Strongly-Correlated Quantum Matter
Carlson, Joseph A.
2017-01-01
Strongly correlated quantum matter is ubiquitous in physics from cold atoms to nuclei to the cold dense matter found in neutron stars. Experiments from table-top to the extremely large scale experiments including FRIB and LIGO will help determine the properties of matter across an incredible scale of distances and energies. Questions to be addressed include the existence of exotic states of matter in cold atoms and nuclei, the response of this correlated matter to external probes, and the behavior of matter in extreme astrophysical environments. A more complete understanding is required, both to understand these diverse phenomena and to employ this understanding to probe for new underlying physics in experiments including neutrinoless double beta decay and accelerator neutrino experiments. I will summarize some aspects of our present understanding and highlight several important prospects for the future.
Exploring Few- and Many-Body Dipolar Quantum Phenomena with Ultracold Erbium Atoms
Ferlaino, Francesca
2016-05-01
Given their strong magnetic moment and exotic electronic configuration, rare-earth atoms disclose a plethora of intriguing phenomena in ultracold quantum physics with dipole-dipole interaction. Here, we report on the first degenerate Fermi gas of erbium atoms, based on direct cooling of identical fermions via dipolar collisions. We reveal universal scattering laws between identical dipolar fermions close to zero temperature, and we demonstrate the long-standing prediction of a deformed Fermi surface in dipolar gas. Finally, we present the first experimental study of an extended Bose-Hubbard model using bosonic Er atoms in a three-dimensional optical lattice and we report on the first observation of nearest-neighbor interactions.
Topological strings from quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 1}. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Topological Strings from Quantum Mechanics
Grassi, Alba; Marino, Marcos
2014-01-01
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Phys...
Strange Bedfellows: Quantum Mechanics and Data Mining
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin [SLAC National Accelerator Laboratory, Stanford, CA (United States)
2010-02-15
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
On the tomographic picture of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ibort, A., E-mail: albertoi@math.uc3m.e [Departamento de Matematicas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Ventriglia, F., E-mail: ventriglia@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2010-06-07
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.
Strange Bedfellows: Quantum Mechanics and Data Mining
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin; /SLAC
2009-12-16
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Sheu, Yae-lin; Hsu, Liang-Yan
2015-01-01
Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several of quantum systems, a systematic comparison among these methods is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, indicating the versatility of TF analysis as a new viable venue for exploring quantum dynamics.
Quantum mechanical treatment of parametric amplification in an absorptive nonlinear medium
Inoue, K.
2017-01-01
Generally, loss phenomena are known to affect the quantum properties of a light wave. This paper describes a quantum mechanical treatment of parametric amplification in an absorptive nonlinear medium. An expression of the quantum mechanical field operator in such a physical system is presented based on the Heisenberg equation, using which the quantum properties of traveling light suffering from medium absorption are quantitatively evaluated. Calculations using the obtained operator indicate that some degradation of noise performance is caused by the absorption. The influence of the absorption on the squeezing performance in phase-sensitive parametric amplification is also evaluated.
A New Interpretation to The Quantum Mechanics
Feng, Yulei
2012-01-01
In this paper, we try to give a new interpretation to the quantum mechanics from the point of view of (non-relativistic) quantum field theory. After field quantization, we obtain the Heisenberg equations for the momentum and coordinate operators of the particles excited from the (Schrodinger) field. We then give the probability concepts of quantum mechanics on the base of a statistical assemble realizing the assemble interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially the quantum measurement theory; in the end, we try to solve the EPR paradox with the use of our new ideas. In addition, we also give a field theoretical description to the double-slit interference experiment, obtaining the particle number distribution, in the appendix.
A new introductory quantum mechanics curriculum
Kohnle, Antje; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2013-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of interpretive aspects of quantum mechanics and quantum information theory. This article gives an overview of the resources available at the IOP website. The core text is presented as around 80 articles co-authored by leading experts that are arranged in themes and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is part of the resource. Solutions to activities are available ...
Realism and Objectivism in Quantum Mechanics
Karakostas, Vassilios
2012-01-01
The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning t...
Quantum ballistic evolution in quantum mechanics application to quantum computers
Benioff, P
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also pr...
Quantum Mechanics Fundamentals and Applications to Technology
Singh, Jasprit
1996-01-01
Explore the relationship between quantum mechanics and information-age applications. This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulati
A condensed course of quantum mechanics
Cejnar, Pavel
2013-01-01
This book represents a concise summary of non-relativistic quantum mechanics on the level suitable for university students of physics. It covers, perhaps even slightly exceeds, a one-year course of about 50 lectures, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure.The exposition is succinct, with minimal narration, but witha maximum of explicit and hierarchically structured mathematical derivations. The text covers all essential topics of university courses of quantum mechanics - from general mathematical formalism to specif
Optimization of a relativistic quantum mechanical engine
Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.
2016-08-01
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
Theoretical and quantum mechanics fundamentals for chemists
Ivanov, Stefan
2006-01-01
Provides the basics of theoretical and quantum mechanics in one place and emphasizes the continuity between themUniquely presented to be used for self-taught courses covering theoretical and quantum mechanicsEach chapter includes a detailed outline, a summary, self-assessment questions for which answers can be found in the textInvaluable for chemistry undergraduate and graduate students, chemists, other non-physical scientists, engineering students of modern techniques and technology, specialists who need a better understanding of quantum mechanics.
Philosophical foundations of interpretations of quantum mechanics
Bezlepkin, Evgeny
2016-01-01
It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the vector of state. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Playing Games with Quantum Mechanics
Phoenix, Simon J D
2012-01-01
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playab...
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
On the principles of quantum mechanics
Sakai, E
2004-01-01
We propose five principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, and probability principle. We deductively establish quantum mechanics on the basis of them. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant as a proportionality constant between energy and frequency due to one of Einstein-de Broglie formulas. Fourth, we define mass as a proportionality constant between momentum and velocity. We have succeeded to obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definiti...
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Quantum Mechanics as a Principle Theory
Bub, J
1999-01-01
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).
Quantum mechanics as electrodynamics of curvilinear waves
2002-01-01
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.
Quantum mechanics in simple matrix form
Jordan, Thomas F
1986-01-01
With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part of the quantum language and to employ this new skill in solving problems.
Quantum Mechanics at the Crossroads New Perspectives from History, Philosophy and Physics
Evans, James
2007-01-01
Quantum mechanics is a beautiful, strange and successful theory that originated in the 1920s. The theory, which Niels Bohr regarded as finished and complete, has in the last few decades rapidly developed in unexpected directions. An intense new focus on the stranger aspects of the theory, including entanglement and nonlocality, has resulted in new perceptions of the foundations of quantum mechanics, as well as surprising new exploitations of quantum phenomena. Historians and philosophers of science have also renewed their attention to quantum mechanics, opening up its human dimensions and asking searching questions about its meaning. This volume brings together new insights from different vantage points: Historians of physics, such as J. L. Heilbron; philosophers of science, such as Abner Shimony and Michel Bitbol; and quantum physicists, such as Wolfgang Ketterle and Roland Omnès, join forces to tackle essential questions in quantum mechanics and its interpretation. All the authors have written for a broad ...
Are All Probabilities Fundamentally Quantum Mechanical?
Pradhan, Rajat Kumar
2011-01-01
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum double slit interference experiments are discussed as illustrative prototype examples. Absence of multi-order quantum interference effects in multiple-slit experiments and the Experimental tests of complementarity in Wheeler's delayed-choice type experiments are explained using the involvement of the observer.
Babaei, Hassan; Mostafazadeh, Ali
2017-08-01
A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.
Avoiding Negative Probabilities in Quantum Mechanics
Nyambuya, Golden Gadzirayi
2013-01-01
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative probabilities are what led the great Paul Dirac in 1928 to the esoteric discovery of the Dirac Equation. The Dirac Equation led to one of the greatest advances in our understanding of the physical world. In this reading, we ask the seemingly senseless question, "Do negative probabilities exist in quantum mechanics?" In an effort to answer this question, we arrive at the conclusion that depending on the choice one makes of the quantum probability current, one will obtain negative probabilities. We thus propose a new quantum probability current of the Klein-Gordon theory. This quantum probability current leads directly to positive definite quantum probabilities. Because these negative probabilities are in the bare Klein-Gordon theory, intrinsically a result of negative energie...
Superconducting Qubits as Mechanical Quantum Engines
Sachtleben, Kewin; Mazon, Kahio T.; Rego, Luis G. C.
2017-09-01
We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.
Progress in post-quantum mechanics
Sarfatti, Jack
2017-05-01
Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantum mechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantum mechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantum mechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantum mechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.
Is the World Local or Nonlocal? Towards an Emergent Quantum Mechanics in the 21st Century
Walleczek, Jan
2016-01-01
What defines an emergent quantum mechanics (EmQM)? Can new insight be advanced into the nature of quantum nonlocality by seeking new links between quantum and emergent phenomena as described by self-organization, complexity, or emergence theory? Could the development of a future EmQM lead to a unified, relational image of the cosmos? One key motivation for adopting the concept of emergence in relation to quantum theory concerns the persistent failure in standard physics to unify the two pillars in the foundations of physics: quantum theory and general relativity theory (GRT). The total contradiction in the foundational, metaphysical assumptions that define orthodox quantum theory versus GRT might render inter-theoretic unification impossible. On the one hand, indeterminism and non-causality define orthodox quantum mechanics, and, on the other hand, GRT is governed by causality and determinism. How could these two metaphysically-contradictory theories ever be reconciled? The present work argues that metaphysic...
Quantum mechanics: Thought experiments made real
Martín, Fernando
2015-02-01
Elegant experiments performed with X-rays and a double slit formed from molecular oxygen have finally made it possible to realize and test a long-standing and famous gedanken experiment in quantum mechanics.
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Beyond Quantum Mechanics and General Relativity
Gregori, Andrea
2010-01-01
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Four formulations of noncommutative quantum mechanics
Gouba, Laure
2016-01-01
Four formulations of noncommutative quantum mechanics are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. The four formulations are charaterized by a deformed Heisenberg algebra but differ in mathematical and conceptual overview.
Advanced quantum mechanics materials and photons
Dick, Rainer
2016-01-01
In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of�...
Quantum mechanical streamlines. I - Square potential barrier
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
On the geometrization of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Tavernelli, Ivano, E-mail: ita@zurich.ibm.com
2016-08-15
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
2013-04-26
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
Experimental status of quaternionic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Brumby, S.P.; Joshi, G.C.
1995-10-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. The only direct search for quaternionic quantum mechanics yet carried out is reviewed and is proposed to look for quaternionic effects in correlated multi-particle systems. It is also discussed how such experiments might distinguish between the several quaternionic models proposed in the literature. 21 refs.
Implications of conformal symmetry in quantum mechanics
Okazaki, Tadashi
2017-09-01
In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates, which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics, there exist bounds on scaling dimensions of the physical states and the gauge operators.
Some Mutant Forms of Quantum Mechanics
Takeuchi, Tatsu; Lewis, Zachary; Minic, Djordje
2013-01-01
We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.
Antonio Gramsci's Reflection on Quantum Mechanics
Tassani, Isabella
2006-06-01
As the first step of a wider historical reconstruction of the reception of quantum mechanics in the nineteenth-century philosophy, we are going to consider Antonio Gramsci's philosophy. He asks himself about the nature of quantum objects, if their existence depends on the act of measuring by the experimenter and if this kind of relationship can be interpreted as an argument in favour of an immaterialistic philosophy. We will remark how an idealistic interpretation of quantum mechanics found a fertile field in the Italian culture, characterized by an antiscientific attitude and at the same time needing to find in science a term of comparison.
Horizon quantum mechanics of rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)
2017-05-15
The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)
Quantum mechanics of charged particle beam optics
Khan, Sameen Ahmed
2018-01-01
Theory of charged particle beam optics is basic to the design and working of charged particle beam devices from electron microscopes to accelerator machines. Traditionally, the optical elements of the devices are designed and operated based on classical mechanics and classical electromagnetism, and only certain specific quantum mechanical aspects are dealt with separately using quantum theory. This book provides a systematic approach to quantum theory of charged particle beam optics, particularly in the high energy cases such as accelerators or high energy electron microscopy.
THE ROLE OF QUANTUM MECHANICS IN NEUTRINO FACTORIES.
Energy Technology Data Exchange (ETDEWEB)
GALLARDO,J.C.; SESSLER,A.M.; WURTELE,J.
2000-12-06
A compilation is made of the various ways in which quantum phenomena enter into the design and operation of a neutrino factory. They include production of pions, decay of pions into muons, ionization energy loss of muons in material, scattering and energy straggling of muons in material, polarization of muons, and the decay of muons into neutrinos, and the radiation effect of neutrinos. For each process formulas are presented which cover the basic mechanism. A discussion is presented of the areas of uncertainty and of the experiments, underway and proposed, which will reduce the uncertainty to an acceptable level.
Book Review Bohmian Mechanics and Quantum Theory
Jäger, G
1999-01-01
A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed collection contains extensions and hybrid versions of the theory, as are several detailed applications to practical situtations.
Lecture Notes in Quantum Mechanics
Cohen, D
2006-01-01
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
Ultrashort Laser Pulse Phenomena
Diels, Jean-Claude
2006-01-01
Ultrashort Laser Pulse Phenomena, 2e serves as an introduction to the phenomena of ultra short laser pulses and describes how this technology can be used to examine problems in areas such as electromagnetism, optics, and quantum mechanics. Ultrashort Laser Pulse Phenomena combines theoretical backgrounds and experimental techniques and will serve as a manual on designing and constructing femtosecond (""faster than electronics"") systems or experiments from scratch. Beyond the simple optical system, the various sources of ultrashort pulses are presented, again with emphasis on the basic
Integration indicators in immigration phenomena. A statistical mechanics perspective
Barra, Adriano; Sandell, Rickard; Vernia, Cecilia
2013-01-01
Integration of immigrants is a complex socioeconomic phenomenon considered difficult to describe, understand, and predict. We address the problem of how integration changes with immigration density, and we propose a novel approach to its study guided by a statistical mechanics perspective. More precisely, we focus on studying the dependence of classical integration quantifiers such as the percentage of jobs, temporary and permanent, given to immigrants, mixed marriages, and newborns with parents of mixed origin on the density of immigrants in the population. Analysis of the average data behavior shows that while the McFadden discrete choice theory is in excellent agreement with the job market quantifiers, the mixed marriages and newborns quantifiers behave in accordance with an imitative theory similar to the one introduced by Brock and Durlauf and suitably extended to a monomer-dimer model with interacting social network. Our findings show that a model that allows for imitation explains the anomalous high gr...
A new interpretation of quantum mechanics
Golovko, V A
2016-01-01
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields, interaction with a measuring apparatus inclusive, in a deterministic manner without any jumps. Quantum mechanics is an approximate theory because its equations follow from the above equations upon neglecting the self-field of the electron itself. Just this leads to paradoxes, seeming contradictions and jumps in quantum mechanics. The quantum mechanical wavefunction has a dual interpretation. In some problems the square of its modulus represents a real distribution of the electronic density while in others the same square determines the probability distribution of coordinates. It is shown why, given the different interpretations of the wavefunction, it satisfies one and the same Dirac or Schr\\"odinger equation. Description of many-electron systems is also considered in the star...
Energy Technology Data Exchange (ETDEWEB)
Mishchenko, Yuriy [North Carolina State Univ., Raleigh, NC (United States)
2004-12-01
MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Energy Technology Data Exchange (ETDEWEB)
Gevorkyan, A. S., E-mail: g_ashot@sci.am [NAS of Armenia, Institute for Informatics and Automation Problems (Armenia)
2013-08-15
Spontaneous transitions between bound states of an atomic system, the 'Lamb Shift' of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations (fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schroedinger type and is defined on the extended space Double-Struck-Capital-R {sup 3} Circled-Times {Xi}{sup n}, where Double-Struck-Capital-R {sup 3} and {Xi}{sup n} are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Gevorkyan, A. S.
2013-08-01
Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger type and is defined on the extended space ℝ3⊗Ξ n , where ℝ3 and Ξ n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
How to teach quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Passon, Oliver [Fachbereich Physik, University of Wuppertal, Postfach 100127, 42097 Wuppertal (Germany)
2004-11-01
In the spirit and style of John S Bell's well-known paper on How to teach special relativity it is argued that a 'Bohmian pedagogy' provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONGGui－Lu; YANHai－Yang; 等
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the "state" of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.
Mindful universe. Quantum mechanics and the participating observer. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Stapp, Henry P. [California Univ., Berkeley, CA (United States). Lawrence Berkeley National Lab.
2011-07-01
The classical mechanistic idea of nature that prevailed in science during the eighteenth and nineteenth centuries was an essentially mindless conception: the physically described aspects of nature were asserted to be completely determined by prior physically described aspects alone, with our conscious experiences entering only passively. During the twentieth century the classical concepts were found to be inadequate. In the new theory, quantum mechanics, our conscious experiences enter into the dynamics in specified ways not fixed by the physically described aspects alone. Consequences of this radical change in our understanding of the connection between mind and brain are described. This second edition contains two new chapters investigating the role of quantum phenomena in the problem of free will and in the placebo effect. (orig.)
Mindful Universe Quantum Mechanics and the Participating Observer
Stapp, Henry P
2011-01-01
The classical mechanistic idea of nature that prevailed in science during the eighteenth and nineteenth centuries was an essentially mindless conception: the physically described aspects of nature were asserted to be completely determined by prior physically described aspects alone, with our conscious experiences entering only passively. During the twentieth century the classical concepts were found to be inadequate. In the new theory, quantum mechanics, our conscious experiences enter into the dynamics in specified ways not fixed by the physically described aspects alone. Consequences of this radical change in our understanding of the connection between mind and brain are described. This second edition contains two new chapters investigating the role of quantum phenomena in the problem of free will and in the placebo effect.
Excitation transfer through open quantum networks: a few basic mechanisms
Venuti, Lorenzo Campos
2011-01-01
A variety of open quantum networks are currently under intense examination to model energy transport in photosynthetic systems. Here we study the coherent transfer of a quantum excitation over a network incoherently coupled with a structured and small environment that effectively models the photosynthetic reaction center. Our goal is to distill a few basic, possibly universal, mechanisms or "effects" that are featured in simple energy-transfer models. In particular, we identify three different phenomena: the congestion effect, the asymptotic unitarity and the staircase effects. We begin with few-site models, in which these effects can be fully understood, and then proceed to study more complex networks similar to those employed to model energy transfer in light-harvesting complexes. Our numerical studies on such networks seem to suggest that some of the effects observed in simple networks may be of relevance for biological systems, or artificial analogues of them as well.
Measurements and mathematical formalism of quantum mechanics
Slavnov, D. A.
2007-03-01
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
Nilpotent Quantum Mechanics: Analogs and Applications
Directory of Open Access Journals (Sweden)
Peter Marcer
2017-07-01
Full Text Available The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state and its environment (vacuum are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on “The ‘Logic’ of Self-Organizing Systems” [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.
On Time. 6b: Quantum Mechanical Time
Raju, C K
2008-01-01
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.
Computations in quantum mechanics made easy
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
The canonical connection in quantum mechanics
Lévai, Peter; Tsutsui, I; Levay, Peter; McMullan, David; Tsutsui, Izumi
1995-01-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.
The canonical connection in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Levay, P. [Budapesti Mueszaki Egyetem, Budapest (Hungary); Mcmullan, D.; Tsutsui, Izumi
1995-04-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry`s phase, can also be found in systems which have slow variables taking values in such a coset space. (author).
Emergent quantum mechanics of finances
Nastasiuk, Vadim A.
2014-06-01
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
Advanced quantum mechanics materials and photons
Dick, Rainer
2012-01-01
Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquir...
On quantum statistical mechanics; A study guide
Majewski, W. A.
2016-01-01
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical mechanics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems, and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite dimensional structures. As an illustration, a quantization of stochastic processes, new formalism...
Quantum mechanics: why complex Hilbert space?
Cassinelli, G; Lahti, P
2017-11-13
We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
The conceptual foundations of quantum mechanics
Eisenbud, Leonard
2007-01-01
This book provides a clear and logical path to understanding what quantum mechanics is about. It will be accessible to undergraduates with minimal mathematical preparation: all that is required is an open mind, a little algebra, and a first course in undergraduate physics. Quantum mechanics is arguably the most successful physical theory. It makes predictions of incredible accuracy. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. But compared with Newtonian mechanics, or even relativity, its teachings seem obscure-they have no coun
Relationship of quantum mechanics to classical electromagnetism and classical relativistic mechanics
Energy Technology Data Exchange (ETDEWEB)
Field, J H [Departement de Physique Nucleaire et Corpusculaire, Universite de Geneve, 24, quai Ernest-Ansermet CH-1211 Geneva 4 (Switzerland)
2004-05-14
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the canonical commutation relations and the Maxwell-Lorentz equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as 'inverse correspondence' since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalization to massive particles leads to the Klein-Gordon and Schroedinger equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.
The mathematical basis for deterministic quantum mechanics
Hooft, G. 't
2006-01-01
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint
The mathematical basis for deterministic quantum mechanics
Hooft, G. 't
2007-01-01
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is
Intrinsic resonance representation of quantum mechanics
DEFF Research Database (Denmark)
Carioli, M.; Heller, E.J.; Møller, Klaus Braagaard
1997-01-01
an optimal representation, based purely on classical mechanics. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies...
Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics
Krause, Decio
2015-01-01
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \\ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are \\ita{non-individuals} in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are \\ita{individuals} in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics an...
Logic and probability in quantum mechanics
1976-01-01
During the academic years 1972-1973 and 1973-1974, an intensive sem inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining articles have been so licited explicitly from individuals who are actively working in the foun dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to ...
Quantum mechanics and quantum information a guide through the quantum world
Fayngold, Moses
2013-01-01
Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
Quantum Mechanics as Quantum Information (and only a little more)
Fuchs, C
2002-01-01
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the in...
Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics
Hooft, Gerard t
2012-01-01
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these t...
The cellular automaton interpretation of quantum mechanics
't Hooft, Gerard
2016-01-01
This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of...
Multichannel framework for singular quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
Holism, Physical Theories and Quantum Mechanics
Seevinck, M P
2004-01-01
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. I propose an operational criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if some determination (measurement) of the global properties in the theory which can be determined by global measurements, can not be implemented by local operations and classical communication. This approach is contrasted with the well known approaches to holism in terms of supervenience. I will argue that the latter have a limited scope and need to be extended using the criterion for holism proposed here in order to satisfactory address the issue for physical theories. I formalize this criterion for classical particle physics and Bohmian mechanics as represented on a Cartesian phase and configuration space, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum ope...
Introductory quantum mechanics for applied nanotechnology
Kim, Dae Mann
2015-01-01
This introductory textbook covers fundamental quantum mechanics from an application perspective, considering optoelectronic devices, biological sensors and molecular imagers as well as solar cells and field effect transistors. The book provides a brief review of classical and statistical mechanics and electromagnetism, and then turns to the quantum treatment of atoms, molecules, and chemical bonds. Aiming at senior undergraduate and graduate students in nanotechnology related areas like physics, materials science, and engineering, the book could be used at schools that offer interdisciplinary but focused training for future workers in the semiconductor industry and for the increasing number of related nanotechnology firms, and even practicing people could use it when they need to learn related concepts. The author is Professor Dae Mann Kim from the Korea Institute for Advanced Study who has been teaching Quantum Mechanics to engineering, material science and physics students for over 25 years in USA and Asia.
Intrinsic periodicity: the forgotten lesson of quantum mechanics
Dolce, Donatello
2013-01-01
Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically "periodic phenomena". However, after nearly 90 years, the physical origin of such undulatory mechanics remains unrevealed. We propose a natural realization of the de Broglie "periodic phenomenon" in terms of harmonic vibrational modes associated to space-time periodicities. In this way we find that, similarly to a vibrating string or a particle in a box, the intrinsic recurrence imposed as a constraint to elementary particles represents a fully consistent quantization condition. The resulting classical cyclic dynamics formally match ordinary relativistic Quantum Mechanics in both the canonical and Feynman formulations. Interactions are introduced in a geometrodynamical way, similarly to general relativity, by simply considering that variations of kinematical state can be equivalently described in terms of modulations of space-time recurrences, as known from undulatory mechanics. We ...
Quantum Mechanics of Palladium Nanostructures
Hira, Ajit; McKeough, James; Ortiz, Bridget; Diaz, Juan
We continue our interest in the chemisorption of different atomic and molecular species on small clusters of metallic elements, by examining the interactions of H, H2, Li and O adsorbates with Pdn clusters (n = 2 thru 20). The study of clusters can reveal the effects of substrate geometry on the behavior of adsorbates. Transition-metal clusters are especially suited for the study of quantum size effects and for formation of metallic states, and are ideal candidates for catalytic processes. Hybrid ab initio methods of quantum chemistry (particularly the DFT-B3LYP model) are used to derive optimal geometries for the clusters of interest. We compare calculated binding energies, bond-lengths, ionization potentials, electron affinities and HOMO-LUMO gaps for the clusters. Of particular interest are the comparisons of binding strengths at the three important types of sites: edge (E), hollow (H), on-top (T), threefold sites and fourfold sites. Effects of crystal symmetries corresponding to the bulk structures are investigated. The capacity of Pd clusters to adsorb H atoms will be compared to Ni clusters. Admixture with Pt atoms will also be considered.
Rauch, Helmut
2015-01-01
The quantum interference of de Broglie matter waves is probably one of the most startling and fundamental aspects of quantum mechanics. It continues to tax our imaginations and leads us to new experimental windows on nature. Quantum interference phenomena are vividly displayed in the wide assembly of neutron interferometry experiments, which have been carried out since the first demonstration of a perfect silicon crystal interferometer in 1974. Since the neutron experiences all four fundamental forces of nature (strong, weak, electromagnetic, and gravitational), interferometry with neutrons provides a fertile testing ground for theory and precision measurements. Many Gedanken experiments of quantum mechanics have become real due to neutron interferometry. Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the second edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivation...
Concept of consciousness in the context of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Menskii, Mikhail B [P.N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2005-04-30
Conceptual problems of the quantum theory of measurement are considered, which are embodied in well-known paradoxes and in Bell's inequalities. Arguments are advanced in favor of the viewpoint that these problems may hardly be solved without direct inclusion of the observer's consciousness in the theoretical description of a quantum measurement. Discussed in this connection is the so-called many-worlds interpretation of quantum mechanics proposed by Everett, as is the extension of Everett's concept, which consists in the assumption that separating the quantum state components corresponding to alternative measurements is not only associated with the observer's consciousness but is completely identified with it. This approach is shown to open up qualitatively new avenues for the unification of physics and psychology and, more broadly, of the sciences and the humanities. This may lead to an extension of the theory of consciousness and shed light on significant and previously misunderstood phenomena in the sphere of consciousness. (reviews of topical problems)
Emergence and mechanism in the fractional quantum Hall effect
Bain, Jonathan
2016-11-01
For some authors, an adequate notion of emergence must include an account of a mechanism by means of which emergent behavior is realized. This appeal to mechanism is problematic in the case of the fractional quantum Hall effect (FQHE). There is a consensus among physicists that the FQHE exhibits emergent phenomena, but there are at least four alternative explanations of the latter that, arguably, appeal to ontologically distinct mechanisms, both at the microphysics level and at the level of general organizing principles. In light of this underdetermination of mechanism, one is faced with the following options: (I) deny that emergence is present in the FQHE; (II) argue for the priority of one mechanistic explanation over the others; or (III) temper the desire for a mechanism-centric account of emergence. I will argue that there are good reasons to reject (I) and (II) and accept (III). In particular, I will suggest that a law-centric account of emergence does just fine in explaining the emergent phenomena associated with the FQHE.
Gallilei covariant quantum mechanics in electromagnetic fields
Directory of Open Access Journals (Sweden)
H. E. Wilhelm
1985-01-01
Full Text Available A formulation of the quantum mechanics of charged particles in time-dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.
Quantum Mechanical Studies of DNA and LNA
DEFF Research Database (Denmark)
Koch, Troels; Shim, Irene; Lindow, Morten;
2014-01-01
Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the e......Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies...
An Axiomatic Basis for Quantum Mechanics
Cassinelli, Gianni; Lahti, Pekka
2016-10-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
Quantum mechanics new approaches to selected topics
Lipkin, Harry J
2007-01-01
Acclaimed as ""excellent"" (Nature) and ""very original and refreshing"" (Physics Today), this collection of self-contained studies is geared toward advanced undergraduates and graduate students. Its broad selection of topics includes the Mössbauer effect, many-body quantum mechanics, scattering theory, Feynman diagrams, and relativistic quantum mechanics.Author Harry J. Lipkin, a well-known teacher at Israel's Weizmann Institute, takes an unusual approach by introducing many interesting physical problems and mathematical techniques at a much earlier point than in conventional texts. This meth
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
A new introductory quantum mechanics curriculum
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
Bauer, M
2016-01-01
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
Quantum Mechanics in the Light of Quantum Cosmology
Gell-Mann, Murray; Hartle, James B.
We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its
The Emergent Copenhagen Interpretation of Quantum Mechanics
Hollowood, Timothy J
2013-01-01
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint p...
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
Practical quantum mechanics modern tools and applications
Manousakis, Efstratios
2016-01-01
Quantum mechanics forms the foundation of all modern physics, including atomic, nuclear, and molecular physics, the physics of the elementary particles, condensed matter physics. Modern astrophysics also relies heavily on quantum mechanics. Quantum theory is needed to understand the basis for new materials, new devices, the nature of light coming from stars, the laws which govern the atomic nucleus, and the physics of biological systems. As a result the subject of this book is a required course for most physics graduate students. While there are many books on the subject, this book targets specifically graduate students and it is written with modern advances in various fields in mind. Many examples treated in the various chapters as well as the emphasis of the presentation in the book are designed from the perspective of such problems. For example, the book begins by putting the Schrodinger equation on a spatial discrete lattice and the continuum limit is also discussed, inspired by Hamiltonian lattice gauge ...
Using quantum mechanics to synthesize electronic devices
Schmidt, Petra; Levi, Anthony
2005-03-01
Adaptive quantum design [1] has been used to explore the possibility of creating new classes of electronic semiconductor devices. We show how non-equilibrium electron transmission through a synthesized conduction band potential profile can be used to obtain a desired current - voltage characteristic. We illustrate our methodology by designing a two-terminal linear resistive element in which current is limited by quantum mechanical transmission through a potential profile and power is dissipated non-locally in the electrodes. As electronic devices scale to dimensions in which the physics of operation is dominated by quantum mechanical effects, classical designs fail to deliver the desired functionality. Our device synthesis approach is a way to realize device functionality that may not otherwise be achieved. [1] Y.Chen, R.Yu, W.Li, O.Nohadani, S.Haas, A.F.J. Levi, Journal of Applied Physics, Vol.94, No.9, p6065, 2003
Fluid mechanics phenomena in microgravity; ASME Winter Annual Meeting, Anaheim, CA, Nov. 8-13, 1992
Siginer, Dennis A. (Editor); Weislogel, Mark M. (Editor)
1992-01-01
This paper is the first in a series of symposia presenting research activity in microgravity fluid mechanics. General topics addressed include two-phase flow and transport phenomena, thermo-capillary flow, and interfacial stability. Papers present mathmatical models of fluid dynamics in the microgravity environment. Applications suggested include space manufacturing and storage of liquids in low gravity.
Fluid mechanics phenomena in microgravity; ASME Winter Annual Meeting, Anaheim, CA, Nov. 8-13, 1992
Siginer, Dennis A. (Editor); Weislogel, Mark M. (Editor)
1992-01-01
This paper is the first in a series of symposia presenting research activity in microgravity fluid mechanics. General topics addressed include two-phase flow and transport phenomena, thermo-capillary flow, and interfacial stability. Papers present mathmatical models of fluid dynamics in the microgravity environment. Applications suggested include space manufacturing and storage of liquids in low gravity.
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; YAN Hai-Yang; LI Yan-Song; TU Chang-Cun; ZHU Sheng-Jiang; RUAN Dong; SUN Yang; TAO Jia-Xun; CHEN Hao-Ming
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the "state" of anaverage particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure state densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
Clarke, M. L.
2014-01-01
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
Riemann hypothesis and quantum mechanics
Planat, Michel; Solé, Patrick; Omar, Sami
2011-04-01
In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β), where β is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ∏qk = 1pk is the primorial number of order q and ψb is a generalized Dedekind ψ function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature β > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < β < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten
A new exact quantum mechanical propagator
Wiegel, F.W.; Andel, van P.W.
1987-01-01
The authors derive a closed-form expression for the time-dependent propagator for a quantum mechanical particle which is subject to an external force which is the sum of (i) a reflecting half-plane barrier with a straight edge, and (ii) a harmonic force pointing towards a point of the edge. This new
Quantum mechanics for two-timers
Indian Academy of Sciences (India)
P Mitra
2001-02-01
Extensions of standard quantum mechanics with joint probability distributions for position coordinates and momenta have been proposed in the literature. Time is assumed to be onedimensional in these studies. In view of recent interest in two-dimensional time, the construction is extended to this situation and found to satisfy the necessary consistency conditions.
Quantum Mechanical Effects in Gravitational Collapse
Greenwood, Eric
2010-01-01
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the pos...
Student Difficulties with Quantum Mechanics Formalism
Singh, Chandralekha
2016-01-01
We discuss student difficulties in distinguishing between the physical space and Hilbert space and difficulties related to the Time-independent Schroedinger equation and measurements in quantum mechanics. These difficulties were identified by administering written surveys and by conducting individual interviews with students.
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Kuckert, B; Kuckert, Bernd; Mund, Jens
2004-01-01
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.
Holism, physical theories and quantum mechanics
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Approaching the Standard Quantum Limit of Mechanical Torque Sensing
Kim, P H; Doolin, C; Souris, F; Davis, J P
2016-01-01
Mechanical transduction of torque has been key to probing a number of physical phenomena, such as gravity, the angular momentum of light, the Casimir effect, magnetism, and quantum oscillations. Following similar trends as mass and force sensing, mechanical torque sensitivity can be dramatically improved by scaling down the physical dimensions, and therefore moment of inertia, of a torsional spring. Yet now, through precision nanofabrication and sub-wavelength cavity optomechanics, we have reached a point where geometric optimization can only provide marginal improvements to torque sensitivity. Instead, nanoscale optomechanical measurements of torque are overwhelmingly hindered by thermal noise. Here we present cryogenic measurements of a cavity-optomechanical torsional resonator cooled in a dilution refrigerator to a temperature of 25 mK, corresponding to an average phonon occupation of = 35, that demonstrate a record-breaking torque sensitivity of 2.9 yNm/Hz^{1/2}. This a 270-fold improvement over previous...
Directory of Open Access Journals (Sweden)
Ivan Kanev
2013-03-01
Full Text Available Our studies reveal previously unidentified electrical properties of chromosomes: (1 chromosomes are amazingly similar in construction and function to electrical transformers; (2 chromosomes possess in their construction and function, components similar to those of electric generators, conductors, condensers, switches, and other components of electrical circuits; (3 chromosomes demonstrate in nano-scale level electromagnetic interactions, resonance, fusion and other phenomena similar to those described by equations in classical physics. These electrical properties and phenomena provide a possible explanation for unclear and poorly understood mechanisms in clinical genetics including: (a electrically based mechanisms responsible for breaks, translocations, fusions, and other chromosomal abnormalities associated with cancer, intellectual disability, infertility, pregnancy loss, Down syndrome, and other genetic disorders; (b electrically based mechanisms involved in crossing over, non-disjunction and other events during meiosis and mitosis; (c mechanisms demonstrating heterochromatin to be electrically active and genetically important.
Directory of Open Access Journals (Sweden)
Ivan Kanev
2013-03-01
Full Text Available Our studies reveal previously unidentified electrical properties of chromosomes: (1 chromosomes are amazingly similar in construction and function to electrical transformers; (2 chromosomes possess in their construction and function, components similar to those of electric generators, conductors, condensers, switches, and other components of electrical circuits; (3 chromosomes demonstrate in nano-scale level electromagnetic interactions, resonance, fusion and other phenomena similar to those described by equations in classical physics. These electrical properties and phenomena provide a possible explanation for unclear and poorly understood mechanisms in clinical genetics including: (a electrically based mechanisms responsible for breaks, translocations, fusions, and other chromosomal abnormalities associated with cancer, intellectual disability, infertility, pregnancy loss, Down syndrome, and other genetic disorders; (b electrically based mechanisms involved in crossing over, non-disjunction and other events during meiosis and mitosis; (c mechanisms demonstrating heterochromatin to be electrically active and genetically important.
A New Approach of Quantum Mechanics for Neutron Single-Slit Diffraction
Institute of Scientific and Technical Information of China (English)
WU Xiang-Yao; YANG Jing-Hai; LIU Xiao-Jing; WANG Li; LIU Bing; FAN Xi-Hui; GUO Yi-Qing
2007-01-01
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments are explained by many theoretical works. We study neutron single-slit diffraction with a quantum mechanical approach. It is found that the obvious diffraction patterns can be obtained when the singleslit width a is in the range of 3λ～ 60λ. We also find a new quantum effect of the thickness of single-slit which can make a large impact on the diffraction pattern. The new quantum effect predicted in our work can be tested by the neutron single-slit diffraction experiment.
Interactive Quantum Mechanics Quantum Experiments on the Computer
Brandt, S; Dahmen, H.D
2011-01-01
Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: • harmonic waves and wave packets, • free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), • two-particle systems, coupled harmonic oscillators, • distinguishable and indistinguishable particles, • coherent and squeezed states in time-dependent motion, • quantized angular momentum, • spin and magnetic resonance, • hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...
On Quantum Mechanics on Noncommutative Quantum Phase Space
Institute of Scientific and Technical Information of China (English)
A.E.F. DjemaI; H. Smail
2004-01-01
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.
Quantum mechanical studies of carbon structures
Energy Technology Data Exchange (ETDEWEB)
Bartelt, Norman Charles [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Ward, Donald [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Zhou, Xiaowang [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Foster, Michael E. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Schultz, Peter A. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Wang, Bryan M. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Univ. of California, Riverside, CA (United States); McCarty, Kevin F. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2015-10-01
Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high-fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.
Quantum mechanical coherence, resonance, and mind
Energy Technology Data Exchange (ETDEWEB)
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Global and Local Horizon Quantum Mechanics
Casadio, R; Giusti, A
2016-01-01
Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determine by spatially localised modes.
Quantum mechanics of 4-derivative theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [Universidad Autonoma de Madrid and Instituto de Fisica Teorica IFT-UAM/CSIC, Departamento de Fisica Teorica, Madrid (Spain); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); CERN, Theory Division, Geneva (Switzerland); INFN, Pisa (Italy)
2016-04-15
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm. (orig.)
Quantum mechanical coherence, resonance, and mind
Stapp, Henry P
1995-01-01
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Global and local horizon quantum mechanics
Casadio, Roberto; Giugno, Andrea; Giusti, Andrea
2017-02-01
Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.
Quantum mechanics of 4-derivative theories.
Salvio, Alberto; Strumia, Alessandro
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
Spinning Particles in Quantum Mechanics and Quantum Field Theory
Corradini, Olindo
2015-01-01
The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
A mathematical theory for deterministic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)
2007-05-15
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
On the missing axiom of Quantum Mechanics
D'Ariano, G M
2005-01-01
Quantum Non Locality, ruling out an epistemic interpretation of quantum probabilities for an ontic one, elevates Quantum Mechanics to the level of a Theory of Knowledge. In such context the superposition principle becomes an unacceptable extrinsic axiom of non "gnoseological" nature. We are thus lead to seek a purely operational axiomatization that supersedes the current mathematical one based on Hilbert spaces, with the purpose of deriving the latter from the former. In the present work I present a set of axioms for a general operational approach, based on a general definition of "experiment". As we will see, this starting point logically entails a sequel of notions [state, conditional state, local state, pure state, faithful state, instrument, propensity (i.e. "effect"), dynamical and informational equivalence, dynamical and informational compatibility, predictability, discriminability, programmability, locality, a-causality, rank of the state, maximally chaotic state, maximally entangled state, information...
Transport phenomena in correlated quantum liquids: Ultracold Fermi gases and F/N junctions
Li, Hua
Landau Fermi-liquid theory was first introduced by L. D. Landau in the effort of understanding the normal state of Fermi systems, where the application of the concept of elementary excitations to the Fermi systems has proved very fruitful in clarifying the physics of strongly correlated quantum systems at low temperatures. In this thesis, I use Landau Fermi-liquid theory to study the transport phenomena of two different correlated quantum liquids: the strongly interacting ultracold Fermi gases and the ferromagnet/normal-metal (F/N) junctions. The detailed work is presented in chapter II and chapter III of this thesis, respectively. Chapter I holds the introductory part and the background knowledge of this thesis. In chapter II, I study the transport properties of a Fermi gas with strong attractive interactions close to the unitary limit. In particular, I compute the transport lifetimes of the Fermi gas due to superfluid fluctuations above the BCS transition temperature Tc. To calculate the transport lifetimes I need the scattering amplitudes. The scattering amplitudes are dominated by the superfluid fluctuations at temperatures just above Tc. The normal scattering amplitudes are calculated from the Landau parameters. These Landau parameters are obtained from the local version of the induced interaction model for computing Landau parameters. I also calculate the leading order finite temperature corrections to the various transport lifetimes. A calculation of the spin diffusion coefficient is presented in comparison to the experimental findings. Upon choosing a proper value of F0a, I am able to present a good match between the theoretical result and the experimental measurement, which indicates the presence of the superfluid fluctuations near Tc. Calculations of the viscosity, the viscosity/entropy ratio and the thermal conductivity are also shown in support of the appearance of the superfluid fluctuations. In chapter III, I study the spin transport in the low
Theoretical physics 6 quantum mechanics : basics
Nolting, Wolfgang
2017-01-01
This textbook offers a clear and comprehensive introduction to the basics of quantum mechanics, one of the core components of undergraduate physics courses. It follows on naturally from the previous volumes in this series, thus developing the physical understanding further on to quantized states. The first part of the book introduces wave equations while exploring the Schrödinger equation and the hydrogen atom. More complex themes are covered in the second part of the book, which describes the Dirac formulism of quantum mechanics. Ideally suited to undergraduate students with some grounding in classical mechanics and electrodynamics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this...
Symmetry and Covariance of Non-relativistic Quantum Mechanics
Omote, Minoru; kamefuchi, Susumu
2000-01-01
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.
Absorbers in the Transactional Interpretation of Quantum Mechanics
Boisvert, Jean-Sébastien; Marchildon, Louis
2013-03-01
The transactional interpretation of quantum mechanics, following the time-symmetric formulation of electrodynamics, uses retarded and advanced solutions of the Schrödinger equation and its complex conjugate to understand quantum phenomena by means of transactions. A transaction occurs between an emitter and a specific absorber when the emitter has received advanced waves from all possible absorbers. Advanced causation always raises the specter of paradoxes, and it must be addressed carefully. In particular, different devices involving contingent absorbers or various types of interaction-free measurements have been proposed as threatening the original version of the transactional interpretation. These proposals will be analyzed by examining in each case the configuration of absorbers and, in the special case of the so-called quantum liar experiment, by carefully following the development of retarded and advanced waves through the Mach-Zehnder interferometer. We will show that there is no need to resort to the hierarchy of transactions that some have proposed, and will argue that the transactional interpretation is consistent with the block-universe picture of time.
Origin of quantum randomness in the pilot wave quantum mechanics
Shtanov, Yuri
1997-01-01
We account for the origin of the laws of quantum probabilities in the de Broglie-Bohm (pilot wave) formulation of quantum theory by considering the property of ergodicity likely to characterise the dynamics of microscopic quantum systems.
A Quantum Mechanical Approach to Nuclear Rotations
Zettili, Nouredine
2014-09-01
We deal with the study of collective motion within the context of a quantum mechanical method - the nuclear Born-Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states. Additionally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model. We deal with the study of collective motion within the context of a quantum mechanical method - the nuclear Born-Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states
Dummett vs Bell on quantum mechanics
Ben-Menahem, Yemima
The purpose of this paper is to cast doubt on the common allegation that quantum mechanics (QM) is incompatible with realism. I argue that the results usually considered inimical to realism, notably the violation of Bells inequality, in fact play the opposite role-they support realism. The argument is not intended, however, to demonstrate realism or refute its alternatives as general metaphysical positions. It is directed specifically at the view that QM differs from classical mechanics in that, unlike classical mechanics, it is not amenable to a realist interpretation.
Introduction to quantum mechanics a time-dependent perspective
Tannor, David J
2007-01-01
"Introduction to Quantum Mechanics" covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.
Challenges in Large Scale Quantum Mechanical Calculations
Ratcliff, Laura E; Huhs, Georg; Deutsch, Thierry; Masella, Michel; Genovese, Luigi
2016-01-01
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.
Events and the Ontology of Quantum Mechanics
Dorato, Mauro
2015-01-01
In the first part of the paper I argue that an ontology of events is precise, flexible and general enough so as to cover the three main alternative formulations of quantum mechanics as well as theories advocating an antirealistic view of the wave function. Since these formulations advocate a primitive ontology of entities living in four-dimensional spacetime, they are good candidates to connect that quantum image with the manifest image of the world. However, to the extent that some form of realism about the wave function is also necessary, one needs to endorse also the idea that the wave function refers to some kind of power. In the second part, I discuss some difficulties raised by the recent proposal that in Bohmian mechanics this power is holistically possessed by all the particles in the universe.
Galoisian Approach to Supersymmetric Quantum Mechanics
Acosta-Humanez, Primitivo B
2009-01-01
This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\\"odinger equation, specially the integrable cases in the sense of the Picard-Vessiot theory and the main algorithmic tools used here are the Kovacic algorithm and the \\emph{algebrization method} to obtain linear differential equations with rational coefficients. We analyze the Darboux transformations, Crum iterations and supersymmetric quantum mechanics with their \\emph{algebrized} versions from a Galoisian approach. Applying the algebrization method and the Kovacic's algorithm we obtain the ground state, the set of eigenvalues, eigenfunctions, the differential Galois groups and eigenrings of some Schr\\"odinger equation with potentials such as exactly solvable and shape invariant potentials. Finally, we introduce one methodology to find exactly solvable potentials: to construct other potentials, we apply the algebrization alg...
Conserved symmetries in noncommutative quantum mechanics
Kupriyanov, V G
2014-01-01
We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of the rotational symmetry in quantum mechanics or the Lorentz symmetry in f{i}eld theory. Since the canonical (Moyal) noncommutativity breaks the above symmetries one should work with more general case of coordinate-dependent noncommutative spaces, when the commutator between coordinates is a function of these coordinates. F{i}rst we describe in general lines how to construct the quantum mechanics on coordinate-dependent noncommutative spaces. Then we consider the particular examples: the Hydrogen atom on rotationally invariant noncommutative space and the Dirac equation on covariant noncommutative space-time.
Conserved symmetries in noncommutative quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Kupriyanov, V.G. [CMCC, Universidade Federal do ABC, Santo Andre, SP (Brazil)
2014-09-11
We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of the rotational symmetry in quantum mechanics or the Lorentz symmetry in field theory. Since the canonical (Moyal) noncommutativity breaks the above symmetries one should work with more general case of coordinate-dependent noncommutative spaces, when the commutator between coordinates is a function of these coordinates. First we describe in general lines how to construct the quantum mechanics on coordinate-dependent noncommutative spaces. Then we consider the particular examples: the Hydrogen atom on rotationally invariant noncommutative space and the Dirac equation on covariant noncommutative space-time. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Applications of computational quantum mechanics
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts
Quantum mechanics and elements of reality
Mohrhoff, Ulrich
1999-01-01
It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized elements of reality without casting doubt on the widely accepted sufficiency condition for `ordinary' elements of reality. In this paper I show that ...
Landau problem in noncommutative quantum mechanics
Institute of Scientific and Technical Information of China (English)
Sayipjamal Dulat; LI Kang
2008-01-01
The Landau problem in non-commutative quantum mechanics (NCQM) is studied.First by solving the Schr(o)dinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity.Then we discuss the noncommutative phase space case,namely,space-space and momentum-momentum non-commutative case,and we get the explicit expression of the Hamfltonian as well as the corresponding eigenfunctions and eigenvalues.
Exceptional polynomials and SUSY quantum mechanics
Indian Academy of Sciences (India)
K V S Shiv Chaitanya; S Sree Ranjani; Prasanta K Panigrahi; R Radhakrishnan; V Srinivasan
2015-07-01
We show that for the quantum mechanical problem which admit classical Laguerre/Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the potential. Then, we claim that the existence of these exceptional polynomials leads to the presence of non-trivial supersymmetry.
Quantum Mechanics and the Cookie Cutter Paradigm
Mohrhoff, U
2000-01-01
What has so far prevented us from decrypting quantum mechanics is the Cookie Cutter Paradigm, according to which the world's synchronic multiplicity derives from surfaces that carve up space in the manner of three-dimensional cookie cutters. This insidious notion is shown to be rooted in our neurophysiological make-up. An effort is made to liberate the physical world from this innate fallacy.
Quantum mechanical theory behind "dark energy"?
Colin Johnson, R
2007-01-01
"The mysterious increase in the acceleration of the universe, when intuition says it should be slowing down, is postulated to be caused by dark energy - "dark" because it is undetected. Now a group of scientists in the international collaboration Essence has suggested that a quantum mechanical interpretation of Einstein's proposed "cosmological constant" is the simplest explanation for dark energy. The group measured dark energy to within 10 percent." (1,5 page)
A Global Optimization Approach to Quantum Mechanics
Huang, Xiaofei
2006-01-01
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of a global optimization method deployed by nature so that (sub)atomic systems can find their ground states corresponding to the global minimum of some energy function associated with the system. The classic time-independent Schrodinger equation is shown to b...
The Central Mystery of Quantum Mechanics
Ghose, Partha
2009-01-01
A critical re-examination of the double-slit experiment and its variants is presented to clarify the nature of what Feynmann called the ``central mystery'' and the ``only mystery'' of quantum mechanics, leading to an interpretation of complementarity in which a `wave {\\em and} particle' description rather than a `wave {\\em or} particle' description is valid for the {\\em same} experimental set up, with the wave culminating in the particle sequentially in time. This interpretation is different ...
Generalized Borel transform technique in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Epele, L.N.; Fanchiotti, H.; Garcia Canal, C.A.; Marucho, M
2003-03-13
We present the Generalized Borel Transform (GBT). This new approach allows one to obtain approximate solutions of Laplace/Mellin transform valid in both, perturbative and non-perturbative regimes. We compare the results provided by the GBT for a solvable model of quantum mechanics with those provided by standard techniques, as the conventional Borel sum, or its modified versions. We found that our approach is very efficient for obtaining both the low and the high energy behavior of the model.
Mechanics of transport phenomena in multi-component sessile drops with solidification
Su, Yeong-Jen; Yang, Wen-Jei; Liu, Jiaching
1990-01-01
The mechanics of transport phenomena in multicomponent sessile drops with internal solidification is determined on the basis of an experimental study. A shadowgraph-schlieren system and a microscope-video system are used for the study. It is suggested that present data can be used to enhance the solid or crystal quality in a reduced-gravity environment where both thermo- and diffuso-capillary effects of solidification and crystal growth are dominant.
A Local Interpretation of Quantum Mechanics
Lopez, Carlos
2016-04-01
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the "virtual" paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
The Objective Indefiniteness Interpretation of Quantum Mechanics
Ellerman, David
2014-01-01
The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with this "properties all the way down" picture of micro-reality. Are there other coherent alternative views of reality? A logic of partitions, dual to the Boolean logic of subsets (partitions are dual to subsets), was recently developed along with a logical version of information theory. In view of the subset-partition duality, partition logic is the alternative to Boolean subset logic and thus it abstractly describes the alternative dual view of micro-reality. Perhaps QM is compatible with this dual view? Indeed, when the mathematics of partitions using sets is "lifted" from sets to vector spaces, then it yields the mathematics and relations of quantum mechanics. Thus the vision of micro-reality abstractly characterized by partition logic matches that described by quantum mechan...
Lecture Script: Introduction to Computational Quantum Mechanics
Schmied, Roman
2014-01-01
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, fo...
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...
Spin First vs. Position First instructional approaches to teaching introductory quantum mechanics
Sadaghiani, Homeyra
2017-01-01
As part of ongoing research in teaching and learning quantum mechanics, we are investigating student learning of basic introductory quantum concepts in two different paradigms. In one paradigm, students are introduced to the postulates of quantum mechanics by discrete bases of Spin-half (Spin First) before being introduced to Schrödinger's equation. In the second paradigm, continuous bases of position probability wave functions (Position First) are the context within which students first encounter quantum mechanical phenomena. In this paper, we compare student learning of basic introductory quantum ideas in two sections of a sophomore level modern physics course at Cal Poly Pomona that were taught using these two approaches by means of their performances on a research-based concept posttest. Based on our results, the students who were taught using Spin First outperformed their peers in Position First group with average score of 53 +/- 3% vs. 34 +/- 5% in Quantum Mechanics Concept Assessment (QMCA), suggesting that the Spin First approach might improve some aspects of student learning of quantum mechanics. NSF 1626482.
Donets, E. E.; Pashnev, A.; Juan Rosales, J.; Tsulaia, M. M.
2000-02-01
The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with one-quarter, one-half, and three-quarters of unbroken (broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM, while the one-dimensional N=4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N=4 superconformal quantum-mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
Simoes, Fernando; Pfaff, Robert; Berthelier, Jean-Jacques; Klenzing, Jeffrey
2012-01-01
Investigation of coupling mechanisms between the troposphere and the ionosphere requires a multidisciplinary approach involving several branches of atmospheric sciences, from meteorology, atmospheric chemistry, and fulminology to aeronomy, plasma physics, and space weather. In this work, we review low frequency electromagnetic wave propagation in the Earth-ionosphere cavity from a troposphere-ionosphere coupling perspective. We discuss electromagnetic wave generation, propagation, and resonance phenomena, considering atmospheric, ionospheric and magnetospheric sources, from lightning and transient luminous events at low altitude to Alfven waves and particle precipitation related to solar and magnetospheric processes. We review in situ ionospheric processes as well as surface and space weather phenomena that drive troposphere-ionosphere dynamics. Effects of aerosols, water vapor distribution, thermodynamic parameters, and cloud charge separation and electrification processes on atmospheric electricity and electromagnetic waves are reviewed. We also briefly revisit ionospheric irregularities such as spread-F and explosive spread-F, sporadic-E, traveling ionospheric disturbances, Trimpi effect, and hiss and plasma turbulence. Regarding the role of the lower boundary of the cavity, we review transient surface phenomena, including seismic activity, earthquakes, volcanic processes and dust electrification. The role of surface and atmospheric gravity waves in ionospheric dynamics is also briefly addressed. We summarize analytical and numerical tools and techniques to model low frequency electromagnetic wave propagation and solving inverse problems and summarize in a final section a few challenging subjects that are important for a better understanding of tropospheric-ionospheric coupling mechanisms.
Geometrical Description of Quantum Mechanics - Transformations and Dynamics
Marmo, G.; Volkert, G. F.
2010-01-01
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of separability and entanglement for states of composite quantum systems.
On Quantum Mechanical Hankel Transform and Its Applications
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.
Path integration in relativistic quantum mechanics
Redmount, I H; Redmount, Ian H.; Suen, Wai-Mo
1993-01-01
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.
Problems in quantum mechanics with solutions
d'Emilio, Emilio
2017-01-01
This second edition of an extremely well-received book presents more than 250 nonrelativistic quantum mechanics problems of varying difficulty with the aim of providing students didactic material of proven value, allowing them to test their comprehension and mastery of each subject. The coverage is extremely broad, from themes related to the crisis of classical physics through achievements within the framework of modern atomic physics to lively debated, intriguing aspects relating to, for example, the EPR paradox, the Aharonov-Bohm effect, and quantum teleportation. Compared with the first edition, a variety of improvements have been made and additional topics of interest included, especially focusing on elementary potential scattering. The problems themselves range from standard and straightforward ones to those that are complex but can be considered essential because they address questions of outstanding importance or aspects typically overlooked in primers. The book offers students both an excellent tool f...
Specker's fundamental principle of quantum mechanics
Cabello, Adan
2012-01-01
I draw attention to the fact that three recently proposed physical principles, namely "local orthogonality", "global exclusive disjunction", and "compatible orthogonality" are not new principles, but different versions of a principle that Ernst Specker noticed long ago. I include a video of Specker stating this principle in 2009 in the following terms: "Do you know what, according to me, is the fundamental theorem of quantum mechanics? (...) That is, if you have several questions and you can answer any two of them, then you can also answer all of them". I overview some results that suggest that Specker's principle may be of fundamental importance for explaining quantum contextuality. Specker passed away in December 10, 2011, at the age of 91.
Zeroth WKB Approximation in Quantum Mechanics
Sergeenko, M N
2002-01-01
Solution of the Schr\\"odinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection formulas we derive from basic requirements of continuity and finiteness for the wave function in quantum mechanics. We show that, for conservative quantum systems, not only total energy, but also momentum is the constant of motion. We derive the quantization conditions for two and more turning point problems. Exact energy eigenvalues for solvable and some ``insoluble'' potentials are obtained. The eigenfunctions have the form of a standing wave, $A_n\\cos(k_nx+\\delta_n)$, and are the asymptote of the exact solution.
Surveying Students' Understanding of Quantum Mechanics
Singh, Chandralekha
2016-01-01
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these d...
Noncommutative Spacetime Symmetries from Covariant Quantum Mechanics
Directory of Open Access Journals (Sweden)
Alessandro Moia
2017-01-01
Full Text Available In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates. However, spacetime noncommutativity can also be introduced into single-particle covariant quantum mechanics, replacing the commuting operators representing the particle’s spacetime coordinates with noncommuting ones. In this paper, we provide a full characterization of a wide class of physically sensible single-particle noncommutative spacetime models and the associated deformed relativistic symmetries. In particular, we prove that they can all be obtained from the standard Minkowski model and the usual Poincaré transformations via a suitable change of variables. Contrary to previous studies, we find that spacetime noncommutativity does not affect the dispersion relation of a relativistic quantum particle, but only the transformation properties of its spacetime coordinates under translations and Lorentz transformations.
Mechanical impact of dynamic phenomena in Francis turbines at off design conditions
Duparchy, F.; Brammer, J.; Thibaud, M.; Favrel, A.; Lowys, P. Y.; Avellan, F.
2017-04-01
At partial load and overload conditions, Francis turbines are subjected to hydraulic instabilities that can potentially result in high dynamic solicitations of the turbine components and significantly reduce their lifetime. This study presents both experimental data and numerical simulations that were used as complementary approaches to study these dynamic solicitations. Measurements performed on a reduced scale physical model, including a special runner instrumented with on-board strain gauges and pressure sensors, were used to investigate the dynamic phenomena experienced by the runner. They were also taken as reference to validate the numerical simulation results. After validation, advantage was taken from the numerical simulations to highlight the mechanical response of the structure to the unsteady hydraulic phenomena, as well as their impact on the fatigue damage of the runner.
Quantum selfish gene (biological evolution in terms of quantum mechanics)
Ozhigov, Yuri I
2014-01-01
I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical lev...
Quantum Mechanics/Molecular Mechanics Modeling of Drug Metabolism
DEFF Research Database (Denmark)
Lonsdale, Richard; Fort, Rachel M; Rydberg, Patrik;
2016-01-01
The mechanism of cytochrome P450(CYP)-catalyzed hydroxylation of primary amines is currently unclear and is relevant to drug metabolism; previous small model calculations have suggested two possible mechanisms: direct N-oxidation and H-abstraction/rebound. We have modeled the N-hydroxylation of (R......)-mexiletine in CYP1A2 with hybrid quantum mechanics/molecular mechanics (QM/MM) methods, providing a more detailed and realistic model. Multiple reaction barriers have been calculated at the QM(B3LYP-D)/MM(CHARMM27) level for the direct N-oxidation and H-abstraction/rebound mechanisms. Our calculated barriers...... indicate that the direct N-oxidation mechanism is preferred and proceeds via the doublet spin state of Compound I. Molecular dynamics simulations indicate that the presence of an ordered water molecule in the active site assists in the binding of mexiletine in the active site...
Modified Noether theorem and arrow of time in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Asadov, V V; Kechkin, O V, E-mail: asadov@neurok.co, E-mail: kechkin@gmail.co [Neur OK-III, Lomonosov Moscow State University, Vorob' jovy Gory, 119899 Moscow (Russian Federation)
2010-06-01
Relativistic quantum mechanics is presented with modified Noether theorem. It was shown that Noether charges are related with thermodynamic potentials in such scheme. Broken symmetries generated by thermodynamic mode lead to gravity appearance as effective quantum field.
Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C
2014-06-13
Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.
Quartic quantum theory: an extension of the standard quantum mechanics
Zyczkowski, Karol
2008-01-01
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system ...
A Continuous Transition Between Quantum and Classical Mechanics (I)
Ghose, Partha
2001-01-01
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical mechanics which provides a continuous transition to quantum mechanics via environment-induced decoherence.
Counting Trees in Supersymmetric Quantum Mechanics
Cordova, Clay
2015-01-01
We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.
Notions of controllability for quantum mechanical systems
Albertini, F
2001-01-01
In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that, for the system of two interacting spin 1/2 particles, not every state transfer can be obtained in arbitrary small time.
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
Directory of Open Access Journals (Sweden)
Bhashyam Balaji
2009-02-01
Full Text Available An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr¨odinger equation.
Quantum mechanics with non-unitary symmetries
Bistrovic, B
2000-01-01
This article shows how to properly extend symmetries of non-relativistic quantum mechanics to include non-unitary representations of Lorentz group for all spins. It follows from this that (almost) all existing relativistic single particle Lagrangians and equations are incorrect. This is shown in particular for Dirac's equation and Proca equations. It is shown that properly constructed relativistic extensions have no negative energies, zitterbewegung effects and have proper symmetric energy-momentum tensor and angular momentum density tensor. The downside is that states with negative norm are inevitable in all representations.
BiHermitian supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V Irnerio 46, I-40126 Bologna (Italy)
2007-04-21
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian Supersymmetric Quantum Mechanics
Zucchini, R
2006-01-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian supersymmetric quantum mechanics
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
The many worlds interpretation of quantum mechanics
Dewitt, Bryce Seligman
2015-01-01
A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. In his interpretation, Dr. Everett denies the existence of a separate classical realm and asserts the propriety of considering a state vector for the whole universe. Because this state vector never collapses, reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality customarily perceived; rather, it is a reality composed of many worlds. By vir
Influence of many-particle interactions on slow light phenomena in quantum dots
DEFF Research Database (Denmark)
Houmark-Nielsen, Jakob; Jauho, Antti-Pekka; Nielsen, Torben Roland;
2008-01-01
We investigate the impact of many-particle interactions on group-velocity slowdown achieved via Electromagnetically Induced Transparency (EIT) in quantum dots. Using a ladder scheme we find in the steady-state an increase in maximum slow-down as compared to the non-interacting case, which can...
Classical and quantum Fisher information in the geometrical formulation of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Facchi, Paolo [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Kulkarni, Ravi [Vivekananda Yoga Research Foundation, Bangalore 560 080 (India); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, Giuseppe [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Sudarshan, E.C.G. [Department of Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, Franco [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy)
2010-11-01
The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.
Mechanisms and effective control of physiological browning phenomena in plant cell cultures.
Dong, Yan-Shan; Fu, Chun-Hua; Su, Peng; Xu, Xiang-Ping; Yuan, Jie; Wang, Sheng; Zhang, Meng; Zhao, Chun-Fang; Yu, Long-Jiang
2016-01-01
Browning phenomena are ubiquitous in plant cell cultures that severely hamper scientific research and widespread application of plant cell cultures. Up to now, this problem still has not been well controlled due to the unclear browning mechanisms in plant cell cultures. In this paper, the mechanisms were investigated using two typical materials with severe browning phenomena, Taxus chinensis and Glycyrrhiza inflata cells. Our results illustrated that the browning is attributed to a physiological enzymatic reaction, and phenolic biosynthesis regulated by sugar plays a decisive role in the browning. Furthermore, to confirm the specific compounds which participate in the enzymatic browning reaction, transcriptional profile and metabolites of T. chinensis cells, and UV scanning and high-performance liquid chromatography-mass spectrometry (HPLC-MS) profile of the browning compounds extracted from the brown-turned medium were analyzed, flavonoids derived from phenylpropanoid pathway were found to be the main compounds, and myricetin and quercetin were deduced to be the main substrates of the browning reaction. Inhibition of flavonoid biosynthesis can prevent the browning occurrence, and the browning is effectively controlled via blocking flavonoid biosynthesis by gibberellic acid (GA3 ) as an inhibitor, which further confirms that flavonoids mainly contribute to the browning. On the basis above, a model elucidating enzymatic browning mechanisms in plant cell cultures was put forward, and effective control approaches were presented.
Paul, William; Oliver, David; Miyahara, Yoichi; Grütter, Peter
2013-11-29
We report on transient adhesion and conductance phenomena associated with tip wetting in mechanical contacts produced by the indentation of a clean W(111) tip into a Au(111) surface. A combination of atomic force microscopy and scanning tunneling microscopy was used to carry out indentation and to image residual impressions in ultra-high vacuum. The ∼7 nm radii tips used in these experiments were prepared and characterized by field ion microscopy in the same instrument. The very first indentations of the tungsten tips show larger conductance and pull-off adhesive forces than subsequent indentations. After ∼30 indentations to a depth of ∼1.7 nm, the maximum conductance and adhesion forces reach steady state values approximately 12 × and 6 × smaller than their initial value. Indentation of W(111) tips into Cu(100) was also performed to investigate the universality of tip wetting phenomena with a different substrate. We propose a model from contact mechanics considerations which quantitatively reproduces the observed decay rate of the conductance and adhesion drops with a 1/e decay constant of 9-14 indentation cycles. The results show that the surface composition of an indenting tip plays an important role in defining the mechanical and electrical properties of indentation contacts.
BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)
Mahler, G.
2004-07-01
that theory, construed as a description of reality.' This is taken to be entirely different within quantum mechanics. `The core idea of quantum mechanics is to describe our activities as knowledge-seeking and knowledge-using agents.' `21st century science does not reduce human beings to mechanical automata. Rather it elevates human beings to agents whose free choices can, according to the known laws, actually influence their behaviour.' An example with respect to perception is discussed: `Why, when we look at a triangle, do we experience three lines joined at three points and not some pattern of neuron firings?' The brain `does not convert an actual whole triangle into some jumbled set of particle motions; rather it converts a concatenation of separate external events into the actualization of some single integrated pattern of neural activity that is congruent to the perceived whole triangle.' How convincing is this proposal? It is hard to tell. I think Henry Stapp did a good job, but there are tight limitations to any such endeavour. Quantum mechanics is often strange indeed, but it also gives rise to our classical world around us. For the emergence of classicality jumps and measurement projections (the basic phenomena connected with those fundamental events of choice) are not needed. Therefore, I doubt whether the explanation of the evolution of our world really allows (or requires) that much free choice. On the other hand, most scientist will agree that empirical science was not possible without free will: we could not ask independent questions if this asking was part of a deterministic trajectory. The fact that the result of a quantum measurement is indeterminate (within given probabilities) does certainly not explain free will. How about the type of measurment? The experimentalist will have to assume that he can select the pertinent observable within some limits. But given a certain design the so-called pointer basis (producing stable measurement results) is no
Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons
Scammell, H. D.; Sushkov, O. P.
2017-01-01
Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.
Cataloglu, Erdat
The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p Cronbach-alpha reliability coefficient of the QMVI was found to be 0.82. Limited findings were drawn on students' understanding of introductory quantum mechanics concepts. Data suggested that the construct of quantum mechanics
Quantum mechanical wavefunction: visualization at undergraduate level
Chhabra, Mahima; Das, Ritwick
2017-01-01
Quantum mechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantum mechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.