NASA Astrophysics Data System (ADS)
Commins, Eugene D.
2014-10-01
Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein-Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.
Graduate quantum mechanics reform
NASA Astrophysics Data System (ADS)
Carr, L. D.; McKagan, S. B.
2009-04-01
We address four main areas in which graduate quantum mechanics education 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 these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50years, used textbooks that include such content, incorporated 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. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.
Bohmian quantum mechanics with quantum trajectories
NASA Astrophysics Data System (ADS)
Jeong, Yeuncheol
The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...
Quantum mechanics and quantum information theory
NASA Astrophysics Data System (ADS)
van Camp, Wesley William
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches -- that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism -- fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel
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.
Main Port Mechanism for PRISMA
NASA Astrophysics Data System (ADS)
Caprini, G. C.; Ceccherini, M.; Brotini, M.; Bini, A.; Corsini, R.; Gasparini, L.; Battazza, F.; Formaro, R.
2013-09-01
A high complexity Main Port Mechanism (MPM) has been designed and produced by Selex ES in co- operation with HighFTech Engineering, an Italian PMI, in the frame of PRISMA (PRecursore IperSpettrale della Missione Applicativa) instrument.The Main Port Mechanism is located at the entrance of the Optical Head having the function of opening and closing a door.The paper describes the requirements drived the conceptual design, the detailed design and the qualification tests performed on the mechanism. A description of the foreseen test flow and set-up is also given.
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.
Relativity and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
2007-12-01
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time- and length-scales and (ii) examine the possibility and flexibility of so-called general Jordan block formations. The present viewpoint asks for a new perspective on the age-old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein-Gordon-Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
Kapustin, Anton
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 From the Cradle?
ERIC Educational Resources Information Center
Martin, John L.
1974-01-01
States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
Quantum Mechanics From the Cradle?
ERIC Educational Resources Information Center
Martin, John L.
1974-01-01
States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
NASA Astrophysics Data System (ADS)
Blencowe, Miles
The emergence of the macroscopic classical world from the microscopic quantum world is commonly understood to be a consequence of the fact that any given quantum system is open, unavoidably interacting with unobserved environmental degrees of freedom that will cause initial quantum superposition states of the system to decohere, resulting in classical mixtures of either-or alternatives. A fundamental question concerns how large a macroscopic object can be placed in a manifest quantum state, such as a center of mass quantum superposition state, under conditions where the effects of the interacting environmental degrees of freedom are reduced (i.e. in ultrahigh vacuum and at ultralow temperatures). Recent experiments have in fact demonstrated manifest quantum behavior in nano-to-micron-scale mechanical systems. Gravity has been invoked in various ways as playing a possible fundamental role in enforcing classicality of matter systems beyond a certain scale. Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that it is possible to describe quantitatively how gravity as an environment can induce the decoherence of matter superposition states. The justification for such an approach follows from the fact that we are considering laboratory scale systems, where the matter is localized to regions of small curvature. As with other low energy effects, such as the quantum gravity correction to the Newtonian potential between two ordinary masses, it should be possible to quantitatively evaluate gravitationally induced decoherence rates by employing standard perturbative quantum gravity as an effective field theory; whatever the final form the eventual correct quantum theory of gravity takes, it must converge in its predictions with the effective field theory description at low energies. Research supported by the National Science Foundation (NSF
The quantum mechanics of cosmology.
NASA Astrophysics Data System (ADS)
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
Grassmann matrix quantum mechanics
Anninos, Dionysios; Denef, Frederik; Monten, Ruben
2016-04-21
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less
Grassmann matrix quantum mechanics
Anninos, Dionysios; Denef, Frederik; Monten, Ruben
2016-04-21
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
Time Asymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr
2011-09-01
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) 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 t0≤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.
NASA Astrophysics Data System (ADS)
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.
Introduction to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Griffiths, David J.
2016-09-01
Part I. Theory: 1. The wave function; 2. Time-independent Schrödinger equation; 3. Formalism; 4. Quantum mechanics in three dimensions; 5. Identical particles; Part II. Applications: 6. Time-independent perturbation theory; 7. The variational principle; 8. The WKB approximation; 9. Time-dependent perturbation theory; 10. The adiabatic approximation; 11. Scattering; 12. Afterword; Appendix. Linear algebra.
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.
NASA Astrophysics Data System (ADS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Frank
1986-06-01
Beginning students of quantum mechanics frequently experience difficulties separating essential underlying principles from the specific examples to which these principles have been historically applied. Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.
Supersymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
David, J.; Fernández, C.
2010-10-01
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Pöschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Jones, Robert
2011-03-01
I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.
Quantum Mechanics: Myths and Facts
NASA Astrophysics Data System (ADS)
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.
Diagrammatic quantum mechanics
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.; Lomonaco, Samuel J.
2015-05-01
This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.
Bell's theorem and quantum mechanics
NASA Astrophysics Data System (ADS)
Rosen, Nathan
1994-02-01
Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor
Klein's programme and quantum mechanics
NASA Astrophysics Data System (ADS)
Clemente-Gallardo, Jesús; Marmo, Giuseppe
2015-04-01
We review the geometrical formulation of quantum mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the C*-algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group.
Decoherence in quantum mechanics and quantum cosmology
NASA Technical Reports Server (NTRS)
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.
Quantum inertia stops superposition: Scan Quantum Mechanics
NASA Astrophysics Data System (ADS)
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.
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.
Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
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.
QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES
G. GEIGER; ET AL
2000-11-01
The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.
Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Eck, John S.; Thompson, W. J.
1977-01-01
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Eck, John S.; Thompson, W. J.
1977-01-01
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
From Classical to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Sudarshan, George
2010-06-01
Preface; Acknowledgements; Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory; 2. Classical dynamics; 3. Wave equations; 4. Wave mechanics; 5. Applications of wave mechanics; 6. Introduction to spin; 7. Perturbation theory; 8. Scattering theory; Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization; 10. Harmonic oscillators and quantum optics; 11. Angular momentum operators; 12. Algebraic methods for eigenvalue problems; 13. From density matrix to geometric phases; Part III. Selected Topics: 14. From classical to quantum statistical mechanics; 15. Lagrangian and phase-space formulations; 16. Dirac equation and no-interaction theorem; References; Index.
From Classical to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Sudarshan, George
2004-03-01
Preface; Acknowledgements; Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory; 2. Classical dynamics; 3. Wave equations; 4. Wave mechanics; 5. Applications of wave mechanics; 6. Introduction to spin; 7. Perturbation theory; 8. Scattering theory; Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization; 10. Harmonic oscillators and quantum optics; 11. Angular momentum operators; 12. Algebraic methods for eigenvalue problems; 13. From density matrix to geometric phases; Part III. Selected Topics: 14. From classical to quantum statistical mechanics; 15. Lagrangian and phase-space formulations; 16. Dirac equation and no-interaction theorem; References; Index.
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.
Quantum Mechanics in Insulators
Aeppli, G.
2009-08-20
Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).
Non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
Jones-Smith, Katherine
The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. One of the fundamental assumptions used in formulating the theory is that operators are represented by Hermitian matrices. In recent years it has been shown that quantum mechanics can be formulated consistently without making this assumption, using instead a combination of the parity (P) and time-reversal (T) operators and a number of other requirements related to P and T. Only the case of even T has been analyzed in the literature; here we generalize the principles to include odd time-reversal. We use this generalization to construct a non-Hermitian version of the Dirac equation, and in doing so discover a new type of particle not allowed within the (Hermitian) Standard Model. Finally we present a potential application of the ideas of non-Hermitian quantum mechanics to the unsolved problems of quantum magnetism and high temperature superconductivity.
ERIC Educational Resources Information Center
DeWitt, Bryce S.
1970-01-01
Discusses the quantum theory of measurement and von Neumann's catastrophe of infinite regression." Examines three ways of escapint the von Neumann catastrophe, and suggests that the solution to the dilemma of inteterminism is a universe in which all possible outcomes of an experiment actually occur. Bibliography. (LC)
Kowalevski top in quantum mechanics
Matsuyama, A.
2013-09-15
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.
Quantum Mechanics and Narratability
NASA Astrophysics Data System (ADS)
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.
Self-Referential Quantum Mechanics
NASA Astrophysics Data System (ADS)
Mitchell, Mark Kenneth
1993-01-01
A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta operators are introduced which make possible new operations in the quantum phase. Two interpretations are presented utilizing the nonlinear quantum system: the idealistic interpretation based upon consciousness focused upon the measurement problem, and the statistical interpretation focused upon stochastic quantum fluctuations. Experimental properties are examined, beginning with a proposed analog of the Bohm-Aharonov experiment. Interference due to difference in path length for a split electron beam is effected in a region of spacetime where electromagnetic field and the vector potential are enclosed within but screened to be zero at the paths. If the wavefunction's geometrical phase contribution along the paths is different, then there should be interference induced purely by the wave-function alone. A positive result would be due to a purely wavefunction dependent effect. The spin phase of the wavefunction is postulated to be the source of the zitterbewegung of the electron. Reduction of the wavefunction in measurement is examined for self -referential quantum systems arising from consciousness and then arising from a stochastic quantum spacetime model. These results are applied to the mind-brain as a quantum processor producing a behavioral double slit experiment (ideation experiments) and nonlocal transferred potentials in an EPR-style experiment. Looking at the universe as a whole as a quantum self-referential system, leads to a modified zitterbewegung Wheeler-DeWitt equation; and, the transition from quantum-to-classical on a cosmological scale for
Quantum Mechanical Earth: Where Orbitals Become Orbits
ERIC Educational Resources Information Center
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
ERIC Educational Resources Information Center
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 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.
Historical Review of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Prashant, Prashant
2007-03-01
Quantum Mechanics is being taught for the last many decades at both undergraduate as well as post graduate levels in universities world over. Inclusion of historical background i.e. development of the subject in chronological order, description of Gedanken experiments, information regarding Solvay, Copenhagen Conferences and biographies of well known contributors in this field may definitely give a broader understanding of the subject. This may create an interest in understanding the new developments and this article is an attempt in that direction to highlight the rich past of Quantum Mechanics and how it got shaped by great minds to its present form. Keywords: Quantum mechanics, historical, Copenhagen, Solvay, Bohr, Einstein. note: http://www.arxiv.org/abs/physics/0512104
Energy conservation in quantum mechanics
NASA Astrophysics Data System (ADS)
Prentis, Jeffrey J.; Fedak, William A.
2004-05-01
In the classical mechanics of conservative systems, the position and momentum evolve deterministically such that the sum of the kinetic energy and potential energy remains constant in time. This canonical trademark of energy conservation is absent in the standard presentations of quantum mechanics based on the Schrödinger picture. We present a purely canonical proof of energy conservation that focuses exclusively on the time-dependent position x(t) and momentum p(t) operators. This treatment of energy conservation serves as an introduction to the Heisenberg picture and illuminates the classical-quantum connection. We derive a quantum-mechanical work-energy theorem and show explicitly how the time dependence of x and p and the noncommutivity of x and p conspire to bring about a perfect temporal balance between the evolving kinetic and potential parts of the total energy operator.
Intrusion Detection With Quantum Mechanics: A Photonic Quantum Fence
2008-12-01
computing and quantum key distribution (QKD). Some of the most remarkable examples include quantum teleportation for the non-local transfer of...1 INTRUSION DETECTION WITH QUANTUM MECHANICS: A PHOTONIC QUANTUM FENCE T. S. Humble*, R. S. Bennink, and W. P. Grice Oak Ridge National...use of quantum -mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no
Canonical Transformations in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Anderson, A.
1994-06-01
Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schrödinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations.
Minkowski Space and Quantum Mechanics
NASA Astrophysics Data System (ADS)
O'Hara, Paul
A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo
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.
Machine Learning and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Chapline, George
The author has previously pointed out some similarities between selforganizing neural networks and quantum mechanics. These types of neural networks were originally conceived of as away of emulating the cognitive capabilities of the human brain. Recently extensions of these networks, collectively referred to as deep learning networks, have strengthened the connection between self-organizing neural networks and human cognitive capabilities. In this note we consider whether hardware quantum devices might be useful for emulating neural networks with human-like cognitive capabilities, or alternatively whether implementations of deep learning neural networks using conventional computers might lead to better algorithms for solving the many body Schrodinger equation.
Improving student understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2015-04-01
Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.
Emergent quantum mechanics of finances
NASA Astrophysics Data System (ADS)
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.
Quantum mechanics and the psyche
NASA Astrophysics Data System (ADS)
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.
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
NASA Astrophysics Data System (ADS)
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.
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
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
Faster than Hermitian Quantum Mechanics
Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.
2007-01-26
Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
Facets of contextual realism in quantum mechanics
Pan, Alok Kumar; Home, Dipankar
2011-09-23
In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.
Treating time travel quantum mechanically
NASA Astrophysics Data System (ADS)
Allen, John-Mark A.
2014-10-01
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Quantum statistical mechanics in arithmetic topology
NASA Astrophysics Data System (ADS)
Marcolli, Matilde; Xu, Yujie
2017-04-01
This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes system, with knots replacing primes, and cyclic branched coverings of the 3-sphere replacing abelian extensions of the field of rational numbers. The operator algebraic properties of this system differ significantly from the Bost-Connes case, due to the properties of the action of the semigroup of knots on a direct limit of knot groups. The resulting algebra of observables is a noncommutative Bernoulli product. We describe the main properties of the associated quantum statistical mechanical system and of the relevant partition functions, which are obtained from simple knot invariants like genus and crossing number.
Teaching Quantum Mechanics on an Introductory Level.
ERIC Educational Resources Information Center
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.
ERIC Educational Resources Information Center
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)
Deformation of noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
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 .
Matrix quantum mechanics from qubits
NASA Astrophysics Data System (ADS)
Hartnoll, Sean A.; Huijse, Liza; Mazenc, Edward A.
2017-01-01
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-mechanical twin paradox
NASA Astrophysics Data System (ADS)
Franson, J. D.
2016-10-01
In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys. 18 093050) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer.
Mechanism for quantum speedup in open quantum systems
NASA Astrophysics Data System (ADS)
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Quantum localization of classical mechanics
NASA Astrophysics Data System (ADS)
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.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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.
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
Scholes, Gregory
2012-02-01
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2009-02-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2011-09-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Scattering in PT-symmetric quantum mechanics
Cannata, Francesco . E-mail: Francesco.Cannata@bo.infn.it; Dedonder, Jean-Pierre . E-mail: dedonder@paris7.jussieu.fr; Ventura, Alberto . E-mail: Alberto.Ventura@bologna.enea.it
2007-02-15
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.
Speakable and Unspeakable in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Bell, J. S.; Aspect, Introduction by Alain
2004-06-01
List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantum mechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantum mechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantum mechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantum mechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantum mechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantum mechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.
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.
NASA Astrophysics Data System (ADS)
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.
Towards a Constructive Foundation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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.
BOOK REVIEWS: Quantum Mechanics: Fundamentals
NASA Astrophysics Data System (ADS)
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
What is the main mechanism of tramadol?
Minami, Kouichiro; Ogata, Junichi; Uezono, Yasuhito
2015-10-01
Tramadol is an analgesic that is used worldwide for pain, but its mechanisms of action have not been fully elucidated. The majority of studies to date have focused on activation of the μ-opioid receptor (μOR) and inhibition of monoamine reuptake as mechanisms of tramadol. Although it has been speculated that tramadol acts primarily through activation of the μOR, no evidence has revealed whether tramadol directly activates the μOR. During the past decade, major advances have been made in our understanding of the physiology and pharmacology of ion channels and G protein-coupled receptor (GPCR) signaling. Several studies have shown that GPCRs and ion channels are targets for tramadol. In particular, tramadol has been shown to affect GPCRs. Here, the effects of tramadol on GPCRs, monoamine transporters, and ion channels are presented with a discussion of recent research on the mechanisms of tramadol.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
Carinena, J. F.; Ibort, A.; Marmo, G.; Morandi, G.
2009-05-06
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
Quantum mechanics without potential function
Alhaidari, A. D.; Ismail, M. E. H.
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
NASA Astrophysics Data System (ADS)
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.
Relationship between quantum walks and relativistic quantum mechanics
Chandrashekar, C. M.; Banerjee, Subhashish; Srikanth, R.
2010-06-15
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.
[Neuroplasticity: main mechanisms and their clinical significance].
Damulin, I V
2009-01-01
Common mechanisms of neuroplasticity and their manifestations in different neurological diseases are reviewed. The ambiguity of physiological and clinical changes caused by neuroplasticity is emphasized. Special attention is drawn to the functional post-stroke rehabilitation. The author emphasizes the importance of "cerebral reserve" in normal ageing and Alzheimer's disease. Possibilities of neuroplasticity activation are reviewed. The efficacy of cerebrolysin in the treatment of dementia and stroke is mentioned.
Kindergarten Quantum Mechanics: Lecture Notes
Coecke, Bob
2006-01-04
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 which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.
Quantum mechanics, relativity and time
NASA Astrophysics Data System (ADS)
Basini, Giuseppe; Capozziello, Salvatore
2005-01-01
A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a reduction procedure from 5D to 4D, dynamics leads to the natural emergence of two time arrows and ofa scalar-tensor theory of gravity. In this framework, phenomena like entanglement of systems and topology changes can be naturally accounted and, furthermore, several experimental evidences as gamma ray bursts, sizes of astrophysical structures and the observed values of cosmological parameters can be explained. The identification, thanks to conservation laws, of a covariant symplectic structure as a general feature also for gravity can be seen as a deep link common to all the interactions.
Quantum mechanics: A new chapter?
NASA Astrophysics Data System (ADS)
Hofer, Werner A.
2012-12-01
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Grössing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.
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. © 2011 American Institute of Physics
Quantum Mechanics and physical calculations
NASA Astrophysics Data System (ADS)
Karayan, H. S.
2014-03-01
We suggest to realize the computer simulation and calculation by the algebraic structure built on the basis of the logic inherent to processes in physical systems (called physical computing). We suggest a principle for the construction of quantum algorithms of neuroinformatics of quantum neural networks. The role of academician Sahakyan is emphasized in the development of quantum physics in Armenia.
Einstein's equivalence principle in quantum mechanics revisited
NASA Astrophysics Data System (ADS)
Nauenberg, Michael
2016-11-01
The gravitational equivalence principle in quantum mechanics is of considerable importance, but it is generally not included in physics textbooks. In this note, we present a precise quantum formulation of this principle and comment on its verification in a neutron diffraction experiment. The solution of the time dependent Schrödinger equation for this problem also gives the wave function for the motion of a charged particle in a homogeneous electric field, which is also usually ignored in textbooks on quantum mechanics.
The transactional interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
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."
Elucidating reaction mechanisms on quantum computers
NASA Astrophysics Data System (ADS)
Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias
2017-07-01
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.
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.
Consistent interpretations of quantum mechanics
Omnes, R. )
1992-04-01
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
Quantum Mechanics with a Little Less Mystery
ERIC Educational Resources Information Center
Cropper, William H.
1969-01-01
Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…
Polymer quantum mechanics and its continuum limit
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2007-08-15
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.
Does quantum mechanics tell an atomistic spacetime?
NASA Astrophysics Data System (ADS)
Elze, Hans-Thomas
2009-06-01
The canonical answer to the question posed is "Yes." - tacitly assuming that quantum theory and the concept of spacetime are to be unified by 'quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? - We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.
Improving students' understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Zhu, Guangtian
2011-12-01
Learning physics is challenging at all levels. Students' difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students' preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students' common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students' difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that students' understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students' understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James
2011-06-01
The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.
NASA Astrophysics Data System (ADS)
Cataloglu, Erdat
positive correlation coefficient of 0.42 observed between students' QMVI scores and their final course grades was also consistent with expectations in a valid instrument. In addition, the 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 understanding is most likely multidimensional and the Main Topic defined as "Quantum Mechanics Postulates" may be an especially important factor for students in acquiring a successful understanding of quantum mechanics.
Strange Bedfellows: Quantum Mechanics and Data Mining
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.
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.
Principles and Dynamics of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2009-05-01
Quantum mechanics can be founded on three principles: particle waves, concurrent states and averaged energy relations. The Schrodinger, time-evolution and Dirac equations are derived to be the conditions the wavefunction must satisfy in order to fulfill the corresponding averaged energy relations. Adopting a particle and wave balanced approach we attain a clear, consistent and justified quantum theory.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S.
2006-12-15
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Quantum mechanics: The subtle pull of emptiness
Seife, C.
1997-01-10
Classic physics dictates that the vacuum is devoid not only of matter but also of energy. But quantum mechanics often seems to depart from common sense. A paper in the Physical Review Letters describes the first successful measurement of the ultimate quantum free lunch: the Casimir force, a pressure exerted by empty space. This paper describes the background and the experiment.
Mechanical equivalent of quantum heat engines.
Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice
2008-06-01
Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.
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.
NASA Astrophysics Data System (ADS)
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.
Kinetic potentials in quantum mechanics
NASA Astrophysics Data System (ADS)
Hall, Richard L.
1984-09-01
Suppose that the Hamiltonian H=-Δ+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins≳0(s+vf¯nl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' f¯nl(s) associated with f(r) are defined by f¯nl(s) =infDnl supψ∈Dnl, ∥ψ∥=1 ∫ ψ(r) f ([ψ,-Δψ)/s]1/2r)ψ(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(θ,φ), m=0, and contained in the domain D(H) of H. If the potential has the form f(r)=∑Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ∑Ni=1 g(i)( f¯nl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.
Dynamics of nonrelativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2017-01-01
We show that the wavefunction of an electron interacting with an electric potential is accurately represented by the superposition of plane waves that fulfills the total energy relation. As a result, we explicitly derive the Schrödinger, Pauli, Klein-Gordon, and Dirac equations. While the traditional nonrelativistic quantum dynamics is based on postulates, the dynamics we introduce is theoretically justified, in agreement with experimental measurements, and consistent with the fundamental theory of quantum electrodynamics.
Superconducting Qubits as Mechanical Quantum Engines
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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.
Quantum mechanical streamlines. I - Square potential barrier
NASA Technical Reports Server (NTRS)
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.
Quantum mechanical stabilization of Minkowski signature wormholes
Visser, M.
1989-05-19
When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.
Fundamental Quantum Mechanics--A Graphic Presentation
ERIC Educational Resources Information Center
Wise, M. N.; Kelley, T. G.
1977-01-01
Describes a presentation of basic quantum mechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)
Supersymmetric q-deformed quantum mechanics
Traikia, M. H.; Mebarki, N.
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.
On the geometrization of quantum mechanics
Tavernelli, Ivano
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.
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.
Geometric Hamiltonian quantum mechanics and applications
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2016-08-01
Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.
On the geometrization of quantum mechanics
NASA Astrophysics Data System (ADS)
Tavernelli, Ivano
2016-08-01
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.
Possible Quantum Mechanical Effect on Beam Echo
Chao, Alex
2000-12-07
The echo effect in charged particle beams provides a link between macroscopic measurable beam parameters and microscopic phase space motion of the beam. Since quantum mechanics dictates a granularization of the phase space, it influences how the phase space behaves microscopically, and thus potentially affect how the echo effect behaves macroscopically. In this study, we propose to examine the possible measurable macroscopic effects of quantum mechanics on beams through its echo effect.
Implications of conformal symmetry in quantum mechanics
NASA Astrophysics Data System (ADS)
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.
Horizon quantum mechanics of rotating black holes
NASA Astrophysics Data System (ADS)
Casadio, Roberto; Giugno, Andrea; Giusti, Andrea; Micu, Octavian
2017-05-01
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.
Antonio Gramsci's Reflection on Quantum Mechanics
NASA Astrophysics Data System (ADS)
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.
Quantum mechanics near closed timelike lines
NASA Astrophysics Data System (ADS)
Deutsch, David
1991-11-01
The methods of the quantum theory of computation are used to analyze the physics of closed timelike lines. This is dominated, even at the macroscopic level, by quantum mechanics. In classical physics the existence of such lines in a spacetime imposes ``paradoxical'' constraints on the state of matter in their past and also provides means for knowledge to be created in ways that conflict with the principles of the philosophy of science. In quantum mechanics the first of these pathologies does not occur. The second is mitigated, and may be avoidable without such spacetimes being ruled out. Several novel and distinctive (but nonparadoxical) quantum-mechanical effects occur on and near closed timelike lines, including violations of the correspondence principle and of unitarity. It becomes possible to ``clone'' quantum systems and to measure the state of a quantum system. A new experimental test of the Everett interpretation against all others becomes possible. Consideration of these and other effects sheds light on the nature of quantum mechanics.
On reconciling quantum mechanics and local realism
NASA Astrophysics Data System (ADS)
Graft, Donald A.
2013-10-01
Accepting nonlocal quantum correlations requires us to reject special relativity and/or probability theory. We can retain both by revising our interpretation of quantum mechanics regarding the handling of separated systems, as quantum mechanics conflicts with local realism only in its treatment of separated systems. We cannot use the joint probability formula for cases of separated measurements. We use the marginals (partial traces) together with whatever priors we have from an understanding of the system. This program can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but we argue that the experiments have been misinterpreted, and that when correctly interpreted they confirm local realism. We describe a local realistic account of one important Einstein-Poldosky-Rosen-Bohm (EPRB) experiment (Weihs et al6) that claims to demonstrate nonlocal entanglement. We present a local realistic system (experiment) that can be calibrated into both quantum and classical correlation domains via adjustment of parameters (`hidden variables') of the apparatus. Weihs incorrectly dismisses these parameters as uncritical. Nonlocal entanglement is seen to be an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Freed from the incoherent idea of nonlocal entanglement, we can leverage powerful classical ideas, such as semiclassical radiation theory, stochastic dynamics, classical noncommutativity/contextuality, measurement effects on state, etc., to augment or complement quantum mechanics. When properly interpreted and applied, quantum mechanics lives in peaceful harmony with the local realist conception, and both perspectives offer useful paradigms for describing systems.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, Alexander
1996-02-20
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.
ERIC Educational Resources Information Center
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…
ERIC Educational Resources Information Center
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.
Nonrelativistic Quantum Mechanics with Fundamental Environment
NASA Astrophysics Data System (ADS)
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.
Photon Quantum Mechanics in the Undergraduate Curriculum
NASA Astrophysics Data System (ADS)
Pearson, Brett; Carson, Zack; Jackson, David
2011-05-01
Although it has been discussed for centuries, the true nature of light is still being debated. In fact, the quantum mechanical aspects of light have only been observed within the past 30 years. Recent advances in technology have decreased the complexity of such tests, and the Department of Physics and Astronomy at Dickinson College has worked to infuse various quantum optics experiments throughout our curriculum. We describe a set of experiments that includes the existence of photons, single-photon interference, the quantum eraser, and tests of Bell's theorem. A primary motivation is bringing undergraduate students face to face with some of the fascinating and subtle aspects of quantum mechanics in a hands-on setting. Supported by Dickinson College and NSF DUE-0737230.
Measurements and mathematical formalism of quantum mechanics
NASA Astrophysics Data System (ADS)
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.
Optimal guidance law in quantum mechanics
Yang, Ciann-Dong Cheng, Lieh-Lieh
2013-11-15
Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function Ψ{sup ∗}Ψ. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.
Computations in quantum mechanics made easy
NASA Astrophysics Data System (ADS)
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.
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).
Coherent states in noncommutative quantum mechanics
Ben Geloun, J.; Scholtz, F. G.
2009-04-15
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.
Observation and superselection in quantum mechanics
NASA Astrophysics Data System (ADS)
Landsman, N. P.
We attempt to clarify the main conceptual issues in approaches to 'objectification' or 'measurement' in quantum mechanics which are based on superselection rules. Such approaches venture to derive the emergence of classical 'reality' relative to a class of observers; those believing that the classical world exists intrinsically and absolutely are advised against reading this paper. The prototype approach (K. Hepp, Helv. Phys. Acta 45 (1972), 237-248) where superselection sectors are assumed in the state space of the apparatus is shown to be untenable. Instead, one should couple system and apparatus to an environment, and postulate superselection rules for the latter. These are motivated by the locality of any observer or other (actual or virtual) monitoring system. In this way 'environmental' solutions to the measurement problem (H.D. Zeh, Found. Phys. 1 (1970), 69-76; W. H. Zurek, Phys. Rev. D26 (1982), 1862-1880 and Progr. Theor. Phys. 89 (1993), 281-312) become consistent and acceptable, too. Points of contact with the modal interpretation are briefly discussed. We propose a minimal value attribution to observables in theories with superselection rules, in which only central observables have properties. In particular, the eigenvector-eigenvalue link is dropped. This is mainly motivated by Ockham's razor.
Quantum mechanics and the physical reality concept
von Borzeszkowski, H.H.; Wahsner, R.
1988-06-01
The difference between the measurement bases of classical and quantum mechanics is often interpreted as a loss of reality arising in quantum mechanics. In this paper it is shown that this apparent loss occurs only if one believes that refined everyday experience determines the Euclidean space as the real space, instead of considering this space, both in classical and quantum mechanics, as a theoretical construction needed for measurement and representing one part of a dualistic space conception. From this point of view, Einstein's program of a unified field theory can be interpreted as the attempt to find a physical theory that is less dualistic. However, if one regards this dualism as resulting from the requirements of measurements, one can hope for a weakening of the dualism but not expect to remove it completely.
Multichannel framework for singular quantum mechanics
Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.
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.
Quantum Mechanics of Palladium Nanostructures
NASA Astrophysics Data System (ADS)
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.
A proof of von Neumann's postulate in Quantum Mechanics
Conte, Elio
2010-05-04
A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.
An Axiomatic Basis for Quantum Mechanics
NASA Astrophysics Data System (ADS)
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.
Two basic Uncertainty Relations in Quantum Mechanics
Angelow, Andrey
2011-04-07
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Two basic Uncertainty Relations in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Angelow, Andrey
2011-04-01
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schrödinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
A new introductory quantum mechanics curriculum
NASA Astrophysics Data System (ADS)
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 Mechanical Aspects of Free Electron Lasers.
NASA Astrophysics Data System (ADS)
Saritepe, Selcuk
Scope of study. A 2-D quantum theory of the Free Electron Laser (FEL) has been developed based on the solutions of Dirac equation for the motion of electrons moving in various wiggler geometries, uniform, tapered and enhanced by an axial guide field. It is shown that these solutions can be written in terms of Mathieu functions of fractional order. Using these solutions a perturbational analysis is carried out to calculate the frequencies and the gain of the FEL in each magnet configuration. Finally, an optical model for the FEL interaction is developed to explain the saturation behaviour and the short-pulse effects such as Laser Lethargy. Findings and conclusions. It is found that the quantum mechanical effects due to transverse momentum correction were gamma (Lorentz factor) times larger than the quantum recoil and spin effects and therefore important for the short wavelength FELs. These quantum mechanical effects cause a broadening in the spontaneous emission lineshape, a decrease in gain and an increase in the rate of harmonic frequency generation. In the presence of an axial field, gain is increased, harmonic frequency rate is reduced and Dirac solutions exhibit instability. The optical model developed in this thesis correctly predicts the oscillator rise time and uses a simpler algorithm to calculate the nonlinear saturation behaviour. Optical model also incorporates inhomogeneous broadening and quantum mechanical effects and explains the Laser Lethargy effect as an optical pulse compression phenomenon.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T.
2014-03-15
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T.
2014-03-15
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
Quantum Mechanics in the Light of Quantum Cosmology
NASA Astrophysics Data System (ADS)
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 geometry of real reducible polarizations in quantum mechanics
NASA Astrophysics Data System (ADS)
Tejero Prieto, Carlos; Vitolo, Raffaele
2017-03-01
The formulation of geometric quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle. The existence of reducible quantum structures leads to considering the class of Liouville symplectic manifolds. Our main application of this modified geometric quantization scheme is to quantum mechanics on Riemannian manifolds. With this method we obtain an energy operator without the scalar curvature term that appears in the standard formulation, thus agreeing with the usual expression found in the physics literature.
Simplified quantum mechanics of light detection for quantum cryptography
NASA Astrophysics Data System (ADS)
Myers, John M.; Madjid, F. Hadi
2004-08-01
Strong light signals are detected reliably on a time scale of a nanosecond; however, known detectors of weak light signals used in quantum key distribution (QKD) are much slower; they involve pulse-shaping arbiters based on flip-flops that take many nanoseconds to produce a stable output. Based on a recently shown logical independence of quantum particles from the devices that they are employed to explain, we make use of quantum mechanics fine-tuned so that particles serve not as rigid foundations but as improvised hypotheses useful in models that describe the recorded behavior of devices. On the experimental side, we augment the arbitrating flip-flop of a detector so that it fans out to a matched pair of auxiliary flip-flops, and show how this imparts to a detector a "self-awareness" of its own teetering, as announced by disagreements between the auxiliary flip-flops. We introduce a quantum model of this arrangement, invoking a pair of probe particles, and show this model corresponds well to an experiment. The matched pair of auxiliary flip-flops not only confirms the model of hesitation in a detector, but serves as an instrument, both conceptual and practical, that gives an added dimension to the characterization of signal sources.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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
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.
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
1979-01-01
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
1979-01-01
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Quantum mechanics is compatible with realism
Burgos, M.E.
1987-08-01
A new paradox of quantum mechanics has recently been proposed by an author claiming that any attempt to inject realism in physical theory is bound to lead to inconsistencies. In this paper the author shows that the mentioned paradox is not such a one and that at present there are no reasons to reject realism.
Holism, physical theories and quantum mechanics
NASA Astrophysics Data System (ADS)
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.
Time and the foundations of quantum mechanics
NASA Astrophysics Data System (ADS)
Pashby, Thomas
Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
The Compton effect: Transition to quantum mechanics
NASA Astrophysics Data System (ADS)
Stuewer, R. H.
2000-11-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.
Time in classical and in quantum mechanics
NASA Astrophysics Data System (ADS)
Elçi, A.
2010-07-01
This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the Dirac-Heisenberg-von Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the Dirac-Heisenberg-von Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.
Quantum Mechanics and the Interpretation Problem
NASA Astrophysics Data System (ADS)
Lonney, Lawrence William, Jr.
1990-01-01
Although many well articulated approaches to theory choice exist, no general approach to interpretation choice is available. This lacking is particularly troublesome for quantum mechanics because its mathematical formalism is associated with many well-developed interpretations. The lack of a method for choosing among the various interpretations of quantum mechanics has motivated the construction of this dissertation. The search for an appropriate method focuses on two areas: attempts to establish the superiority of one particular interpretation of quantum mechanics over another and general methods for choosing one theory over another. Regarding the former area, two attempts to choose the Statistical Ensemble interpretation of quantum mechanics over the Copenhagen interpretation are analyzed. One of these is authored by L. E. Ballentine and the other by J. L. Park. The conclusion of this analysis is that both attempts did not succeed and a general approach to interpretation choice could not be extracted from either. The desired approach was eventually found in one of the general methods for choosing among theories. The essential element of this approach to interpretation choice lies in the recognition that each interpretation contains the seed of a unique research program. If the program is cultivated, it can eventually be judged relative to others which have sprouted from the same theory. The criteria for such a judgment are contained in the Methodology of Scientific Research Programmes approach to theory choice. This method is applied to the Statistical Ensemble and Copenhagen interpretations of quantum mechanics. Even though it did not result in an immediate choice between the two, it did provide guidance for identifying what is needed to make such a choice.
Quantum mechanical studies of carbon structures
Bartelt, Norman Charles; Ward, Donald; Zhou, Xiaowang; Foster, Michael E.; Schultz, Peter A.; Wang, Bryan M.; McCarty, Kevin F.
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 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.
Global and local horizon quantum mechanics
NASA Astrophysics Data System (ADS)
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.
A Primer on Resonances in Quantum Mechanics
Rosas-Ortiz, Oscar; Fernandez-Garcia, Nicolas; Cruz y Cruz, Sara
2008-11-13
After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy (Gamow-Siegert functions). Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.
Quantum mechanical coherence, resonance, and mind
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.
Neutrino oscillations: quantum mechanics vs. quantum field theory
NASA Astrophysics Data System (ADS)
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-04-01
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.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
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.
Quantum mechanics concept assessment: Development and validation study
NASA Astrophysics Data System (ADS)
Sadaghiani, Homeyra R.; Pollock, Steven J.
2015-06-01
As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum mechanics assessment tool (QMAT) to a multiple-choice (MC) format. Further question refinement, development of effective distractors, adding new questions, and robust statistical analysis has led to a 31-item quantum mechanics concept assessment (QMCA) test. The QMCA is used as post-test only to assess students' knowledge about five main topics of quantum measurement: the time-independent Schrödinger equation, wave functions and boundary conditions, time evolution, and probability density. During two years of testing and refinement, the QMCA has been given in alpha (N =61 ) and beta versions (N =263 ) to students in upper division quantum mechanics courses at 11 different institutions with an average post-test score of 54%. By allowing for comparisons of student learning across different populations and institutions, the QMCA provides instructors and researchers a more standard measure of effectiveness of different curricula or teaching strategies on student conceptual understanding of quantum mechanics. In this paper, we discuss the construction of effective distractors and the use of student interviews and expert feedback to revise and validate both questions and distractors. We include the results of common statistical tests of reliability and validity, which suggest the instrument is presently in a stable, usable, and promising form.
The emergent Copenhagen interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.
2014-05-01
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. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. 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 probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.
Investigating learners' epistemological framings of quantum mechanics
NASA Astrophysics Data System (ADS)
Dini, Vesal
Classical mechanics challenges students to use their intuitions and experiences as a basis for understanding, in effect to approach learning as "a refinement of everyday thinking'' (Einstein, 1936). Moving on to quantum mechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that intuitive knowledge and mathematics play in the pursuit of coherent understanding (these are adjustments to aspects of their epistemologies). In this dissertation, I explore how some students manage the epistemological transition. I began this work by recruiting both graduate and undergraduate students, interviewing each subject several times as they moved through coursework in QM. The interviews featured, among other things, how students tried to fit ideas together in mutually consistent ways, including with respect to intuitive knowledge, mathematics and experiment, if at all. I modeled these dynamic cognitive processes as different epistemological framings (i.e., tacit, in-the-moment responses to the question "How should I approach knowledge?''). Through detailed qualitative analyses of students' reasoning and a systematic coding of their interviews, I explored how these coherence seeking related framings impacted their learning. The dissertation supports three main findings: (1) students' patterns of epistemological framing are mostly stable within a given course; (2) students who profess epistemologies aligned with the coordination of coherence seeking framings tend to be more stable in demonstrating them; and (3) students aware that their understanding of QM ultimately anchors in its mathematics tend to produce more coherent explanations and perform better in their courses. These findings are consistent with existing research on student epistemologies in QM and imply that epistemologies, in particular whether and how students seek coherence, require greater attention and emphasis in instruction.
``the Human BRAIN & Fractal quantum mechanics''
NASA Astrophysics Data System (ADS)
Rosary-Oyong, Se, Glory
In mtDNA ever retrieved from Iman Tuassoly, et.al:Multifractal analysis of chaos game representation images of mtDNA''.Enhances the price & valuetales of HE. Prof. Dr-Ing. B.J. HABIBIE's N-219, in J. Bacteriology, Nov 1973 sought:'' 219 exist as separate plasmidDNA species in E.coli & Salmonella panama'' related to ``the brain 2 distinct molecular forms of the (Na,K)-ATPase..'' & ``neuron maintains different concentration of ions(charged atoms'' thorough Rabi & Heisenber Hamiltonian. Further, after ``fractal space time are geometric analogue of relativistic quantum mechanics''[Ord], sought L.Marek Crnjac: ``Chaotic fractals at the root of relativistic quantum physics''& from famous Nottale: ``Scale relativity & fractal space-time:''Application to Quantum Physics , Cosmology & Chaotic systems'',1995. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.
Gravitomagnetism and Spinor Quantum Mechanics
Adler, Ronald J.; Chen, Pisin; Varani, Elisa; /Unlisted
2012-09-14
We give a systematic treatment of a spin 1=2 particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it is largely self-contained and may serve as an introduction to spinors in a Riemann space. The analysis is based on the Dirac equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The restriction to a slowly moving matter source, such as the earth, allows us to describe the gravitational field by a gravitoelectric (Newtonian) potential and a gravitomagnetic (frame-dragging) vector potential, the existence of which has recently been experimentally verified. Our main interest is the coupling of the orbital and spin angular momenta of the particle to the gravitomagnetic field. Specifically we calculate the gravitational gyromagnetic ratio as g{sub g} = 1 ; this is to be compared with the electromagnetic gyromagnetic ratio of g{sub e} = 2 for a Dirac electron.
Dummett vs Bell on quantum mechanics
NASA Astrophysics Data System (ADS)
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.
Hidden variables and nonlocality in quantum mechanics
NASA Astrophysics Data System (ADS)
Hemmick, Douglas Lloyd
1997-05-01
Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call
Quantum-Mechanical Prediction of Nanoscale Photovoltaics.
Zhang, Yu; Meng, LingYi; Yam, ChiYung; Chen, GuanHua
2014-04-03
Previous simulations of photovoltaic devices are based on classical models, which neglect the atomistic details and quantum-mechanical effects besides the dependence on many empirical parameters. Here, within the nonequilibrium Green's function formalism, we present a quantum-mechanical study of the performance of inorganic nanowire-based photovoltaic devices. On the basis of density-functional tight-binding theory, the method allows simulation of current-voltage characteristics and optical properties of photovoltaic devices without relying on empirical parameters. Numerical studies of silicon nanowire-based devices of realistic sizes with 10 000 atoms are performed, and the results indicate that atomistic details and nonequilibrium conditions have a clear impact on the photoresponse of the devices.
Projection quantum mechanics and neutrino mixing
NASA Astrophysics Data System (ADS)
Góźdź, A.; Góźdź, M.
2017-03-01
The theory of neutrino oscillations rests on the assumption, that the interaction basis and the physical (mass) basis of neutrino states are different. Therefore neutrino is produced in a certain welldefined superposition of three mass eigenstates, which propagate separately and may be detected as a different superposition. This is called flavor oscillations. It is, however, not clear why neutrinos behave this way, i.e., what is the underlying mechanism which leads to the production of a superposition of physical states in a single reaction. In this paper we argue, that one of the reasons may be connected with the temporal structure of the process. In order to discuss the role of time in processes on the quantum level, we use a special formulation of the quantum mechanics, which is based on the projection time evolution. We arrive at the conclusion, that for short reaction times the formation of a superposition of states of similar masses is natural.
The preparation of states in quantum mechanics
Fröhlich, Jürg; Schubnel, Baptiste
2016-04-15
The important problem of how to prepare a quantum mechanical system, S, in a specific initial state of interest—e.g., for the purposes of some experiment—is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare S in a preassigned initial state with certainty, i.e., the probability of success in preparing S in a given state is unity. This method relies on coupling S to an open quantum-mechanical environment, E, in such a way that the dynamics of S∨E pulls the state of S towards an “attractor,” which is the desired initial state of S. This method is analyzed in detail.
Applications of computational quantum mechanics
NASA Astrophysics Data System (ADS)
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
Condensed Matter Physics: Does Quantum Mechanics Matter?
NASA Astrophysics Data System (ADS)
Fisher, Michael E.
Herman Feshbach, the organizer of this Symposium in honor of Niels Bohr, asked me, in his original invitation, for a review of the present state of condensed matter physics, with emphasis on major unsolved problems and comments on any overlap with Bohr's ideas regarding the fundamentals of quantum mechanics. That is surely a difficult assignment and, indeed, goes well beyond what is attempted here; nevertheless, I will take the liberty of raising one issue of a philosophical or metaphysical flavor.
A quantum mechanics glimpse to standard cosmology
Barbosa-Cendejas, N.; Reyes, M.
2010-07-12
In this work we present a connection between a standard cosmology model for inflation and quantum mechanics. We consider a time independent Schroedinger type equation derived from the equations of motion for a single scalar field in a flat space time with a FRW metric and a cosmological constant; the fact that the equation of motion is precisely a Schroedinger equation allows us to investigate on the algebraic relations between the two models and probe the consequences derived from this point of view.
Collocation method for fractional quantum mechanics
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A.; Fernandez, Francisco M.
2010-12-15
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.
Grounding quantum probability in psychological mechanism.
Love, Bradley C
2013-06-01
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data.
Quantum Mechanics - Fundamentals and Applications to Technology
NASA Astrophysics Data System (ADS)
Singh, Jasprit
1996-10-01
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 formulation has been derived in a given chapter, the connection to important technological problems is summarily described. The many helpful features include * Twenty-eight application-oriented sections that focus on lasers, transistors, magnetic memories, superconductors, nuclear magnetic resonance (NMR), and other important technology-driving materials and devices * One hundred solved examples, with an emphasis on numerical results and the connection between the physics and its applications * End-of-chapter problems that ground the student in both fundamental and applied concepts * Numerous figures and tables to clarify the various topics and provide a global view of the problems under discussion * Over two hundred illustrations to highlight problems and text A book for the information age, Quantum Mechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.
Hunting for Snarks in Quantum Mechanics
Hestenes, David
2009-12-08
A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.
Classical and quantum-mechanical state reconstruction
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Mello, P. A.; Revzen, M.
2012-07-01
The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that used in medical imaging known as computer-aided tomography. It is remarkable that this method can be taken over to quantum mechanics, where it leads to a description of the quantum state in terms of the Wigner function which, although it may take on negative values, plays the role of the probability density in phase space in classical physics. We then present another approach to quantum state reconstruction based on the notion of mutually unbiased bases—a notion of current research interest, for which we give explanatory remarks—and indicate the relation between these two approaches. Since the subject of state reconstruction is rarely considered at the level of textbooks, the presentation in this paper is aimed at graduate-level readers.
Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices
NASA Astrophysics Data System (ADS)
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
2016-10-01
We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.
Exponential energy growth due to slow parameter oscillations in quantum mechanical systems.
Turaev, Dmitry
2016-05-01
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.
48. MAIN WAREHOUSE THIRD LEVEL Elevator drive mechanism is ...
48. MAIN WAREHOUSE - THIRD LEVEL Elevator drive mechanism is seen to the right, while drive wheels, belt wheels and chain drives are visible in the wooden wall framing. The horizontal metal conveyor (at the top of the wall Just under the inverted 'V' brace) is part of the empty can supply system connected to the external can conveyor. See Photo No. 28. - Hovden Cannery, 886 Cannery Row, Monterey, Monterey County, CA
Quantum mechanics with coordinate dependent noncommutativity
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2013-11-01
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G.
2013-11-15
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
An approach to nonstandard quantum mechanics
NASA Astrophysics Data System (ADS)
Raab, A.
2004-12-01
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to nonrelativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Mo/ller wave operators and the S-matrix.
Indirect Acquisition of Information in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ballesteros, M.; Fraas, M.; Fröhlich, J.; Schubnel, B.
2016-02-01
Long sequences of successive direct (projective) measurements or observations of just a few "uninteresting" physical quantities pertaining to a quantum system, such as clicks of some detectors, may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition observations and measurements in quantum mechanics. Our attempt leads us to make some novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.
Quantum mechanical hamiltonian models of turing machines
NASA Astrophysics Data System (ADS)
Benioff, Paul
1982-11-01
Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.
Bohmian Mechanics In A Macroscopic Quantum System
NASA Astrophysics Data System (ADS)
Haven, Emmanuel
2006-01-01
In the so called `causal' interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.
Unstable trajectories and the quantum mechanical uncertainty
Moser, Hans R.
2008-08-15
There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.
Unstable trajectories and the quantum mechanical uncertainty
NASA Astrophysics Data System (ADS)
Moser, Hans R.
2008-08-01
There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.
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.
QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.
Tesche, C
2000-10-27
In 1935, Erwin Schrödinger suggested his famous gedanken experiment of the cat that is simultaneously "dead" and "alive" inside its box until the box is opened. But as Tesche explains in her Perspective, such a macroscopic manifestation of quantum mechanics has remained elusive until recently. The experiments by van der Wal et al. are an important step toward demonstrating that quantum mechanics can describe macroscopic phenomena. The approach may be exploited in quantum computing and quantum cryptography.
Statistical Mechanics of Quantum Integrable Systems
NASA Astrophysics Data System (ADS)
Wadati, Miki; Kato, Go; Iida, Toshiaki
Recent developments in statistical mechanics of quantum integrable systems are reviewed. Those studies are fundamental and have a renewed interest related to newly developing fields such as atomic Bose-Einstein condensations, photonic crystals and quantum computations. After a brief summary of the basic concepts and methods, the following three topics are discussed. First, by the thermal Bethe ansatz (TBA), a hard-core Bose gas is exactly solved. The model includes fully the effect of excluded volume and is identified to be a c=1 conformal field theory. Second, the cluster expansion method based on the periodic boundary condition for the Bethe wave function, which we call the Bethe ansatz cluster expansion (BACE) method, is developed for a δ-function gas and the XXX Heisenberg chain. This directly proves the TBA and reveals intrinsic properties of quantum integrable systems. Third, for a δ-function gas, the integral equations for the distribution functions of the quasi-momentum and the quasi-particle energy are solved in the form of power series. In the weak coupling case, the results reproduce those of Bogoliubov theory.
The metaphysics of quantum mechanics: Modal interpretations
NASA Astrophysics Data System (ADS)
Gluck, Stuart Murray
2004-11-01
This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.
The Simpson's paradox in quantum mechanics
NASA Astrophysics Data System (ADS)
Selvitella, Alessandro
2017-03-01
In probability and statistics, the Simpson's paradox is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, while the reverse trend appears for the aggregate data. In this paper, we give some results about the occurrence of the Simpson's paradox in quantum mechanics. In particular, we prove that the Simpson's paradox occurs for solutions of the quantum harmonic oscillator both in the stationary case and in the non-stationary case. In the non-stationary case, the Simpson's paradox is persistent: if it occurs at any time t =t ˜ , then it occurs at any time t ≠t ˜ . Moreover, we prove that the Simpson's paradox is not an isolated phenomenon, namely, that, close to initial data for which it occurs, there are lots of initial data (a open neighborhood), for which it still occurs. Differently from the case of the quantum harmonic oscillator, we also prove that the paradox appears (asymptotically) in the context of the nonlinear Schrödinger equation but at intermittent times.
Investigation into mechanical properties of bone and its main constituents
NASA Astrophysics Data System (ADS)
Evdokimenko, Ekaterina
Bone is a hierarchically structured natural composite material, consisting of organic phase (type-I collagen), inorganic phase (hydroxyapatite), and water. Studies of the two main bone constituents, utilizing controlled demineralization and deproteinization, can shed light on mineral-collagen interaction which makes bone such a unique biological material. This knowledge is necessary for computational analysis of bone structure to identify preferential sites in the collagen matrix and mineral network that degrade more easily. The main goal of this work is to develop a comprehensive picture of mechanical properties of bone and its main constituents. Following the Introduction, Chapter 2 presents an investigation of microstructure and compressive mechanical properties of bovine femur cortical bone carried out on completely demineralized, completely deproteinized, and untreated bone samples in three anatomical directions. Anisotropic nature of bone was clearly identified in all cases. Extra levels of porosity along with microstructural differences for the three directions were found to be the main sources of the anisotropy. In Chapter 3, a new theoretical model of cortical and trabecular bone as composite materials with hierarchical structure spanning from nanometer (collagen-mineral) level to millimeter (bone) level was developed. Compression testing was performed on untreated, demineralized, and deproteinized cortical and trabecular bovine femur bone samples to verify the model. The experimental data were compared with theoretical predictions; excellent agreement was found between the theory and experiments for all bone phases. Optical microscopy, scanning electron microscopy, and micro-computed tomography techniques were applied to characterize the structure of the samples at multiple length scales and provide further inputs for the modeling. Chapter 4 presents a comparative study of mechanical properties, microstructure, and porosity of mature and young bovine
Quantum Mechanical Studies of Molecular Hyperpolarizabilities.
1980-04-30
exponent , reflects the screening of an electron in a given orbital by the interior electrons in the atom or molecule. In practice, when studying...Basis sets have evolved over the years in molecular quantum mechanics until sets of orbital exponents for the different atoms composing the molecule have...and R. P. Hurst , J. Chem. Phys. 46, 2356 (1967); S. P. LickmannI and J. W. Moskowitz, J. Chem. Phys. 54, 3622 7T971). 26. T. H. Dunning, J. Chem. Phys
Supersymmetric quantum mechanics and its applications
Sukumar, C.V.
2004-12-23
The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.
BiHermitian supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
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].
Attosecond delays in photoionization: time and quantum mechanics
NASA Astrophysics Data System (ADS)
Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard
2014-10-01
This article addresses topics regarding time measurements performed on quantum systems. The motivation is linked to the advent of ‘attophysics’ which makes feasible to follow the motion of electrons in atoms and molecules, with time resolution at the attosecond (1 as = 10-18 s) level, i.e. at the natural scale for electronic processes in these systems. In this context, attosecond ‘time-delays’ have been recently measured in experiments on photoionization and the question arises if such advances could cast a new light on the still active discussion on the status of the time variable in quantum mechanics. One issue still debatable is how to decide whether one can define a quantum time operator with eigenvalues associated to measurable ‘time-delays’, or time is a parameter, as it is implicit in the Newtonian classical mechanics. One objective of this paper is to investigate if the recent attophysics-based measurements could shed light on this parameter-operator conundrum. To this end, we present here the main features of the theory background, followed by an analysis of the experimental schemes that have been used to evidence attosecond ‘time-delays’ in photoionization. Our conclusion is that these results reinforce the view that time is a parameter which cannot be defined without reference to classical mechanics.
Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons
NASA Astrophysics Data System (ADS)
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.
Quantum Mechanical Study of Nanoscale MOSFET
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Differentiability of correlations in realistic quantum mechanics
Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique; Tresser, Charles
2015-09-15
We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.
Quantum mechanical wavefunction: visualization at undergraduate level
NASA Astrophysics Data System (ADS)
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.
Mathematical model I. Electron and quantum mechanics
NASA Astrophysics Data System (ADS)
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Molecular model with quantum mechanical bonding information.
Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F
2011-11-17
The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.
A quantum protective mechanism in photosynthesis
NASA Astrophysics Data System (ADS)
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-03-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life.
Student Understanding of Time Dependence in Quantum Mechanics
ERIC Educational Resources Information Center
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Student Understanding of Time Dependence in Quantum Mechanics
ERIC Educational Resources Information Center
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Anyons in quantum mechanics with a minimal length
NASA Astrophysics Data System (ADS)
Buisseret, Fabien
2017-02-01
The existence of anyons, i.e. quantum states with an arbitrary spin, is a generic feature of standard quantum mechanics in (2 + 1) -dimensional Minkowski spacetime. Here it is shown that relativistic anyons may exist also in quantum theories where a minimal length is present. The interplay between minimal length and arbitrary spin effects are discussed.
Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy
Grant, A.K.; Rosner, J.L. )
1994-05-01
The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.
New type of N = 4 supersymmetric quantum mechanics
Ivanov, Evgeny; Sidorov, Stepan
2014-07-23
We overview a new type of supersymmetric quantum mechanics models based on the worldline realizations of the supergroup SU(2|1). Our main focus is on the models associated with the chiral multiplets (2,4,2). Considering two nonequivalent deformations of the standard N = 4, d = 1 superspace, we define the relevant chiral superfields and construct their SU(2|1) invariant actions. We give off- and on-shell descriptions of these models and perform their quantization. The basic peculiarities of such models and interrelations between them are briefly discussed.
Foundation of quantum mechanics from the principle of relativity
Nottale, Laurent
2007-04-28
We briefly recall the main steps by which we suggest to found quantum mechanics and gauge field theories on the principle of relativity, once it is extended to scale transformations of the reference system. The wave functions are constructed as consequences of the nondifferentiability of a continuous space-time, while the Schroedinger and Dirac equations are obtained from its geodesics equations. In this framework, the gauge fields emerge as manifestation of the fractal geometry, and the gauge charges as the conservative quantities which are built from its internal symmetries.
Surveying Instructors' Attitudes and Approaches to Teaching Quantum Mechanics
NASA Astrophysics Data System (ADS)
Siddiqui, Shabnam; Singh, Chandralekha
2010-10-01
Understanding instructors' attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, students' preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.
Exponential complexity and ontological theories of quantum mechanics
Montina, A.
2008-02-15
Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.
Paul A.M. Dirac's The Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
2006-12-01
Paul A.M. Dirac’s book, The Principles of Quantum Mechanics, summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use. I discuss the successive editions of Dirac’s book and their critical reception, noting changes, especially in the formulation of the general theory and in its treatment of relativistic quantum theory and quantum electrodynamics. In the case of the later editions, I discuss Dirac’s negative attitude toward renormalized quantum electrodynamics.
Tampering detection system using quantum-mechanical systems
Humble, Travis S [Knoxville, TN; Bennink, Ryan S [Knoxville, TN; Grice, Warren P [Oak Ridge, TN
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.
Sun, Qiming; Chan, Garnet Kin-Lic
2014-09-09
Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.
Testing quantum mechanics using third-order correlations
NASA Astrophysics Data System (ADS)
Kinsler, Paul
1996-04-01
Semiclassical theories similar to stochastic electrodynamics are widely used in optics. The distinguishing feature of such theories is that the quantum uncertainty is represented by random statistical fluctuations. They can successfully predict some quantum-mechanical phenomena; for example, the squeezing of the quantum uncertainty in the parametric oscillator. However, since such theories are not equivalent to quantum mechanics, they will not always be useful. Complex number representations can be used to exactly model the quantum uncertainty, but care has to be taken that approximations do not reduce the description to a hidden variable one. This paper helps show the limitations of ``semiclassical theories,'' and helps show where a true quantum-mechanical treatment needs to be used. Third-order correlations are a test that provides a clear distinction between quantum and hidden variable theories in a way analogous to that provided by the ``all or nothing'' Greenberger-Horne-Zeilinger test of local hidden variable theories.
A short course on quantum mechanics and methods of quantization
NASA Astrophysics Data System (ADS)
Ercolessi, Elisa
2015-07-01
These notes collect the lectures given by the author to the "XXIII International Workshop on Geometry and Physics" held in Granada (Spain) in September 2014. The first part of this paper aims at introducing a mathematical oriented reader to the realm of Quantum Mechanics (QM) and then to present the geometric structures that underline the mathematical formalism of QM which, contrary to what is usually done in Classical Mechanics (CM), are usually not taught in introductory courses. The mathematics related to Hilbert spaces and Differential Geometry are assumed to be known by the reader. In the second part, we concentrate on some quantization procedures, that are founded on the geometric structures of QM — as we have described them in the first part — and represent the ones that are more operatively used in modern theoretical physics. We will discuss first the so-called Coherent State Approach which, mainly complemented by "Feynman Path Integral Technique", is the method which is most widely used in quantum field theory. Finally, we will describe the "Weyl Quantization Approach" which is at the origin of modern tomographic techniques, originally used in optics and now in quantum information theory.
Statistical origin of classical mechanics and quantum mechanics
NASA Astrophysics Data System (ADS)
Chu, Shu-Yuan
1993-11-01
The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.
Harmonizing General Relativity with Quantum Mechanics
NASA Astrophysics Data System (ADS)
Alfonso-Faus, Antonio
2007-04-01
Gravitation is the common underlying texture between General Relativity and Quantum Mechanics. We take gravitation as the link that can make possible the marriage between these two sciences. We use here the duality of Nature for gravitation: A continuous warped space, wave-like, and a discrete quantum gas, particle-like, both coexistent and producing an equilibrium state in the Universe. The result is a static, non expanding, spherical, unlimited and finite Universe, with no cosmological constant and no dark energy. Macht's Principle is reproduced here by the convergence of the two cosmological equations of Einstein. From this a Mass Boom concept is born given by M = t, M the mass of the Universe and t its age. Also a decreasing speed of light is the consequence of the Mass Boom, c = 1/t, which explains the Supernovae Type Ia observations without the need of expansion (nor, of course, accelerated expansion). Our Mass Boom model completely wipes out the problems and paradoxes built in the Big Bang model, like the horizon, monopole, entropy, flatness, fine tuning, etc. It also eliminates the need for inflation.
Causal localizations in relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Castrigiano, Domenico P. L.; Leiseifer, Andreas D.
2015-07-01
Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac's localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.
Dynamical phase transitions in quantum mechanics
NASA Astrophysics Data System (ADS)
Rotter, Ingrid
2012-02-01
The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
Internal clock formulation of quantum mechanics
NASA Astrophysics Data System (ADS)
Małkiewicz, Przemysław; Miroszewski, Artur
2017-08-01
The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational field, which is subject to dynamics. The lack of time does not imply the lack of evolution but rather brings to the forefront the role of internal clocks which are some largely arbitrary internal degrees of freedom with respect to which the evolution of timeless systems can be described. We take this idea seriously and try to understand what it implies for quantum mechanics when the fixed external time is replaced by an arbitrary internal clock. We put the issue in a solid, mathematically rigorous framework. We find that the dynamical interpretation of a quantum state of a timeless system depends on the employed internal clock. In particular, we find that the continuous spectra of well-known dynamical observables like the position of a free particle on the real line may turn discrete if measured in unusual clocks. We discuss the meaning of our result for attempts at quantization of global gravitational degrees of freedom.
Causal localizations in relativistic quantum mechanics
Castrigiano, Domenico P. L. Leiseifer, Andreas D.
2015-07-15
Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.
Extending quantum mechanics entails extending special relativity
NASA Astrophysics Data System (ADS)
Aravinda, S.; Srikanth, R.
2016-05-01
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.
Are quantum-mechanical-like models possible, or necessary, outside quantum physics?
NASA Astrophysics Data System (ADS)
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.
Gauge invariance and reciprocity in quantum mechanics
Leung, P. T.; Young, K.
2010-03-15
Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of e and the flux is produced by a condensate of particles with charge 2e.
Quantum mechanical calculations to chemical accuracy
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.
1991-01-01
The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.
Quantum mechanics of a generalised rigid body
NASA Astrophysics Data System (ADS)
Gripaios, Ben; Sutherland, Dave
2016-05-01
We consider the quantum version of Arnold’s generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of type I) by methods of harmonic analysis. We show how the method can be extended to cosets, generalising the linear rigid rotor. As examples, we consider all connected and simply connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.
Waveform information from quantum mechanical entropy.
Funkhouser, Scott; Suski, William; Winn, Andrew
2016-06-01
Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated 'total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.
Quantum-mechanical suppression of bremsstrahlung
Becker-Szendy, R.; Keller, L.; Niemi, G.; Perl, M.; Rochester, L.; Anthony, P. |; Bosted, P.; Cavalli-Sforza, M.; Kelley, L.; Klein, S.
1994-12-01
The authors have studied quantum-mechanical suppression of bremsstrahlung of low-energy 1-500 MeV photons from high-energy 25 GeV electrons. They have measured the LPM effect, where multiple scattering of the radiating electron destroys coherence required for the emission of low-energy photons, and the dielectric effect, where the emitted photon traveling in the radiator medium interferes with itself. For the experiment, the collaboration developed a novel method of extracting a parasitic low-intensity high-energy electron beam into the fixed target area during normal SLC operation of the accelerator. The results agree quantitatively with Migdal`s calculation of the LPM effect. Surface effects, for which there is no satisfactory theoretical prediction, are visible at low photon energies. For very thin targets, the suppression disappears, as expected. Preliminary results on dielectric suppression of bremsstrahlung are in qualitative agreement with the expectation.
Time Operator in Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Khorasani, Sina
2017-07-01
It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.
Twist deformation of rotationally invariant quantum mechanics
Chakraborty, B.; Kuznetsova, Z.; Toppan, F.
2010-11-15
Noncommutative quantum mechanics in 3D is investigated in the framework of an abelian Drinfeld twist which deforms a given Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential), and the Coulomb potential.
On some hydrodynamical aspects of quantum mechanics
NASA Astrophysics Data System (ADS)
Spera, Mauro
2010-02-01
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial ( i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this “Schrödinger fluid”, together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.
On some hydrodynamical aspects of quantum mechanics
NASA Astrophysics Data System (ADS)
Spera, Mauro
2010-02-01
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial (i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this "Schrödinger fluid", together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.
Categorical quantum mechanics II: Classical-quantum interaction
NASA Astrophysics Data System (ADS)
Coecke, Bob; Kissinger, Aleks
2016-08-01
This is the second part of a three-part overview, in which we derive the category-theoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part, we focus on classical-quantum interaction. Classical and quantum systems are treated as distinct types, of which the respective behavioral properties are specified in terms of processes and their compositions. In particular, classicality is witnessed by ‘spiders’ which fuse together whenever they connect. We define mixedness and show that pure processes are extremal in the space of all processes, and we define entanglement and show that quantum theory indeed exhibits entanglement. We discuss the classification of tripartite qubit entanglement and show that both the GHZ-state and the W-state come from spider-like families of processes, which differ only in how they behave when they are connected by two or more wires. We define measurements and provide fully comprehensive descriptions of several quantum protocols involving classical data flow. Finally, we give a notion of ‘genuine quantumness’, from which special processes called ‘phase spiders’ arise, and get a first glimpse of quantum nonlocality.
New methods for quantum mechanical reaction dynamics
Thompson, Ward Hugh
1996-12-01
Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L^{2}) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC^{-} can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC^{-} geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H_{3}O^{-} system, providing information about the potential energy surface for the OH + H_{2} reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the
Mechanical properties of thermoelectric lanthanum telluride from quantum mechanics
NASA Astrophysics Data System (ADS)
Li, Guodong; Aydemir, Umut; Wood, Max; Goddard, William A., III; Zhai, Pengcheng; Zhang, Qingjie; Snyder, G. Jeffrey
2017-07-01
Lanthanum telluride (La3Te4) is an n-type high-performance thermoelectric material in the high temperature range, but its mechanical properties remain unknown. Since we want robust mechanical properties for their integration into industrial applications, we report here quantum mechanics (QM) simulations to determine the ideal strength and deformation mechanisms of La3Te4 under pure shear deformations. Among all plausible shear deformation paths, we find that shearing along the (0 0 1)/< \\text{1} 0 0> slip system has the lowest ideal shear strength of 0.99 GPa, making it the most likely slip system to be activated under pressure. We find that the long range La-Te ionic interactions play the predominant role in resisting shear deformation. To enhance the mechanical strength, we suggest improving the long ionic La-Te bond stiffness to strengthen the ionic La-Te framework in La3Te4 by a defect-engineering strategy, such as partial substitution of La by Ce or Pr having isotypic crystal structures. This work provides the fundamental information to understand the intrinsic mechanics of La3Te4.
Quantum mechanics of Klein-Gordon-type fields and quantum cosmology
NASA Astrophysics Data System (ADS)
Mostafazadeh, Ali
2004-01-01
based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.
Reverse Causation and the Transactional Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Cramer, John G.
2006-10-01
In the first part of the paper we present the transactional interpretation of quantum mechanics, a method of viewing the formalism of quantum mechanics that provides a way of visualizing quantum events and experiments. In the second part, we present an EPR gedankenexperiment that appears to lead to observer-level reverse causation. A transactional analysis of the experiment is presented. It easily accounts for the reported observations but does not reveal any barriers to its modification for reverse causation.
BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)
NASA Astrophysics Data System (ADS)
Mahler, G.
2004-07-01
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic
Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts
ERIC Educational Resources Information Center
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
2010-01-01
In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…
In Defense of a Heuristic Interpretation of Quantum Mechanics
ERIC Educational Resources Information Center
Healy, Eamonn F.
2010-01-01
Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…
Design and Validation of the Quantum Mechanics Conceptual Survey
ERIC Educational Resources Information Center
McKagan, S. B.; Perkins, K. K.; Wieman, C. E.
2010-01-01
The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…
Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems
ERIC Educational Resources Information Center
Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih
2009-01-01
In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…
Categorization of Quantum Mechanics Problems by Professors and Students
ERIC Educational Resources Information Center
Lin, Shih-Yin; Singh, Chandralekha
2010-01-01
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Do Free Quantum-Mechanical Wave Packets Always Spread?
ERIC Educational Resources Information Center
Klein, James R.
1980-01-01
The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is addressed. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Teaching implications are given.…
A comparative review of four formulations of noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Gouba, Laure
2016-07-01
Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.
Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts
ERIC Educational Resources Information Center
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
2010-01-01
In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…
Quantum Mechanics from Periodic Dynamics: the bosonic case
Dolce, Donatello
2010-05-04
Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.
Do Free Quantum-Mechanical Wave Packets Always Spread?
ERIC Educational Resources Information Center
Klein, James R.
1980-01-01
The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is addressed. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Teaching implications are given.…
An overview of the transactional interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Cramer, J. G.
We summarize the transactional interpretation (TI) of quantum mechanics (QM) and consider various points concerning the TI and its relation to the Copenhagen interpretation (CI). Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantum mechanical interpretations to experimental tests and results are discussed.
An Overview of the Transactional Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Cramer, John G.
1988-02-01
The transactional interpretation of quantum mechanics (TI) is summarized and various points concerning the TI and its relation to the Copenhagen interpretation (CI) are considered. Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantum mechanical interpretations to experimental tests and results are discussed.
Effect of violation of quantum mechanics on neutrino oscillation
Liu, Y.; Hu, L.; Ge, M.
1997-11-01
The effect of quantum mechanics violation due to quantum gravity on neutrino oscillation is investigated. It is found that the mechanism introduced by Ellis, Hagelin, Nanopoulos, and Srednicki through the modification of the Liouville equation can affect neutrino oscillation behavior and may be taken as a new solution of the solar neutrino problem. {copyright} {ital 1997} {ital The American Physical Society}
Categorization of Quantum Mechanics Problems by Professors and Students
ERIC Educational Resources Information Center
Lin, Shih-Yin; Singh, Chandralekha
2010-01-01
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems
ERIC Educational Resources Information Center
Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih
2009-01-01
In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…
Design and Validation of the Quantum Mechanics Conceptual Survey
ERIC Educational Resources Information Center
McKagan, S. B.; Perkins, K. K.; Wieman, C. E.
2010-01-01
The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…
Quantum mechanics on (anti)-de Sitter background
NASA Astrophysics Data System (ADS)
Chung, Won Sang; Hassanabadi, Hassan
2017-08-01
In this paper, the quantum mechanics on the (anti) de Sitter background is investigated. the extended uncertainty principle and the deformed calculus are discussed for the quantum mechanics on the (anti)-de Sitter background. As examples one-dimensional box problem and one-dimensional harmonic oscillator problem are discussed.
In Defense of a Heuristic Interpretation of Quantum Mechanics
ERIC Educational Resources Information Center
Healy, Eamonn F.
2010-01-01
Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…
Quantum mechanical features of optically pumped CW FIR lasers
NASA Technical Reports Server (NTRS)
Seligson, D.; Leite, J. R. R.; Sanchez, A.; Feld, M. S.; Ducloy, M.
1977-01-01
Quantum mechanical predictions for the gain of an optically pumped CW FIR laser are presented for cases in which one or both of the pump and FIR transitions are pressure or Doppler broadened. The results are compared to those based on the rate equation model. Some of the quantum mechanical predictions are verified in CH3OH.
From scalar field theories to supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Bazeia, D.; Bemfica, F. S.
2017-04-01
In this work, we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here, we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.
A snapshot of foundational attitudes toward quantum mechanics
NASA Astrophysics Data System (ADS)
Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton
2013-08-01
Foundational investigations in quantum mechanics, both experimental and theoretical, gave birth to the field of quantum information science. Nevertheless, the foundations of quantum mechanics themselves remain hotly debated in the scientific community, and no consensus on essential questions has been reached. Here, we present the results of a poll carried out among 33 participants of a conference on the foundations of quantum mechanics. The participants completed a questionnaire containing 16 multiple-choice questions probing opinions on quantum-foundational issues. Participants included physicists, philosophers, and mathematicians. We describe our findings, identify commonly held views, and determine strong, medium, and weak correlations between the answers. Our study provides a unique snapshot of current views in the field of quantum foundations, as well as an analysis of the relationships between these views.
Chirality, quantum mechanics, and biological determinism
NASA Astrophysics Data System (ADS)
Davies, P. C. W.
2006-08-01
life with biochemical make-up resembling that of known life. Whilst the experimental search for a second sample of life - possibly by detecting a chiral "anomaly" - continues, some theoretical investigations may be pursued to narrow down the options. Chiral determinism would be an intrinsically quantum process. There are hints that quantum mechanics plays a key role in biology, but the claim remains contentious. Here I review some of the evidence for quantum aspects of biology. I also summarize some proposals for testing biological determinism by seeking evidence for a multiple genesis events on Earth, and for identifying extant "alien microbes" - micro-organisms descended from an independent origin from familiar life.
Quantum mechanics in an evolving Hilbert space
NASA Astrophysics Data System (ADS)
Artacho, Emilio; O'Regan, David D.
2017-03-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.
Glucocorticoids induce retinal toxicity through mechanisms mainly associated with paraptosis.
Valamanesh, Fatemeh; Torriglia, Alicia; Savoldelli, Michéle; Gandolphe, Christelle; Jeanny, Jean-Claude; BenEzra, David; Behar-Cohen, Francine
2007-09-19
Corticosteroids have recorded beneficial clinical effects and are widely used in medicine. In ophthalmology, besides their treatment benefits, side effects, including ocular toxicity have been observed especially when intraocular delivery is used. The mechanism of these toxic events remains, however, poorly understood. In our present study, we investigated the mechanisms and potential pathways of corticosteroid-induced retinal cell death. Rats were sacrificed 24 h and 8 days after an intravitreous injection of 1 microl (40 microg) of Kenacort Retard. The eyes were processed for ultra structure analysis and detection of activated caspase-3, cytochrome-C, apoptosis-inducing factor (AIF), LEI-L-Dnase II, terminal transferase dUTP nick end labeling (TUNEL), and microtubule-associated protein 1-light chain 3 (MAP-LC3). In vitro, rat retinal pigment epithelial cells (RPE), retinal Müller glial cells (RMG) and human ARPE-19 cells were treated with triamcinolone acetonide (TA) or other glucocorticoids. Cell viability was quantified by 3-(4,5-dimethylthiazol-2-yl)-2,5 phenyltetrazolium bromide test (MTT) assay and cell counts. Nuclei staining, TUNEL assay, annexin-V binding, activated caspase-3 and lactate dehydrogenase (LDH) production characterized cell death. Localization of cytochrome-C, AIF, LEI-and L-Dnase II, and staining with MAP-LC3 or monodansylcadaverine were also carried out. Finally, ARPE-19 cells transfected with AIP-1/Alix were exposed to TA. In vitro incubation of retinal cell in the presence of corticosteroids induced a specific and dose-dependent reduction of cell viability. These toxic events were not associated with the anti-inflammatory activity of these compounds but depended on the hydro solubility of their formulation. Before cell death, extensive cytoplasmic vacuolization was observed in the retinal pigment epithelial (RPE) cells in vivo and in vitro. The cells however, did not show known caspase-dependent or caspase-independent apoptotic reactions
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
Statistical mechanics of quantum-classical systems with holonomic constraints.
Sergi, Alessandro
2006-01-14
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
High-efficiency quantum state transfer and quantum memory using a mechanical oscillator
NASA Astrophysics Data System (ADS)
Sete, Eyob A.; Eleuch, H.
2015-03-01
We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical Q factor it is possible to achieve a transfer efficiency of 99.4 % by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of 96 % employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-Q mechanical oscillator.
Calendar effects in quantum mechanics in view of interactive holography
NASA Astrophysics Data System (ADS)
Berkovich, Simon
2013-04-01
Quantum mechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .
Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations
NASA Astrophysics Data System (ADS)
Torromé, Ricardo Gallego
2017-10-01
A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlations must be instantaneous from the point of view of the spacetime description, but the spatial distance up to which they can be observed must be bounded. It is argued how our mechanism avoids Bell theorem and Kochen-Specken theorem. Evidence for non-signaling faster than the speed of light in our proposal is discussed.
Highlighting the Mechanism of the Quantum Speedup by Time-Symmetric and Relational Quantum Mechanics
NASA Astrophysics Data System (ADS)
Castagnoli, Giuseppe
2016-03-01
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice's measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one.
Quantum Mechanics is Incomplete but it is Consistent with Locality
NASA Astrophysics Data System (ADS)
Perlman, H. S.
2017-07-01
Quantum mechanics is seen to be incomplete not because it cannot explain the correlations that characterize entanglement without invoking either non-locality or realism, both of which, despite special relativity or no-go theorems, are at least conceivable. Quantum mechanics is incomplete, in a perhaps broader than hidden variable sense, because it fails to address within its theoretical structure the question of how even a single particle, by being in a given quantum state, causes the frequency distribution of measurement values specified by the state. This incompleteness of quantum mechanics as it is currently conceived is both fundamental and indefeasible. Failure to address the question of how the states of entangled particles are given effect to yield the correlations they specify is simply a particular albeit attention arresting instance of this incompleteness. But if that is so then quantum mechanics cannot be held to be inconsistent with locality.
Representation of natural numbers in quantum mechanics
Benioff, Paul
2001-03-01
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to k-ary representations of length L and to the axioms for arithmetic modulo k{sup L}. A model of the axioms is described based on an abstract L-fold tensor product Hilbert space H{sup arith}. Unitary maps of this space onto a physical parameter based product space H{sup phy} are then described. Each of these maps makes states in H{sup phy}, and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.
Review of student difficulties in upper-level quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha; Marshman, Emily
2015-12-01
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired 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. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students' problem-solving and metacognitive skills in these courses. Some of these studies were multiuniversity investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor, and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties found via research in introductory physics courses. The reasoning difficulties were often due to overgeneralizations of concepts learned in one context to another context where they are not directly applicable. Reasoning difficulties in distinguishing between closely related concepts and in making sense of the formalism of quantum mechanics were common. We conclude with a brief summary of the research-based approaches that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.
Simulation with quantum mechanics/molecular mechanics for drug discovery.
Barbault, Florent; Maurel, François
2015-10-01
Biological macromolecules, such as proteins or nucleic acids, are (still) molecules and thus they follow the same chemical rules that any simple molecule follows, even if their size generally renders accurate studies unhelpful. However, in the context of drug discovery, a detailed analysis of ligand association is required for understanding or predicting their interactions and hybrid quantum mechanics/molecular mechanics (QM/MM) computations are relevant tools to help elucidate this process. In this review, the authors explore the use of QM/MM for drug discovery. After a brief description of the molecular mechanics (MM) technique, the authors describe the subtractive and additive techniques for QM/MM computations. The authors then present several application cases in topics involved in drug discovery. QM/MM have been widely employed during the last decades to study chemical processes such as enzyme-inhibitor interactions. However, despite the enthusiasm around this area, plain MM simulations may be more meaningful than QM/MM. To obtain reliable results, the authors suggest fixing several keystone parameters according to the underlying chemistry of each studied system.
Simulation with quantum mechanics/molecular mechanics for drug discovery.
Barbault, Florent; Maurel, François
2015-08-08
Biological macromolecules, such as proteins or nucleic acids, are (still) molecules and thus they follow the same chemical rules that any simple molecule follows, even if their size generally renders accurate studies unhelpful. However, in the context of drug discovery, a detailed analysis of ligand association is required for understanding or predicting their interactions and hybrid quantum mechanics/molecular mechanics (QM/MM) computations are relevant tools to help elucidate this process. Areas covered: In this review, the authors explore the use of QM/MM for drug discovery. After a brief description of the molecular mechanics (MM) technique, the authors describe the subtractive and additive techniques for QM/MM computations. The authors then present several application cases in topics involved in drug discovery. Expert opinion: QM/MM have been widely employed during the last decades to study chemical processes such as enzyme-inhibitor interactions. However, despite the enthusiasm around this area, plain MM simulations may be more meaningful than QM/MM. To obtain reliable results, the authors suggest fixing several keystone parameters according to the underlying chemistry of each studied system.
The representation of numbers in quantum mechanics.
Benioff, P.; Physics
2002-12-01
Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to addition of k {l_brace}j-1{r_brace} if j>0 and k {l_brace}j{r_brace} if j<0 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on the successor for j=1 only. This is the only successor defined in the usual axioms of arithmetic.
Quantum mechanical studies of DNA and LNA.
Koch, Troels; Shim, Irene; Lindow, Morten; Ørum, Henrik; Bohr, Henrik G
2014-04-01
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 electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs.
"Mysticism" in Quantum Mechanics: The Forgotten Controversy
ERIC Educational Resources Information Center
Marin, Juan Miguel
2009-01-01
This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…
"Mysticism" in Quantum Mechanics: The Forgotten Controversy
ERIC Educational Resources Information Center
Marin, Juan Miguel
2009-01-01
This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…
Yang, C.-D. . E-mail: cdyang@mail.ncku.edu.tw
2006-12-15
This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schroedinger equation. Using complex canonical variables, a formal proof of the quantization axiom p {sup {yields}} p = -ih{nabla}, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov-Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion.
The physical principles of quantum mechanics. A critical review
NASA Astrophysics Data System (ADS)
Strocchi, F.
2012-01-01
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
Ruling out multi-order interference in quantum mechanics.
Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Laflamme, Raymond; Weihs, Gregor
2010-07-23
Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10(-2) of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.
The actual content of quantum theoretical kinematics and mechanics
NASA Technical Reports Server (NTRS)
Heisenberg, W.
1983-01-01
First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory.
Predicting crystal structure by merging data mining with quantum mechanics.
Fischer, Christopher C; Tibbetts, Kevin J; Morgan, Dane; Ceder, Gerbrand
2006-08-01
Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an algorithm to direct the search through the large space of possible structures is found. We present a new approach to the prediction of structure that rigorously mines correlations embodied within experimental data and uses them to direct quantum mechanical techniques efficiently towards the stable crystal structure of materials.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2016-05-01
We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude that although the time-evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechanics remain as nonlocal as quantum mechanics itself.
Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics
NASA Astrophysics Data System (ADS)
Goff, Allan
2006-11-01
Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child's game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move ("spooky" marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation.
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-14
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.
Burger, Steven K; Schofield, Jeremy; Ayers, Paul W
2013-12-05
We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation
NASA Astrophysics Data System (ADS)
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-01
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
Quantum mechanical generalization of the balistic electron wind theory
NASA Astrophysics Data System (ADS)
Lacina, A.
1980-06-01
The Fiks' quasiclassical theory of the electron wind force is quantum mechanically generalized. Within the framework of this generalization the space dependence of the electron wind force is calculated in the vicinity of an interface between two media. It is found that quantum corrections may be comparable with or even greater than corresponding quasiclassical values.
New Potentials for Old: The Darboux Transformation in Quantum Mechanics
ERIC Educational Resources Information Center
Williams, Brian Wesley; Celius, Tevye C.
2008-01-01
The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…
New Potentials for Old: The Darboux Transformation in Quantum Mechanics
ERIC Educational Resources Information Center
Williams, Brian Wesley; Celius, Tevye C.
2008-01-01
The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…
Why space has three dimensions: A quantum mechanical explanation
NASA Astrophysics Data System (ADS)
Marcer, Peter; Schempp, Walter
2000-05-01
The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual's perception and cognition will be of a three dimensional world, defined similarly in relation to each individual's quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium. .
Quantum Computer Games: Quantum Minesweeper
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum Computer Games: Quantum Minesweeper
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
On Heat in a Quantum Mechanical Process
NASA Astrophysics Data System (ADS)
Deesuwan, Tanapat; Anders, Janet
2013-05-01
Heat is the portion of energy exchange between systems in thermodynamic process which, unlike work, is always associated with the change of the entropies of the systems. In the context of quantum thermodynamics, heat process is described by an incoherent generalised quantum evolution, which is a map between two quantum states that does not preserve the entropy. Based on an information-theoretic reasoning, we propose that heat involving in a general quantum thermodynamic process can be separated into two types: one that is due to the unital subclass of the evolutions and another one that is due to the others. According to these categories, we show how the former type of heat can be incorporated into Jarzynski equality, resulting in a generalised version of the equality. We also derive a Jarzynski inequality which incorporates all heat into the picture and show that this situation is just equivalent to the presence of Maxwell's demon.
Quantum Mechanics in Biology: Photoexcitations in DNA
NASA Astrophysics Data System (ADS)
Bittner, Eric R.; Czader, Arkadiusz
We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson/Crick pairs in localizing an excitation and then quenching it through intersystem crossing and charge transfer.
Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks.
Shen, Lin; Wu, Jingheng; Yang, Weitao
2016-10-11
Molecular dynamics simulation with multiscale quantum mechanics/molecular mechanics (QM/MM) methods is a very powerful tool for understanding the mechanism of chemical and biological processes in solution or enzymes. However, its computational cost can be too high for many biochemical systems because of the large number of ab initio QM calculations. Semiempirical QM/MM simulations have much higher efficiency. Its accuracy can be improved with a correction to reach the ab initio QM/MM level. The computational cost on the ab initio calculation for the correction determines the efficiency. In this paper we developed a neural network method for QM/MM calculation as an extension of the neural-network representation reported by Behler and Parrinello. With this approach, the potential energy of any configuration along the reaction path for a given QM/MM system can be predicted at the ab initio QM/MM level based on the semiempirical QM/MM simulations. We further applied this method to three reactions in water to calculate the free energy changes. The free-energy profile obtained from the semiempirical QM/MM simulation is corrected to the ab initio QM/MM level with the potential energies predicted with the constructed neural network. The results are in excellent accordance with the reference data that are obtained from the ab initio QM/MM molecular dynamics simulation or corrected with direct ab initio QM/MM potential energies. Compared with the correction using direct ab initio QM/MM potential energies, our method shows a speed-up of 1 or 2 orders of magnitude. It demonstrates that the neural network method combined with the semiempirical QM/MM calculation can be an efficient and reliable strategy for chemical reaction simulations.
Jensen-Shannon Divergence: A Multipurpose Distance for Statistical and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lamberti, Pedro W.; Majtey, Ana P.; Madrid, Marcos; Pereyra, María E.
2007-05-01
Many problems of statistical and quantum mechanics can be established in terms of a distance; in the first case the distance is usually defined between probability distributions; in the second one, between quantum states. The present work is devoted to review the main properties of a distance known as the Jensen-Shannon divergence (JSD) in its classical and quantum version. We present two examples of application of this distance: in the first one we use it as a quantifiers of the stochastic resonance phenomenon in ion channels; in the second one we use the JSD to propose a geometrical view of entanglement for two qubits states.
Probabilistic Approach to Teaching the Principles of Quantum Mechanics
ERIC Educational Resources Information Center
Santos, Emilio
1976-01-01
Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)
Particles, Waves, and the Interpretation of Quantum Mechanics
ERIC Educational Resources Information Center
Christoudouleas, N. D.
1975-01-01
Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)
Macroscopic test of quantum mechanics versus stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Chaturvedi, S.; Drummond, Peter D.
1997-02-01
We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.
Generalized Weyl-Wigner map and Vey quantum mechanics
NASA Astrophysics Data System (ADS)
Dias, Nuno Costa; Prata, João Nuno
2001-12-01
The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations, is still missing. In this article we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.
Why are probabilistic laws governing quantum mechanics and neurobiology?
NASA Astrophysics Data System (ADS)
Kröger, Helmut
2005-08-01
We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.
Sachdev–Ye–Kitaev model as Liouville quantum mechanics
Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
2016-08-08
Here, we show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics.
A Simplified Quantum Mechanical Model of Diatomic Molecules
ERIC Educational Resources Information Center
Nielsen, Lars Drud
1978-01-01
Introduces a simple one-dimensional model of a diatomic molecule that can explain all the essential features of a real two particle quantum mechanical system and gives quantitative results in fair agreement with those of a hydrogen molecule. (GA)
Quantum mechanics of the inverted oscillator potential
NASA Astrophysics Data System (ADS)
Barton, G.
1986-02-01
The Hamiltonian ( 1/2m)p 2 - 1/2mω 2x 2 yields equations solvable in closed form; one is led to them by questions about the longest mean sojourn time T allowed by quantum mechanics to a system near unstable equilibrium. These equations are then studied further in their own right. After criticism of earlier arguments, one finds, by aid of the Green's function, that T ˜ ω -1log{ l/( {h̷}/{mω) 1/2}} for sojourn in the region | x| < l, where l is the resolving power of the detector. Without appeal to some parameter like l one would get nonsense estimates T ˜ ω-1 (e.g., from the nondecay probability familiar in the decay of metastable states). in this potential wavepackets Gaussian in position do not split on impact: their peaks are either transmitted or reflected, depending on the sign of the energy E ≷ 0; however, they spread so fast that not all the probability ends up on the same side of the origin as the peak. The energy eigenfunctions (parabolic cylinder functions) identify the transmission and reflection amplitudes as T = (1 + e -2πE) -1/2eiφ, R = -i(1 + e -2πE) -1/2 e -πE e iφ, where φ = arg Γ( 1/2 - iE) (in units where 2m = 1 = ω = h̷). The density of states for the interval | x| ≤ L is 2π -1 log L + π -1ϕ'( E). Wavepackets that are peaked sharply enough in energy travel without dispersion in the asymptotic region | x| > | E|, and do split on impact in the usual way. The travel times and time delays of these packets are determined. For both reflection and transmission, and for both E ≷ 0, the time delays are given by φ'( E), which is a symmetric function of E, with a positive maximum at E = 0. In particular, packets tunneling under the barrier reemerge sooner if their energy is more negative. This paradox (which occurs also in other tunneling problems) is elucidated as far as possible. Coherent states are constructed by analogy to those of the ordinary oscillator. Though not integrable, their probability distributions do have a
Relativistic Quantum Mechanics and Introduction to Field Theory
NASA Astrophysics Data System (ADS)
Yndurain, Francisco J.
This is an advanced textbook meant as a primer in quantum theory for graduate students. A full relativistic treatment of particle dynamics needs to be based on quantum field theory. However, there exists a variety of processes that can be discussed with concepts like potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory the author emphasizes the deduction of the said potentials or currents. The unique feature of this book is the modern presentation of the subject together with many exercises and furthermore the underlying concept to combine a reference book on relativistic quantum mechanics with an introduction into quantum field theory.
Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Auffèves, Alexia; Grangier, Philippe
2016-02-01
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
Probability in the Many-Worlds Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Vaidman, Lev
It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.
Quantum Mechanics/Molecular Mechanics Study of the Sialyltransferase Reaction Mechanism.
Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori
2016-10-11
The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantum mechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an SN1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantum mechanical interaction with CMP.
$\\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS
NASA Astrophysics Data System (ADS)
Tanaka, Toshiaki
2012-03-01
We formulate Ņ-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix two-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems, both of which are characterized by two arbitrary scalar functions, and one of which does not reduce to the scalar system. The obtained systems are all weakly quasi-solvable.
Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.
Goldfarb, Yair; Degani, Ilan; Tannor, David J
2006-12-21
In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.
Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics
Goldfarb, Yair; Degani, Ilan; Tannor, David J.
2006-12-21
In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared--it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification - a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10{sup -7} calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.
Sensible Quantum Mechanics:. are Probabilities Only in the Mind?
NASA Astrophysics Data System (ADS)
Page, Don N.
Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth.
Quantum mechanical effects in plasmonic structures with subnanometre gaps
Zhu, Wenqi; Esteban, Ruben; Borisov, Andrei G.; Baumberg, Jeremy J.; Nordlander, Peter; Lezec, Henri J.; Aizpurua, Javier; Crozier, Kenneth B.
2016-01-01
Metallic structures with nanogap features have proven highly effective as building blocks for plasmonic systems, as they can provide a wide tuning range of operating frequencies and large near-field enhancements. Recent work has shown that quantum mechanical effects such as electron tunnelling and nonlocal screening become important as the gap distances approach the subnanometre length-scale. Such quantum effects challenge the classical picture of nanogap plasmons and have stimulated a number of theoretical and experimental studies. This review outlines the findings of many groups into quantum mechanical effects in nanogap plasmons, and discusses outstanding challenges and future directions. PMID:27255556
Acoustic Analog to Quantum Mechanical Level-Splitting
NASA Astrophysics Data System (ADS)
Hilbert, Shawn
2010-03-01
One difficulty in teaching quantum mechanics is the lack of classroom demonstrations. To sidestep this issue, analogies can provide an enlightening alternative. Acoustics governance by the same time-independent wave equation as quantum mechanics supports it use in such analogies. This presentation examines one such analogy for an infinite potential well with a delta potential perturbation. The physical acoustic system consists of continuous sounds waves traveling in a pair of tubes which are separated by a variable diaphragm. The level-splitting nature of the quantum system can be mimicked in the acoustic system.
Developing mechanical milking in camels? Some main steps to take….
Marnet, Pierre Guy; Atigui, Moufida; Hammadi, Mohamed
2016-06-01
After a first phase of development in the ex-Soviet Union in the 1940s, camel mechanical milking is now developing again in the Arabic peninsula, North and East Africa, Asia, Australia and even in the USA and Europe in a lesser extent, because of the great demand and important health value of camel milk. Nevertheless, such a development remains empirical and uses trial and error methodology, which is generally more time-consuming and more expensive and could create a deadlock in the situation. Nevertheless, developing mechanical milking of camels could be done throughout a step by step well-designed approach rather than this empirical approach. It is the only way to understand the animal/machine interaction and to give us the means to adapt machine milking to the different situations encountered in the world and to animal specificities.After describing the different essential and ancillary steps of this development (knowledge of animal physiology, udder and teat shapes, teat functional characteristics, first functional data of milking including teat reaction, milk emission kinetic, efficiency of milk extraction, weaning procedure, milking procedure, milking behavior of animals, adaptation of material and settings…), we aim to relate, as example, the first results obtained in Tunisian dromedary camels in the last 4 years as basis for more adapted or even specific materials and setting evolution.
Quantum Mechanical Oscillators: NIST-7 and Beyond
NASA Astrophysics Data System (ADS)
Drullinger, Robert E.
1996-03-01
Time and its inverse, frequency, are the most precisely measurable of all quantities. We routinely make measurements to a precision of a part in 10^12 in just one second and a part in 10^17 in one day. As a result of this measurement precision, some other units are cast in terms of frequency; e. g., voltage through the Josephson volt and length through the defined speed of light. Additionally, practical measurements are often made with frequency transducers; e. g., quartz resonator film thickness monitors, temperature probes, and pressure sensors. Time and frequency are also very important in modern telecommunications, navigation, and security systems. For all of these reasons, we need very highly accurate and widely available standards of frequency and time. We use ``quantum mechanical oscillators,'' transitions in atoms and molecules, for these standards because their systematic biases can be determined to a high degree and their frequency is reproducible any place in the universe within the known laws of physics. Fortunately, this area of technology and atomic physics is very dynamic, often leading advances in spectroscopic resolution and technology. Standards for time and frequency have improved five orders of magnitude over the last 35 years and there is no end in sight. We will briefly discuss the historical development of atomic beam standards to show how accuracy has evolved. We will then discuss the design and accuracy evaluation of NIST-7, a state-of-the-art thermal-cesium-beam magnetic-resonance spectrometer with optical state preparation and detection, which is the current US primary frequency standard. Development of this standard has been accompanied by major advances in error analysis methodology. When describing NIST-7 in the terms of an atomic frequency standard, we say each systematic bias can ultimately be evaluated to a fractional frequency uncertainty of a few parts in 10^16 which will result in an overall uncertainty in the accuracy of the
'Mysticism' in quantum mechanics: the forgotten controversy
NASA Astrophysics Data System (ADS)
Marin, Juan Miguel
2009-07-01
This paper argues that a European controversy over a 'mystical' hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s—birth of quantum theory—and concluding with Erwin Schrödinger's lectures published as 'Mind and Matter'. Becoming aware of the issues at stake can help us understand the historical, philosophical and cultural background from which today's physics emerged.
Quantum-mechanical properties of Bessel beams
Jauregui, R.; Hacyan, S.
2005-03-01
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. As we show explicitly, the operators that are usually associated with linear momentum, orbital angular momentum, and spin do not satisfy the algebra of the translation and rotation group. Nevertheless, we identify some components of these operators that represent observable quantities in an appropriate basis, thus characterizing the quantum numbers of Bessel photons. Some physical consequences of these results are discussed.
Quantum mechanics simulation of protein dynamics on long timescale.
Liu, H; Elstner, M; Kaxiras, E; Frauenheim, T; Hermans, J; Yang, W
2001-09-01
Protein structure and dynamics are the keys to a wide range of problems in biology. In principle, both can be fully understood by using quantum mechanics as the ultimate tool to unveil the molecular interactions involved. Indeed, quantum mechanics of atoms and molecules have come to play a central role in chemistry and physics. In practice, however, direct application of quantum mechanics to protein systems has been prohibited by the large molecular size of proteins. As a consequence, there is no general quantum mechanical treatment that not only exceeds the accuracy of state-of-the-art empirical models for proteins but also maintains the efficiency needed for extensive sampling in the conformational space, a requirement mandated by the complexity of protein systems. Here we show that, given recent developments in methods, a general quantum mechanical-based treatment can be constructed. We report a molecular dynamics simulation of a protein, crambin, in solution for 350 ps in which we combine a semiempirical quantum-mechanical description of the entire protein with a description of the surrounding solvent, and solvent-protein interactions based on a molecular mechanics force field. Comparison with a recent very high-resolution crystal structure of crambin (Jelsch et al., Proc Natl Acad Sci USA 2000;102:2246-2251) shows that geometrical detail is better reproduced in this simulation than when several alternate molecular mechanics force fields are used to describe the entire system of protein and solvent, even though the structure is no less flexible. Individual atomic charges deviate in both directions from "canonical" values, and some charge transfer is found between the N and C-termini. The capability of simulating protein dynamics on and beyond the few hundred ps timescale with a demonstrably accurate quantum mechanical model will bring new opportunities to extend our understanding of a range of basic processes in biology such as molecular recognition and enzyme
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Virtual Learning Environment for Interactive Engagement with Advanced Quantum Mechanics
NASA Astrophysics Data System (ADS)
Pedersen, Mads Kock; Skyum, Birk; Heck, Robert; Müller, Romain; Bason, Mark; Lieberoth, Andreas; Sherson, Jacob F.
2016-06-01
A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantum mechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantum mechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantum mechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances.
Deformation quantization: Quantum mechanics lives and works in phase space
NASA Astrophysics Data System (ADS)
Zachos, Cosmas K.
2014-09-01
Wigner's 1932 quasi-probability Distribution Function in phase-space, his first paper in English, is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in semiclassical limits; quantum optics; nuclear and physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" puzzles; molecular Talbot-Lau interferometry; atomic measurements. It is further of great importance in signal processing (time-frequency analysis). Nevertheless, a remarkable aspect of its internal logic, pioneered by H. Groenewold and J. Moyal, has only blossomed in the last quarter-century: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert Space (the gold medal), or Path Integral (the silver medal) formulations, and perhaps more intuitive, since it shares language with classical mechanics: one need not choose sides between coordinate or momentum space variables, since it is formulated simultaneously in terms of position and momentum. This bronze medal formulation is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner, so that it offers unique insights into the classical limit of quantum theory. The observables in this formulation are cnumber functions in phase space instead of operators, with the same interpretation as their classical counterparts, only now composed together in novel algebraic ways using star products. One might then envision an imaginary world in which this formulation of quantum mechanics had preceded the conventional Hilbert-space formulation, and its own techniques and methods had arisen independently, perhaps out of generalizations of classical mechanics and statistical mechanics. A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002), and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in
Quantum mechanics and reality: An interpretation of Everett's theory
NASA Astrophysics Data System (ADS)
Lehner, Christoph Albert
The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious
The Transactional Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Kastner, Ruth E.
2012-10-01
Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.
Classical and Quantum-Mechanical State Reconstruction
ERIC Educational Resources Information Center
Khanna, F. C.; Mello, P. A.; Revzen, M.
2012-01-01
The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…
Classical and Quantum-Mechanical State Reconstruction
ERIC Educational Resources Information Center
Khanna, F. C.; Mello, P. A.; Revzen, M.
2012-01-01
The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…
Quantum mechanics of time travel through post-selected teleportation
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Maccone, Lorenzo; Garcia-Patron, Raul; Giovannetti, Vittorio; Shikano, Yutaka
2011-07-01
This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch’s theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.
NASA Astrophysics Data System (ADS)
Elbaz, Edgard
This book gives a new insight into the interpretation of quantum mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (quantum electrodynamics), supersymmetry and quantum cosmology.
[Study on main pharmacodynamics and underlying mechanisms of 999 Ganmaoling].
Xu, Qi-Hua; He, Rong; Peng, Bo; Ye, Zu-Guang; Li, Jian-Rong; Zhang, Yue-Fei; Dai, Zhi
2016-04-01
To observe synergistic effects of 999 Ganmaoling (GML) and its Chinese/Western materia medica (CMM and WMM) on pharmacodynamic action and to study underlying mechanisms, their anti-inflammatory, antipyretic effects were compared by assaying the increased capillary permeability induced by glacial acetic acid in mice, ear swelling induced by Xylene in mice, non-specific pleurisy induced by carrageenan in rats, and yeast induced fever in rats. Crystal violet (CV) and microbial activity (XTT) assay were used to evaluate the inhibition of GML and its CMM and WMM on KPN biofilm formation, and scanning electron microscopy (SEM) was applied for observing KPN biofilm morphology changes. The results showed that compared with control group, GML could reduce exudation amount of Evans-Blue and the degree of Ear swelling significantly, and CMM and WMM have no significant effects. The concentration of TNF-α and IL-1β of rat pleural effusion in GML, CMM and WMM group decreased significantly. The concentration of TNF-α, IL-1β and IL-8 in GML group, TNF-α, IL-8 in WMM group and IL-8 in CMM in rats serum decreased significantly. The body temperature in rats decreased significantly in GML and WMM group after 4-8 h of administration. CMM group showed no significant difference in rat body temperature compare with control. Compared with control group, GML (55-13.75 g•L⁻¹) could inhibit KPN biofilm formation and reduce number of viable cells in the KPN biofilm. CMM (45-22.5 g•L⁻¹) and WMM (10 g•L⁻¹) could also inhibit KPN biofilm formation and reduce number of viable cells (P<0.01). Result of SEM also showed that GML (55 g•L⁻¹) and its CMM (45 g•L⁻¹) and WMM (10 g•L⁻¹) could interfere the bacterial arrangement of KPN biofilm and extracellular matrix. GML and its CMM & WMM could inhibit the formation of KPN biofilm, CMM & WMM in GML showed synergism and complementation in inhibit KPN biofilm. Results showed that GML had obvious anti-inflammatory and
NASA Astrophysics Data System (ADS)
Socorro, J.; Nuñez, Omar E.
2017-04-01
The multi-scalar field cosmology of the anisotropic Bianchi type-I model is used in order to construct a family of potentials that are the best suited to model the inflation phenomenon. We employ the quantum potential approach to quantum mechanics due to Bohm in order to solve the corresponding Wheeler-DeWitt equation; which in turn enables us to restrict sensibly the aforementioned family of potentials. Supersymmetric Quantum Mechanics (SUSYQM) is also employed in order to constrain the superpotential function, at the same time the tools from SUSY Quantum Mechanics are used to test the family of potentials in order to infer which is the most convenient for the inflation epoch. For completeness solutions to the wave function of the universe are also presented.
A Non-Intuitionist's Approach To The Interpretation Problem Of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Grelland, Hans Herlof
2005-02-01
A philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language-dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.
Analogies between optical and quantum mechanical angular momentum
NASA Astrophysics Data System (ADS)
Nienhuis, Gerard
2017-02-01
The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied. This article is part of the themed issue 'Optical orbital angular momentum'.
A modified Lax-Phillips scattering theory for quantum mechanics
NASA Astrophysics Data System (ADS)
Strauss, Y.
2015-07-01
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Analogies between optical and quantum mechanical angular momentum.
Nienhuis, Gerard
2017-02-28
The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied.This article is part of the themed issue 'Optical orbital angular momentum'.
Quantum mechanics on profinite groups and partial order
NASA Astrophysics Data System (ADS)
Vourdas, A.
2013-02-01
Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group { {Z}}_p and momenta in the group { {Q}}_p/{ {Z}}_p, and a quantum system with positions in the profinite group {\\widehat{ {Z}}} and momenta in the group { {Q}}/{ {Z}}. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T0-topologies, in a quantum mechanical context, is discussed.
Student understanding of time dependence in quantum mechanics
NASA Astrophysics Data System (ADS)
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-12-01
[This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.
A modified Lax-Phillips scattering theory for quantum mechanics
Strauss, Y.
2015-07-15
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Dirac particle in gravitational quantum mechanics
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2011-08-01
In this Letter, we consider the effects of the Generalized (Gravitational) Uncertainty Principle (GUP) on the eigenvalues and the eigenfunctions of the Dirac equation. This form of GUP is consistent with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. The modified Hamiltonian contains two additional terms proportional to a( and a( where αi are Dirac matrices and a∼1/MPlc is the GUP parameter. For the case of the Dirac free particle and the Dirac particle in a box, we solve the generalized Dirac equation and find the modified energy eigenvalues and eigenfunctions.
Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'
Stapp, H.P.
1999-04-14
A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ''smuggled'' in. That argument is examined here and shown, I believe, to be defective.
Quantum Mechanics for Beginning Physics Students
NASA Astrophysics Data System (ADS)
Schneider, Mark B.
2010-10-01
The past two decades of attention to introductory physics education has emphasized enhanced development of conceptual understanding to accompany calculational ability. Given this, it is surprising that current texts continue to rely on the Bohr model to develop a flawed intuition, and introduce correct atomic physics on an ad hoc basis. For example, Halliday, Resnick, and Walker describe the origin of atomic quantum numbers as such: "The restrictions on the values of the quantum number for the hydrogen atom, as listed in Table 39-2, are not arbitrary but come out of the solution to Schrödinger's equation." They give no further justification, but do point out the values are in conflict with the predictions of the Bohr model.
Use of mathematical logical concepts in quantum mechanics: an example
NASA Astrophysics Data System (ADS)
Benioff, Paul
2002-07-01
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown that the relation between the potential meaning, if any, of word states and the quantum algorithmic complexity of the process generating the word states must be quite complex or nonexistent.
Models on the boundary between classical and quantum mechanics.
Hooft, Gerard 't
2015-08-06
Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.
Cosmology and the pilot wave interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Tipler, Frank J.
1984-07-01
Bell has recently revived the pilot wave interpretation of de Broglie and Bohm as a possible scheme for interpreting wave functions in quantum cosmology. I argue that the pilot wave interpretation cannot be applied consistently to systems whose wave functions split into macroscopically distinguishable states. At some stage the pilot wave interpretation must either tacitly invoke wave function reduction in the same manner as the Copenhagen interpretation, or else abandon locality by requiring physical particles to move faster than light. Consequently, the many-worlds interpretation is the only known realist interpretation of the quantum mechanical formalism which can be extended to quantum cosmology.
ysteries, Puzzles, and Paradoxes in Quantum Mechanics. Proceedings
Rodolfo, B.
1999-02-01
These proceedings represent papers presented at the Mysteries, Puzzles, and Paradoxes in Quantum Mechanics Workshop held in Italy, in August 1998. The Workshop was devoted to recent experimental and theoretical advances such as new interference, effects, the quantum eraser, non{minus}disturbing and Schroedinger{minus}cat{minus}like states, experiments, EPR correlations, teleportation, superluminal effects, quantum information and computing, locality and causality, decoherence and measurement theory. Tachyonic information transfer was also discussed. There were 45 papers presented at the conference,out of which 2 have been abstracted for the Energy,Science and Technology database.(AIP)
Mathematical foundations of quantum mechanics: An advanced short course
NASA Astrophysics Data System (ADS)
Moretti, Valter
2016-08-01
This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.
Multiscale quantum mechanics/electromagnetics simulation for electronic devices.
Yam, ChiYung; Meng, Lingyi; Chen, GuanHua; Chen, Quan; Wong, Ngai
2011-08-28
The continuous downsizing of modern electronic devices implies the increasing importance of quantum phenomena. As the feature sizes of transistors inch towards 10 nanometer, simulations including quantum effects and atomistic details are inevitable. Here we report a novel hybrid quantum mechanics and electromagnetics (QM/EM) method to model individual electronic components at the nanoscale. QM and EM models are solved in different regions of the system in a self-consistent manner. As a demonstration, we study a carbon nanotube based electronic device embedded in a silicon block. Good agreement is obtained between simulation by QM/EM method and full QM treatment of the entire system.
Quantum mechanics from an equivalence principle
Faraggi, A.E.; Matone, M.
1997-05-15
The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.
Randomness in quantum mechanics - nature's ultimate cryptogram?
NASA Astrophysics Data System (ADS)
Erber, T.; Putterman, S.
1985-11-01
The possibility that a single atom irradiated by coherent light will be equivalent to an infinite computer with regard to its ability to generate random numbers is addressed. A search for unexpected patterns of order by crypt analysis of the telegraph signal generated by the on/off time of the atom's fluorescence is described. The results will provide new experimental tests of the fundamental principles of quantum theory.
Quantum mechanical models with strictly ergodic disorder
NASA Astrophysics Data System (ADS)
Mavi, Rajinder
We study quantum Hamiltonians with potentials defined by strictly ergodic dynamical systems. Our interest here are models where physical properties are understood in some regimes of disorder and the extent to which they vary in alternate regimes of disorder. For Schrodinger operators we show properties known to hold in the case of analytic potentials on the torus hold even for rough potentials only required to be Holder continuous. Specifically in this case we show, assuming a positive Lyapunov exponent, dynamical localization properties hold; as well as continuity of the measure of the spectrum for all rotations. For the quantum Ising model we show for phase structure that occur in the random regime, there are similar conditions for existence under the assumption of strictly ergodic dynamics. That is, moment conditions for random disorder are paralleled by conditions on the sampling functions in deterministic disorder. We obtain conditions for existence of phase transitions given any strictly egodically defined disorder. In addition, a new multiscale analysis method is developed to show the existence of stretched exponential decay in the random cluster model generalization of the quantum Ising model where only slower decay was obainable by previous methods.
Quantum mechanical signature in exclusive coherent pion production
NASA Technical Reports Server (NTRS)
Deutchman, P. A.; Buvel, R. L.; Maung, K. M.; Norbury, J. W.; Townsend, L. W.
1986-01-01
We calculate the coherent production of pions from subthreshold to relativistic energies in heavy-ion collisions using a quantum, microscopic, many-body model. For the first time, in this approach, we use harmonic oscillator wave functions to describe shell-model information. The theoretical quantum mechanical results obtained for the pion spectra represent an important improvement over our previous microscopic, many-body calculations.
2016 Summer Series - Mark Kasevich: Quantum Mechanics at Macroscopic Scales
2016-06-09
The underpinning of the universe is quantum mechanics. It can be used to explain the observed particle and wave nature of atoms. Atom interferometry uses the wave characteristics of atoms to investigate fundamental physics and advance our understanding of the macroscopic world. NASA is working with Dr. Mark Kasevich to apply this technology to advance astrophysics and improve navigation. In his seminar, Kasevich will delve into the world of atom interferometry, gravitational waves and quantum sensors.
The conceptual and the anecdotal history of quantum mechanics
NASA Astrophysics Data System (ADS)
Beller, Mara
1996-04-01
The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such “anecdotal” factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.
Preparing a mechanical oscillator in non-gaussian quantum states.
Khalili, Farid; Danilishin, Stefan; Miao, Haixing; Müller-Ebhardt, Helge; Yang, Huan; Chen, Yanbei
2010-08-13
We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant approach for solving non-Markovian open quantum dynamics in general linear systems.
Photon physics: from wave mechanics to quantum electrodynamics
NASA Astrophysics Data System (ADS)
Keller, Ole
2009-05-01
When rewritten in an appropriate manner, the microscopic Maxwell-Lorentz equations appear as a wave-mechanical theory for photons, and their quantum physical interaction with matter. A natural extension leads from photon wave mechanics to quantum electrodynamics (QED). In its modern formulation photon wave mechanics has given us valuable new insight in subjects such as spatial photon localization, near-field photon dynamics, transverse photon mass, photon eikonal theory, photon tunneling, and rim-zone electrodynamics. The present review is based on my plenary lecture at the SPIE-Europe 2009 Optics and Optoelectronics International Symposium in Prague.
Investigating Learners' Epistemological Framings of Quantum Mechanics
ERIC Educational Resources Information Center
Dini, Vesal
2017-01-01
Classical mechanics challenges students to use their intuitions and experiences as a basis for understanding, in effect to approach learning as "a refinement of everyday thinking'' (Einstein, 1936). Moving on to quantum mechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that…
Particles on a string: Towards understanding a quantum mechanical divergence
NASA Astrophysics Data System (ADS)
Dekker, H.
1984-11-01
The dynamics of two harmonically coupled solidbodies connected to a finitely extended mechanical field (string) is solved exactly and explicitly in the Lagrange formalism. For infinite length of strings the particles motion becomes damped, but not as a simple linearly damped harmonic oscillator. The model allows for a detailed discussion of its quantum mechanics, in particular of a previously recognized ultraviolet divergence.
Investigations of fundamental phenomena in quantum mechanics with neutrons
NASA Astrophysics Data System (ADS)
Hasegawa, Yuji
2014-04-01
Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.
NASA Astrophysics Data System (ADS)
Leong, Max Kangchien
A method of combined quantum mechanics/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent calculations. The combined QM/MM scheme was successfully applied to model iron picket-fence porphyrin, vitamin B12, aquocobalamin, and vitamin B12 coenzyme molecules.
Gambarota, Giulio
2016-09-03
Magnetic resonance spectroscopy (MRS) is a well established modality for investigating tissue metabolism in vivo. In recent years, many efforts by the scientific community have been directed towards the improvement of metabolite detection and quantitation. Quantum mechanics simulations allow for investigations of the MR signal behaviour of metabolites; thus, they provide an essential tool in the optimization of metabolite detection. In this review, we will examine quantum mechanics simulations based on the density matrix formalism. The density matrix was introduced by von Neumann in 1927 to take into account statistical effects within the theory of quantum mechanics. We will discuss the main steps of the density matrix simulation of an arbitrary spin system and show some examples for the strongly coupled two spin system.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2015-10-01
These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.
Quantum mechanics, gravity and modified quantization relations.
Calmet, Xavier
2015-08-06
In this paper, we investigate a possible energy scale dependence of the quantization rules and, in particular, from a phenomenological point of view, an energy scale dependence of an effective [Formula: see text] (reduced Planck's constant). We set a bound on the deviation of the value of [Formula: see text] at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation has taken place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about 10(16) GeV.
Quantum-mechanical study on the mechanism of peptide bond formation in the ribosome.
Acosta-Silva, Carles; Bertran, Joan; Branchadell, Vicenç; Oliva, Antoni
2012-04-04
Ribosomes transform the genetic information encoded within genes into proteins. In recent years, there has been much progress in the study of this complex molecular machine, but the mechanism of peptide bond formation and the origin of the catalytic power of this ancient enzymatic system are still an unsolved puzzle. A quantum-mechanical study of different possible mechanisms of peptide synthesis in the ribosome has been carried out using the M06-2X density functional. The uncatalyzed processes in solution have been treated with the SMD solvation model. Concerted and two-step mechanisms have been explored. Three main points suggested in this work deserve to be deeply analyzed. First, no zwitterionic intermediates are found when the process takes place in the ribosome. Second, the proton shuttle mechanism is suggested to be efficient only through the participation of the A2451 2'-OH and two crystallographic water molecules. Finally, the mechanisms in solution and in the ribosome are very different, and this difference may help us to understand the origin of the efficient catalytic role played by the ribosome.
Quantum-mechanical transport equation for atomic systems.
NASA Technical Reports Server (NTRS)
Berman, P. R.
1972-01-01
A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.
A deformation quantization theory for noncommutative quantum mechanics
Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz
2010-07-15
We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].
Quantum-mechanical description of in-medium fragmentation
NASA Astrophysics Data System (ADS)
Kopeliovich, B. Z.; Pirner, H.-J.; Potashnikova, I. K.; Schmidt, Ivan; Tarasov, A. V.; Voskresenskaya, O. O.
2008-11-01
We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences and contains all relevant time scales, such as production, coherence, and formation. The cross section includes the probability of prehadron (colorless dipole) production both inside and outside the medium. Moreover, it also includes inside-outside production, which is a typical quantum-mechanical interference effect (like twin-slit electron propagation). We observe a substantial suppression caused by the medium, even if the prehadron is produced outside the medium and no energy loss is involved. This important source of suppression is missed in the usual energy-loss scenario interpreting the effect of jet quenching observed in heavy ion collisions. This may be one reason for the too large gluon density reported by such analyses.
Quantum-mechanical transport equation for atomic systems.
NASA Technical Reports Server (NTRS)
Berman, P. R.
1972-01-01
A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.
Quantum mechanisms of density wave transport
Miller, John H.; Wijesinghe, Asanga I.
2012-01-01
We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe3 and TaS3, as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates. PMID:22711979
Drug-Target Binding Investigated by Quantum Mechanical/Molecular Mechanical (QM/MM) Methods
NASA Astrophysics Data System (ADS)
Rothlisberger, U.; Carloni, P.
Many important drugs, also used in the clinics, exert their function by binding covalently to their targets. Understanding their action requires quantum mechanical simulations. Here, after briefly reviewing few basic concepts of thermodynamics and kinetics of drug-target binding, we summarize principles and applications of Car-Parrinello quantum mechanics/molecular mechanics (QM/MM) simulations. From this discussion, this approach emerges as a computational methodology particularly well suited to investigate covalent binding in systems of pharmacological relevance.
Electron relaxation in quantum dot and quantum well systems by the ICD mechanism
NASA Astrophysics Data System (ADS)
Moiseyev, Nimrod
2014-05-01
Electron relaxation in quantum dot (QD) and quantum well (QW) systems has a significant impact on QD and QW optoelectronic devices such as lasers, photodetectors, and solar cells. Several different fundamental relaxation mechanisms are known. We focus here on inter-coulombic decay (ICD) mechanism. In 2011 we have shown that the electron relaxation in a quantum dot dimer due to the ICD mechanism is on a picoseconds timescale (PRB 83, 113303) and therefore IR QD detectors based on ICD seems to be feasible. Here we discuss the possibility to observe electron relaxation in QWs. In QWs the effective mass of the electron is not continuous, and can affect the lifetime of the ICD process. In order for the ICD to be the dominant decay mechanism, it must prevail over all other possible competitive decay processes. We have found in our setup that the ICD lifetime is on the timescale of picoseconds. An enhancement of the ICD process occurs when the ionized electron temporarily trapped in a shape-type resonance in the continuum. An experiment based on our findings is currently in progress. In this talk another possibility to observe the ICD phenomenon in two coupled QWs is proposed, by transferring an electron through a two coupled quantum wells structure populated by only one electron. An enhancement in the electron transmission would be obtained when the energy of the incoming electrons allows them to be temporarily trapped inside one of the two quantum wells via the ICD mechanism.
Reality in quantum mechanics, Extended Everett Concept, and consciousness
NASA Astrophysics Data System (ADS)
Mensky, M. B.
2007-09-01
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.
The Misapplication of Probability Theory in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Racicot, Ronald
2014-03-01
This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that Quantum Mechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantum mechanics and quantum information theory.
Model of the physical space from quantum mechanics
NASA Astrophysics Data System (ADS)
Kong, Otto C. W.
2017-08-01
The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with ‘quantized’ interpretations. The most important case example is that of spacetime. We examine the picture of the physical space as described by simple, so-called non-relativisitic, quantum mechanics instead of assuming the Newtonian model. The key perspective is that of (relativity) symmetry representation, and the idea that the physical space is to be identified as the configuration space for a free particle. Parallel to the case of the phase space, we have a model of the quantum physical space which reduces to the Newtonian classical model under the classical limit. The latter is to be obtained as a contraction limit of the relativity symmetry.
PREFACE: Progress in supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Aref'eva, I.; Fernández, D. J.; Hussin, V.; Negro, J.; Nieto, L. M.; Samsonov, B. F.
2004-10-01
The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models
Unstable particles in non-relativistic quantum mechanics?
Hernandez-Coronado, H.
2011-10-14
The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of states with different mass and implies that unstable particles cannot be described consistently in non-relativistic quantum mechanics (NRQM). In this paper we claim that Bargmann's rule neglects physical effects and that a proper description of non-relativistic quantum mechanics requires to take into account this phase through the Extended Galilei group and the definition of its action on spacetime coordinates.
Quantum-mechanical treatment of an electron undergoing synchrotron radiation.
NASA Technical Reports Server (NTRS)
White, D.
1972-01-01
The problem of an electron moving perpendicular to an intense magnetic field is approached from the framework of quantum mechanics. A numerical solution to the related rate equations describing the probabilities of occupation of the electron's energy states is put forth along with the expected errors involved. The quantum-mechanical approach is found to predict a significant amount of energy broadening with time for an initially monoenergetic electron beam entering a region of an intense magnetic field as long as the product of initial energy and magnetic field is of order 50 MG BeV or larger.
The uncertainty principle determines the nonlocality of quantum mechanics.
Oppenheim, Jonathan; Wehner, Stephanie
2010-11-19
Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.
Study on a Possible Darwinian Origin of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Baladrón, C.
2011-03-01
A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.
Quantum mechanics, common sense, and the black hole information paradox
NASA Astrophysics Data System (ADS)
Danielsson, Ulf H.; Schiffer, Marcelo
1993-11-01
The purpose of this paper is to analyze, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR, correlations, copying machines, teleportation, mixing produced in subsystems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black hole evaporation through nonlocal processes, or those in which the world is polluted by an infinite number of metastable remnants.
A new teaching approach to quantum mechanical tunneling
NASA Astrophysics Data System (ADS)
Gilfoyle, G. P.
1999-09-01
The transfer matrix method has been used to investigate quantum mechanical tunneling in introductory quantum mechanics. The method is applied first to calculate the transmission coefficient for tunneling through a rectangular barrier and is then extended to the problem of potential barriers of arbitrary shape, in particular, to radioactive decay. This approach uses matrix methods that are accessible to a broader range of undergraduates than other numerical techniques, the connection between the rectangular barrier problem and potential barriers of arbitrary shape is transparent, and it can be readily executed by undergraduates. The classroom experience with this approach is discussed.
Spacetime alternatives in the quantum mechanics of a relativistic particle
Whelan, J.T. Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH )
1994-11-15
Hartle's generalized quantum mechanics formalism is used to examine spacetime coarse grainings, i.e., sets of alternatives defined with respect to a region extended in time as well as space, in the quantum mechanics of a free relativistic particle. For a simple coarse graining and suitable initial conditions, tractable formulas are found for branch wave functions. Despite the nonlocality of the positive-definite version of the Klein-Gordon inner product, which means that nonoverlapping branches are not sufficient to imply decoherence, some initial conditions are found to give decoherence and allow the consistent assignment of probabilities.
Symplectic geometry on the Hilbert phase space and foundations of quantum mechanics
Khrennikov, Andrei
2006-05-04
We show that in the opposition to a rather common opinion quantum mechanics is not complete. It is possible to introduce so called hidden variable -- in our model classical fields -- and combine the statistical predictions of quantum mechanics with deterministic dynamics of those hidden variables. Quantum mechanics can be considered as an approximative description of physical processes based on neglecting by quantities of the magnitude o({alpha}), where {alpha} is the dispersion of fluctuations of the Gaussian background field. In this paper we present the detailed presentation of theory of infinite-dimensional phase space and derive main equations of quantum mechanics (e.g., Schroedinger's equation, Heisenberg's equation and von Neumann equation) from the Hamilton equation on the infinite-dimensional symplectic space. We emphasize (to escape misunderstanding) that our paper is not about quantization of systems with infinite number of degrees of freedom, but about representation of quantum systems as classical systems with infinite number of degrees of freedom. We also investigate the purely mathematical problem of preserving of the dispersion of Gaussian fluctuations by Hamiltonian flows.
Hilbert space for quantum mechanics on superspace
Coulembier, K.; De Bie, H.
2011-06-15
In superspace a realization of sl{sub 2} is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl{sub 2}-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Measurable signatures of quantum mechanics in a classical spacetime
NASA Astrophysics Data System (ADS)
Helou, Bassam; Luo, Jun; Yeh, Hsien-Chi; Shao, Cheng-gang; Slagmolen, B. J. J.; McClelland, David E.; Chen, Yanbei
2017-08-01
We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schrödinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013), 10.1103/PhysRevLett.110.170401]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum's dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light's phase fluctuations' spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.
Geometric control of quantum mechanical and nonlinear classical systems
NASA Astrophysics Data System (ADS)
Nelson, Richard Joseph
1999-10-01
Geometric control refers to the judicious use of the non- commuting nature of inputs and natural dynamics as the basis for control. The last few decades in control system theory have seen the application of differential geometry in proving several important properties of systems, including controllability and observability. Until recently, however, the results of this mathematical geometry have rarely been used as the basis for designing and implementing an actual controller. This thesis demonstrates the application of a judicious selection of inputs, so that if the system is proven to be controllable using geometric methods, one can design input sequences using the same geometry. A demonstration of this method is shown in simulating the attitude control of a satellite: a highly non-linear, non- holonomic control problem. Although not a practical method for large re-orientations of a typical satellite, the approach can be applied to other nonlinear systems. The method is also applied to the closed-loop performance of a quantum mechanical system to demonstrate the feasibility of coherent quantum feedback-something impossible using a conventional controller. Finally, the method is applied in the open-loop control of a quantum mechanical system: in this case, the creation of Greenberger-Horne-Zeilinger correlations among the nuclei of an ensemble of alanine molecules in a nuclear magnetic resonance spectrometer. In each case, the data demonstrate the usefulness of a geometric approach to control. In addition to demonstrations of geometric control in practice, the quantum mechanical experiments also demonstrate for the first time peculiar quantum correlations, including GHZ correlations, that have no classical analog. The quantum experiments further establish nuclear magnetic resonance as a viable and accessible testbed of quantum predictions and processes. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax
NASA Astrophysics Data System (ADS)
Greca, Ileana Maria; Freire, Olival
Teaching physics implies making choices. In the case of teaching quantum physics, besides an educational choice - the didactic strategy - another choice must be made, an epistemological one, concerning the interpretation of quantum theory itself. These two choices are closely connected. We have chosen a didactic strategy that privileges the phenomenological-conceptual approach, with emphasis upon quantum features of the systems, instead of searching for classical analogies. This choice has led us to present quantum theory associated with an orthodox, yet realistic, interpretation of the concept of quantum state, considered as the key concept of quantum theory, representing the physical reality of a system, independent of measurement processes. The results of the mplementation of this strategy, with three groups of engineering students, showed that more than a half of them attained a reasonable understanding of the basics of quantum mechanics (QM) for this level. In addition, a high degree of satisfaction was attained with the classes as 80% of the students of the experimental groups claimed to have liked it and to be interested in learning more about QM.
How Does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Ihly, Rachelle
This thesis explores the understanding of the chemistry and physics of colloidal quantum dots for practical solar energy photoconversion. Solar cell devices that make use of PbS quantum dots generally rely on constant and unchanged optical properties such that band gap energies remain tuned within the device. The design and development of unique experiments to ascertain mechanisms of optical band gap shifts occurring in PbS quantum dot thin-films exposed to air are discussed. The systematic study of the absorption properties of PbS quantum dot films exposed to air, heat, and UV illumination as a function of quantum dot size has been described. A method to improve the air-stability of films with atomic layer deposition of alumina is demonstrated. Encapsulation of quantum dot films using a protective layer of alumina results in quantum dot solids that maintain tuned absorption for 1000 hours. This thesis focuses on the use of atomic force microscopy and electrical variants thereof to study the physical and electrical characteristics of quantum dot arrays. These types of studies have broad implications in understanding charge transport mechanisms and solar cell device operation, with a particular emphasis on quantum dot transistors and solar cells. Imaging the channel potential of a PbSe quantum dot thin-film in a transistor showed a uniform distribution of charge coinciding with the transistor current voltage characteristics. In a second study, solar cell device operation of ZnO/PbS heterojunction solar cells was investigated by scanning active cross-sections with Kelvin probe microscopy as a function of applied bias, illumination and device architecture. This technique directly provides operating potential and electric field profiles to characterize drift and diffusion currents occurring in the device. SKPM established a field-free region occurring in the quantum dot layer, indicative of diffusion-limited transport. These results provide the path to optimization of
Quantum mechanical force field for water with explicit electronic polarization.
Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali
2013-08-07
A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across
Quantum mechanical force field for water with explicit electronic polarization
Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali
2013-01-01
A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 106 self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across
Solvable time-dependent models in quantum mechanics
NASA Astrophysics Data System (ADS)
Cordero-Soto, Ricardo J.
In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrodinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrodinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrodinger equation in Rn with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrodinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models
Quantum Mechanics, Pattern Recognition, and the Mammalian Brain
NASA Astrophysics Data System (ADS)
Chapline, George
2008-10-01
Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.
Horizon quantum mechanics: A hitchhiker’s guide to quantum black holes
NASA Astrophysics Data System (ADS)
Casadio, Roberto; Giugno, Andrea; Micu, Octavian
2016-01-01
It is congruous with the quantum nature of the world to view the spacetime geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the spacetime manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantization of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the “superspace” of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble “minisuperspace” approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability that they are black holes (BHs) rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the “horizon wave function (HWF),” the latter being determined by the quantum state of the source. This formalism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum BHs.
Physics on the boundary between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2014-04-01
Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?
NASA Astrophysics Data System (ADS)
Aspelmeyer, Markus; Schwab, Keith
2008-09-01
The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the
Non-exponential and oscillatory decays in quantum mechanics
Peshkin, Murray; Volya, Alexander; Zelevinsky, Vladimir
2014-08-07
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
Non-exponential and oscillatory decays in quantum mechanics
NASA Astrophysics Data System (ADS)
Peshkin, Murray; Volya, Alexander; Zelevinsky, Vladimir
2014-08-01
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
METHODOLOGICAL NOTES: Irreversibility in quantum mechanics
NASA Astrophysics Data System (ADS)
Kadomtsev, Boris B.
2003-11-01
From the Editorial Board. November 9, 2003 would have marked the seventy-fifth birthday of Boris Borisovich Kadomtsev, were he alive. An outstanding theoretical physicist, teacher, and enlightener, a prominent scientist in plasma physics and controlled nuclear fusion, Kadomtsev was also actively involved in science organization activities. In particular, from 1976 until his untimely death on August 19, 1998, Kadomtsev was the Editor-in-Chief of Physics-Uspekhi, and it is owing to his efforts that the journal improved notably during his tenure. Now, the Editorial Board, with gratitude and sorrow, would like to celebrate his birthday and to honor his blessed memory in these pages. There is, however, a rule — indeed an immutable tradition — in the journal that, except for the Personalia section, no anniversary can be marked in any way other than in a scientific publication. This rule was strictly observed under Kadomtsev, and certainly should not be violated now, even when honoring his memory. Fortunately, there is a video which remained of a lecture on modern problems of quantum physics that Kadomtsev delivered on May 12, 1997. Prepared for publication by M B Kadomtsev, the lecture allows the reader to revisit the heritage of B B Kadomtsev, to appreciate his logic in treating this very difficult area of physics, to hear his voice as it were, to recall Boris Borisovich Kadomtsev and to honor his memory.
Quantum mechanical cluster calculations of critical scintillationprocesses
Derenzo, Stephen E.; Klintenberg, Mattias K.; Weber, Marvin J.
2000-02-22
This paper describes the use of commercial quantum chemistrycodes to simu-late several critical scintillation processes. The crystalis modeled as a cluster of typically 50 atoms embedded in an array oftypically 5,000 point charges designed to reproduce the electrostaticfield of the infinite crystal. The Schrodinger equation is solved for theground, ionized, and excited states of the system to determine the energyand electron wavefunction. Computational methods for the followingcritical processes are described: (1) the formation and diffusion ofrelaxed holes, (2) the formation of excitons, (3) the trapping ofelectrons and holes by activator atoms, (4) the excitation of activatoratoms, and (5) thermal quenching. Examples include hole diffusion in CsI,the exciton in CsI, the excited state of CsI:Tl, the energy barrier forthe diffusion of relaxed holes in CaF2 and PbF2, and prompt hole trappingby activator atoms in CaF2:Eu and CdS:Te leading to an ultra-fast (<50ps) scintillation risetime.
Quantum Mechanics and Conceptual Change in High School Chemistry Textbooks.
ERIC Educational Resources Information Center
Shiland, Thomas W.
1997-01-01
Examines the presentation of quantum mechanics in eight secondary chemistry texts for elements associated with a conceptual change model: (1) dissatisfaction; (2) intelligibility; (3) plausibility; and (4) fruitfulness. Reports that these elements were not present in sufficient quantities to promote conceptual change. Presents recommendations for…
Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator
ERIC Educational Resources Information Center
Quijas, P. C. Garcia; Aguilar, L. M. Arevalo
2007-01-01
Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
ERIC Educational Resources Information Center
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Spin and Uncertainty in the Interpretation of Quantum Mechanics.
ERIC Educational Resources Information Center
Hestenes, David
1979-01-01
Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)
Recursive representation of Wronskians in confluent supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Contreras-Astorga, Alonso; Schulze-Halberg, Axel
2017-03-01
A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation.
Review of Student Difficulties in Upper-Level Quantum Mechanics
ERIC Educational Resources Information Center
Singh, Chandralekha; Marshman, Emily
2015-01-01
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…
The History of Teaching Quantum Mechanics in Greece
ERIC Educational Resources Information Center
Tampakis, Constantin; Skordoulis, Constantin
2007-01-01
In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…
Quantum Mechanics Concept Assessment: Development and Validation Study
ERIC Educational Resources Information Center
Sadaghiani, Homeyra R.; Pollock, Steven J.
2015-01-01
As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum…
A multiscale quantum mechanics/electromagnetics method for device simulations.
Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua
2015-04-07
Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.
Completeness of the Coulomb Wave Functions in Quantum Mechanics
ERIC Educational Resources Information Center
Mukunda, N.
1978-01-01
Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)
A note on misunderstandings of Piron's axioms for quantum mechanics
NASA Astrophysics Data System (ADS)
Foulis, D. J.; Randall, C. H.
1984-01-01
Piron's axioms for a realistically interpreted quantum mechanics are analyzed in detail within the context of a formal mathematical structure expressed in the conventional set-theoretic idiom of mathematics. As a result, some of the serious misconceptions that have encouraged recent criticisms of Piron's axioms are exposed.
Elementary Quantum Mechanics in a High-Energy Process
ERIC Educational Resources Information Center
Denville, A.; And Others
1978-01-01
Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)
Time Symmetric Quantum Mechanics and Causal Classical Physics ?
NASA Astrophysics Data System (ADS)
Bopp, Fritz W.
2017-04-01
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.
The History of Teaching Quantum Mechanics in Greece
ERIC Educational Resources Information Center
Tampakis, Constantin; Skordoulis, Constantin
2007-01-01
In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…
Quantum Mechanics of the Einstein-Hopf Model.
ERIC Educational Resources Information Center
Milonni, P. W.
1981-01-01
The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)
Quantum Mechanics Concept Assessment: Development and Validation Study
ERIC Educational Resources Information Center
Sadaghiani, Homeyra R.; Pollock, Steven J.
2015-01-01
As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum…
Review of Student Difficulties in Upper-Level Quantum Mechanics
ERIC Educational Resources Information Center
Singh, Chandralekha; Marshman, Emily
2015-01-01
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…
Parity-dependent non-commutative quantum mechanics
NASA Astrophysics Data System (ADS)
Chung, Won Sang
2017-01-01
In this paper, we consider the non-commutative quantum mechanics (NCQM) with parity (or space reflection) in two dimensions. Using the parity operators Ri, we construct the deformed Heisenberg algebra with parity in the non-commutative plane. We use this algebra to discuss the isotropic harmonic Hamiltonian with parity.
Spin and Uncertainty in the Interpretation of Quantum Mechanics.
ERIC Educational Resources Information Center
Hestenes, David
1979-01-01
Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
ERIC Educational Resources Information Center
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Equivalent emergence of time dependence in classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Briggs, John S.
2015-05-01
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes another part. Translating this scenario into both classical and quantum mechanics allows a transition to be made from a time-independent mechanics for the closed composite to a time-dependent description of the observed part alone. The use of Hamilton-Jacobi theory yields a very close parallel between the derivations in classical and quantum mechanics. The time-dependent equations, Hamilton-Jacobi or Schrödinger, appear as approximations since no observed system is truly closed. The quantum case has an additional feature in the condition that the observing environment must become classical in order to define a real classical time variable. This condition leads to a removal of entanglement engendered by the interaction between the observed system and the observing environment. Comparison is made to the similar emergence of time in quantum gravity theory.
Efficient Integration of Quantum Mechanical Wave Equations by Unitary Transforms
Bauke, Heiko; Keitel, Christoph H.
2009-08-13
The integration of time dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The energy and momentum spectrum of a wave function imposes fundamental limits on the performance of numerical algorithms for this problem. We demonstrate how unitary transforms can help to surmount these limitations.
Quantum Mechanics of the Einstein-Hopf Model.
ERIC Educational Resources Information Center
Milonni, P. W.
1981-01-01
The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)
Quantum-mechanical theory of optomechanical Brillouin cooling
Tomes, Matthew; Bahl, Gaurav; Carmon, Tal; Marquardt, Florian
2011-12-15
We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.
Completeness of the Coulomb Wave Functions in Quantum Mechanics
ERIC Educational Resources Information Center
Mukunda, N.
1978-01-01
Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)
Quasi-Hermitian quantum mechanics in phase space
Curtright, Thomas; Veitia, Andrzej
2007-10-15
We investigate quasi-Hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.
Note on correlation functions in conformal quantum mechanics
NASA Astrophysics Data System (ADS)
Khodaee, Sadi; Vassilevich, Dmitri
2017-09-01
We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT1) for the fields that transform under a nonlocal representation of 𝔰𝔩(2) basing on the invariance properties. Explicit calculations of two- and three-point correlation functions are presented.
Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator
ERIC Educational Resources Information Center
Quijas, P. C. Garcia; Aguilar, L. M. Arevalo
2007-01-01
Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…
Elementary Quantum Mechanics in a High-Energy Process
ERIC Educational Resources Information Center
Denville, A.; And Others
1978-01-01
Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)
Time Symmetric Quantum Mechanics and Causal Classical Physics ?
NASA Astrophysics Data System (ADS)
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.
Econophysics: from Game Theory and Information Theory to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Jimenez, Edward; Moya, Douglas
2005-03-01
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory.
Testing Quantum Mechanics and Bell's Inequality with Astronomical Observations
NASA Astrophysics Data System (ADS)
Friedman, Andrew S.; Kaiser, David I.; Gallicchio, Jason; Team 1: University of Vienna, InstituteQuantum Optics and Quantum Information; Team 2: UC San Diego Cosmology Group; Team 3: NASA/JPL/Caltech
2016-06-01
We report on an in progress "Cosmic Bell" experiment that will leverage cosmology to test quantum mechanics and Bell's inequality using astronomical observations. Different iterations of our experiment will send polarization-entangled photons through the open air to detectors ~1-100 kilometers apart, whose settings would be rapidly chosen using real-time telescopic observations of Milky Way stars, and eventually distant, causally disconnected, cosmological sources - such as pairs of quasars or patches of the cosmic microwave background - all while the entangled pair is still in flight. This would, for the first time, attempt to fully close the so-called "setting independence" or "free will" loophole in experimental tests of Bell's inequality, whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with unknown, local, causal influences a mere few milliseconds prior to the experiment. A full Cosmic Bell test would push any such influence all the way back to the hot big bang, since the end of any period of inflation, 13.8 billion years ago, an improvement of 20 orders of magnitude compared to the best previous experiments. Redshift z > 3.65 quasars observed at optical wavelengths are the optimal candidate source pairs using present technology. Our experiment is partially funded by the NSF INSPIRE program, in collaboration with MIT, UC San Diego, Harvey Mudd College, NASA/JPL/Caltech, and the University of Vienna. Such an experiment has implications for our understanding of nature at the deepest level. By testing quantum mechanics in a regime never before explored, we would at the very least extend our confidence in quantum theory, while at the same time severely constraining large classes of alternative theories. If the experiment were to uncover discrepancies from the quantum predictions, there could be crucial implications for early-universe cosmology, the security of quantum encryption
NASA Technical Reports Server (NTRS)
Kobayashi, Tsunehiro
1996-01-01
Quantum macroscopic motions are investigated in the scheme consisting of N-number of harmonic oscillators in terms of ultra-power representations of nonstandard analysis. Decoherence is derived from the large internal degrees of freedom of macroscopic matters.
Quantum Mechanics for Everyone: Can it be done with Technology?
NASA Astrophysics Data System (ADS)
Zollman, Dean
2004-10-01
The Visual Quantum Mechanics project has created a series of teaching/learning units to introduce quantum physics to a variety of audiences ranging from high school students who normally would not study these topics to undergraduate physics majors. Most recently we have been developing materials relating modern medical procedures and contemporary physics. In all of these materials interactive computer visualizations are coupled with hands-on experiences to create a series of activities which help students learn about some aspects of quantum mechanics. Our goal is to enable students to obtain a qualitative and, where appropriate, a quantitative understanding of contemporary ideas in physics. Included in the instructional materials are student-centered activities that address a variety of concepts in quantum physics and applications to devices such as the light emitting diode, the electron microscope, an inexpensive infrared detection card, and the Star Trek Transporter. Whenever possible the students begin the study of a new concept with an experiment using inexpensive equipment. They, then, build models of the physical phenomenon using interactive computer visualization and conclude by applying those models to new situations. For physics students these visualizations are usually followed by a mathematical approach. For others the visualizations provide a framework for understanding the concepts. Thus, Visual Quantum Mechanics allows a wide range of students to begin to understand the basic concepts, implications and interpretations of quantum physics. At present we are building on this foundation to create materials which show the connection between contemporary physics and modern medical diagnosis. Additional information is available at http://web.phys.ksu.edu/.
Quantum mechanical calculation of Rydberg-Rydberg autoionization rates
NASA Astrophysics Data System (ADS)
Kiffner, Martin; Ceresoli, Davide; Li, Wenhui; Jaksch, Dieter
2016-10-01
We present quantum mechanical calculations of autoionization rates for two rubidium Rydberg atoms with weakly overlapping electron clouds. We neglect exchange effects and consider tensor products of independent atom states forming an approximate basis of the two-electron state space. We consider large sets of two-atom states with randomly chosen quantum numbers and find that the charge overlap between the two Rydberg electrons allows one to characterise the magnitude of the autoionization rates. If the electron clouds overlap by more than one percent, the autoionization rates increase approximately exponentially with the charge overlap. This finding is independent of the energy of the initial state.
Quantum statistical mechanics of dense partially ionized hydrogen
NASA Technical Reports Server (NTRS)
Dewitt, H. E.; Rogers, F. J.
1972-01-01
The theory of dense hydrogen plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. The statistical mechanical calculation of the plasma equation of state is intended for stellar interiors. The general approach is extended to the calculation of the equation of state of the outer layers of large planets.
Jarzynski equality in PT-symmetric quantum mechanics
Deffner, Sebastian; Saxena, Avadh
2015-04-13
We show that the quantum Jarzynski equality generalizes to PT -symmetric quantum mechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
Accurate energies of the He atom with undergraduate quantum mechanics
NASA Astrophysics Data System (ADS)
Massé, Robert C.; Walker, Thad G.
2015-08-01
Estimating the energies and splitting of the 1s2s singlet and triplet states of helium is a classic exercise in quantum perturbation theory but yields only qualitatively correct results. Using a six-line computer program, the 1s2s energies calculated by matrix diagonalization using a seven-state basis improve the results to 0.4% error or better. This is an effective and practical illustration of the quantitative power of quantum mechanics, at a level accessible to undergraduate students.
Jarzynski Equality in PT-Symmetric Quantum Mechanics.
Deffner, Sebastian; Saxena, Avadh
2015-04-17
We show that the quantum Jarzynski equality generalizes to PT-symmetric quantum mechanics with unbroken PT symmetry. In the regime of broken PT symmetry, the Jarzynski equality does not hold as also the CPT norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system-two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
Developing the Deutsch Hayden approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Hewitt-Horsman, C.; Vedral, V.
2007-05-01
The formalism of Deutsch and Hayden is a useful tool for describing quantum mechanics explicitly as local and unitary, and therefore quantum information theory as concerning a 'flow' of information between systems. In this paper we show that these physical descriptions of flow are unique, and develop the approach further to include the measurement interaction and mixed states. We then give an analysis of entanglement swapping in this approach, showing that it does not in fact contain either nonlocal effects or any form of superluminal signalling.
Efficient hybrid-symbolic methods for quantum mechanical calculations
NASA Astrophysics Data System (ADS)
Scott, T. C.; Zhang, Wenxing
2015-06-01
We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantum mechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.
A perspective on quantum mechanics calculations in ADMET predictions.
Bowen, J Phillip; Güner, Osman F
2013-01-01
Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods.
A wave equation interpolating between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.
2015-10-01
We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.
Delirium Quantum Or, where I will take quantum mechanics if it will let me
NASA Astrophysics Data System (ADS)
Fuchs, Christopher A.
2007-02-01
Once again, I take advantage of the wonderfully liberal and tolerant mood Andrei Khrennikov sets at his yearly conferences by submitting a nonstandard paper for the proceedings. This pseudo-paper consists of excerpts drawn from two of my samizdats [Quantum States: What the Hell Are They? and Darwinism All the Way Down (and Probabilism All the Way Back Up)] that I think best summarize what I am aiming for on the broadest scale with my quantum foundations program. Section 1 tries to draw a picture of a physical world whose essence is "Darwinism all the way down." Section 2 outlines how quantum theory should be viewed in light of that, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of "identical" quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a William Jamesian style "radical pluralism." Sections 4 and 5 further detail how quantum theory should not be viewed so much as a "theory of the world," but rather as a theory of decision-making for agents immersed within a quantum world—that is, a world in continual creation. Finally, Sections 6 and 7 attempt to sketch once again the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantum mechanics hints of.
Statistical Mechanics of Confined Quantum Particles
NASA Astrophysics Data System (ADS)
Bannur, Vishnu M.; Udayanandan, K. M.
We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which is applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Furthermore, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.
Quantum Mechanical Modeling of Ballistic MOSFETs
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan (Technical Monitor)
2001-01-01
The objective of this project was to develop theory, approximations, and computer code to model quasi 1D structures such as nanotubes, DNA, and MOSFETs: (1) Nanotubes: Influence of defects on ballistic transport, electro-mechanical properties, and metal-nanotube coupling; (2) DNA: Model electron transfer (biochemistry) and transport experiments, and sequence dependence of conductance; and (3) MOSFETs: 2D doping profiles, polysilicon depletion, source to drain and gate tunneling, understand ballistic limit.
Functional methods underlying classical mechanics, relativity and quantum theory
NASA Astrophysics Data System (ADS)
Kryukov, A.
2013-04-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.
The simplified Fermi accelerator in classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Karner, Gunther
1994-11-01
We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the "free" Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth "wall oscillations" (typically of C 2 type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that "random boundary conditions" are necessary to model a quantum analog to the chaotic regime of the classical accelerator.
Reflections on Zeilinger-Brukner Information Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2016-07-01
In this short review I present my personal reflections on Zeilinger-Brukner information interpretation of quantum mechanics (QM).In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of irreducible quantum randomness is a very complicated issue which I plan to address in more detail. This note may be useful for general public interested in quantum foundations, especially because I try to analyze essentials of the information interpretation critically (i.e., not just emphasizing its advantages as it is commonly done). This review is written in non-physicist friendly manner. Experts actively exploring this interpretation may be interested in the paper as well, as in the comments of "an external observer" who have been monitoring the development of this approach to QM during the last 18 years. The last part of this review is devoted to the general methodology of science with references to views of de Finetti, Wigner, and Peres.
Quantum mechanical reality according to Copenhagen 2.0
NASA Astrophysics Data System (ADS)
Din, Allan M.
2016-05-01
The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is
Quantum processes as a mechanism in olfaction for smell recognition?
NASA Astrophysics Data System (ADS)
Brookes, Jennifer
2011-03-01
The physics of smell is not well understood. The biological processes that occur following a signalling event are well understood (Buck 1991). However, the reasons how and why a signalling event occurs when a particular smell molecule and receptor combination is made, remains un-established. Luca Turin proposes a signalling mechanism which determines smell molecules by quantum mechanics (Turin 1996). Investigation of this mechanism shows it to be physically robust (Brookes,et al, 2007), and consequences of the theory provides quantitative measurements of smell and interesting potential experiments that may determine whether the recognition of smell is a quantum event. Brookes, J.C, Hartoutsiou, F, Horsfield, A.P and Stoneham, A.M. (2007). Physical Review Letters 98, no. 3 038101 Buck, L. (1991) Cell, 65, no.1 (4): 175-187. Turin, L. (1996) Chemical Sences 21, no 6. 773-791 With many thanks to the Wellcome Trust.
Quantum mechanics on SO(3) via noncommutative dual variables
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Raasakka, Matti
2011-07-01
We formulate quantum mechanics on the group SO(3) using a noncommutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new noncommutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the noncommutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the nontrivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semiclassical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as loop quantum gravity and spin foam models.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Gevorkyan, A. S.
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
NASA Astrophysics Data System (ADS)
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.
Li, Hongzhi; Fajer, Mikolai; Yang, Wei
2007-01-14
A potential scaling version of simulated tempering is presented to efficiently sample configuration space in a localized region. The present "simulated scaling" method is developed with a Wang-Landau type of updating scheme in order to quickly flatten the distributions in the scaling parameter lambdam space. This proposal is meaningful for a broad range of biophysical problems, in which localized sampling is required. Besides its superior capability and robustness in localized conformational sampling, this simulated scaling method can also naturally lead to efficient "alchemical" free energy predictions when dual-topology alchemical hybrid potential is applied; thereby simultaneously, both of the chemically and conformationally distinct portions of two end point chemical states can be efficiently sampled. As demonstrated in this work, the present method is also feasible for the quantum mechanical and quantum mechanical/molecular mechanical simulations.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Giacosa, Francesco
2014-10-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
Subsystem Quantum Mechanics and its Applications to Crystalline Systems
NASA Astrophysics Data System (ADS)
Zou, Pengfei
This thesis reports results of the author's investigations along the theme that both dynamic and static properties of molecules and solids can be expressed in terms of their parts from theoretical and applied aspects. Specifically, the following four main results are obtained: (1) A topological analysis of the charge density in crystals has been developed. This is an extension of the theory of molecular structure to crystalline systems. Relationships between the bulk properties of a crystal and its topological structure have been established. A comparison of the topological properties of molecules and crystals have been made. (2) The theory of atoms in molecules has been extended to a crystal and yields a variational definition of a Wigner-Seitz cell. This definition maximizes the relation of the cell to the physical form exhibited by the charge density and the derived structure factors that account, in a natural way, for the observed intensities of scattered electrons and X-rays. It has been demonstrated that the theory of atoms in molecules and crystals can provide a way to model the behaviour of solids. This is done through the use of the fact that atomic properties are often transferable from one system to another. (3) The subsystem variational principle has been reformulated in terms of quantum field theoretical language and the subsystem Feynman path integrals of electrons have been obtained using the coherent representation. This part contributes to the foundation of the theory of atoms in molecules and crystals. (4) Both dynamic and static quantum mechanical subspace techniques have been extensively investigated. A new variational method has been derived for embedding one system in another using the R-matrix formalism within the density functional approach. A formal subspace perturbation scheme has been proposed. These methods aim to obtain the charge distribution of a subsystem starting from known reference systems. Before I came here I was confused about
Quantum mechanical properties of graphene nano-flakes and quantum dots.
Shi, Hongqing; Barnard, Amanda S; Snook, Ian K
2012-11-07
In recent years considerable attention has been given to methods for modifying and controlling the electronic and quantum mechanical properties of graphene quantum dots. However, as these types of properties are indirect consequences of the wavefunction of the material, a more efficient way of determining properties may be to engineer the wavefunction directly. One way of doing this may be via deliberate structural modifications, such as producing graphene nanostructures with specific sizes and shapes. In this paper we use quantum mechanical simulations to determine whether the wavefunction, quantified via the distribution of the highest occupied molecular orbital, has a direct and reliable relationship to the physical structure, and whether structural modifications can be useful for wavefunction engineering. We find that the wavefunction of small molecular graphene structures can be different from those of larger nanoscale counterparts, and the distribution of the highest occupied molecular orbital is strongly affected by the geometric shape (but only weakly by edge and corner terminations). This indicates that both size and shape may be more useful parameters in determining quantum mechanical and electronic properties, which should then be reasonably robust against variations in the chemical passivation or functionalisation around the circumference.
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.
Memories of Crisis: Bohr, Kuhn, and the Quantum Mechanical ``Revolution''
NASA Astrophysics Data System (ADS)
Seth, Suman
2013-04-01
``The history of science, to my knowledge,'' wrote Thomas Kuhn, describing the years just prior to the development of matrix and wave mechanics, ``offers no equally clear, detailed, and cogent example of the creative functions of normal science and crisis.'' By 1924, most quantum theorists shared a sense that there was much wrong with all extant atomic models. Yet not all shared equally in the sense that the failure was either terribly surprising or particularly demoralizing. Not all agreed, that is, that a crisis for Bohr-like models was a crisis for quantum theory. This paper attempts to answer four questions: two about history, two about memory. First, which sub-groups of the quantum theoretical community saw themselves and their field in a state of crisis in the early 1920s? Second, why did they do so, and how was a sense of crisis related to their theoretical practices in physics? Third, do we regard the years before 1925 as a crisis because they were followed by the quantum mechanical revolution? And fourth, to reverse the last question, were we to call into the question the existence of a crisis (for some at least) does that make a subsequent revolution less revolutionary?
Bosson, Maël; Grudinin, Sergei; Redon, Stephane
2013-03-05
We present a novel Block-Adaptive Quantum Mechanics (BAQM) approach to interactive quantum chemistry. Although quantum chemistry models are known to be computationally demanding, we achieve interactive rates by focusing computational resources on the most active parts of the system. BAQM is based on a divide-and-conquer technique and constrains some nucleus positions and some electronic degrees of freedom on the fly to simplify the simulation. As a result, each time step may be performed significantly faster, which in turn may accelerate attraction to the neighboring local minima. By applying our approach to the nonself-consistent Atom Superposition and Electron Delocalization Molecular Orbital theory, we demonstrate interactive rates and efficient virtual prototyping for systems containing more than a thousand of atoms on a standard desktop computer.
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics
Albeverio, S.; Rezende, J.; Zambrini, J.-C.
2006-06-15
For the largest class of physical systems having a classical analog, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given, in terms of a notion of regularized action function. As a consequence of the study of the symmetries of this action, an associated Noether theorem is obtained. All the quantum symmetries resulting from the canonical quantization procedure follow in this way, as well as a number of symmetries which are new even for the case of the simplest systems. The method is based on the study of a corresponding Lie algebra and an analytical continuation in the time parameter of the probabilistic construction given in paper I of this work. Generically, the associated quantum first integrals are time dependent and the probabilistic model provides a natural interpretation of the new symmetries. Various examples illustrate the physical relevance of our results.
Emergence of a New Quantum Mechanics by Multivalued Logic
NASA Astrophysics Data System (ADS)
de Gerlicz, Claude Gaudeau; Antoine, Mathias; Bobola, Philippe; Flawisky, Nicolas; Hebras, Xavier; Mundedi, Musa
2013-09-01
Quantum Mechanics associated with new logic like Multivalued Logic and Fuzzy Logic has progressed in different ways and their applications can be found in many fields of sciences and technologies. All the concepts attached to this theory are far from the classical view. Classical mechanics can be viewed as crisp limit of a Fuzzy quantum mechanics. This leads to the following interpretation: It is the consequence of an assumption that a quantum particle "reside" in different place or in every path of the continuum of paths which collapse into a single "unique" trajectory of an observed classical motion The reality is "Fuzzy" and nonlocal not only in space but also in time. In this sense, idealised pointlike particles of classical mechanics corresponding to the ultimate sharpness of the fuzziness density emerge in a process of interaction between different parts of fuzzy wholeness. This process is viewed as a continuous process of defuzzification. It transforms a fuzzy reality into a crisp one. It is clear that the emerging crisp reality as a final step of measurements carries less of information that the underlying fuzzy reality. This means that there is an irreversible loss of information usually called "collapse of the wave function". It is not so much a "collapse" as a realization of one of the many possibilities existing within a fuzzy reality. Any measurements rearrange the fuzzy reality leading to different detection outcomes.
Testing Quantum Mechanics and Bell's Inequality with Astronomical Observations
NASA Astrophysics Data System (ADS)
Friedman, Andrew S.; Gallicchio, Jason; Kaiser, David I.; Guth, Alan H.
2015-01-01
We propose an experiment which would leverage cosmology to test quantum mechanics using astronomical observations. Our experiment would send entangled photons to detectors over 100 kilometers apart, whose settings would be rapidly chosen using real-time telescopic observations of distant, causally disconnected, cosmic sources - such as pairs of quasars or patches of the Cosmic Microwave Background - all while the entangled pair is still in flight. This would, for the first time, close close the so-called "setting independence" or "free will" loophole in experimental tests of Bell's inequality, whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with some local "hidden variables" due to unknown causal influences a mere few milliseconds prior to the experiment. Our "Cosmic Bell" experiment would push any such hidden variable conspiracy all the way back to the hot big bang, since the end of any period of inflation, 13.8 Gyr ago, an improvement of 20 orders of magnitude. We demonstrate the real world feasibility of our experimental setup. While causally disjoint patches of the cosmic microwave background radiation at redshift z ~ 1090 could be used to set the detectors, z > 3.65 quasars observed at optical wavelengths are arguably the optimal candidate source pairs using present technology. Our proposal is supported by some of the world's leading quantum experimentalists, who have begun to collaborate with us to conduct the experiment in the next 2-3 years using some of the instrumentation they have already built and used at two astronomical observatories in the Canary Islands. Such an experiment has implications for our understanding of nature at the deepest level. By testing quantum mechanics in a regime never before explored, we would at the very least extend our confidence in quantum theory, while at the same time severely constraining large classes of alternative theories. If the
O the Verge of Collapse: Modal Interpretations of Quantum Mechanics.
NASA Astrophysics Data System (ADS)
Ruetsche, Laura
1995-01-01
The conjunction of Schrodinger dynamics and the usual way of thinking about the conditions under which quantum systems exhibit determinate values implies that measurements don't have outcomes. The orthodox fix to this quantum measurement problem is von Neumann's postulate of measurement collapse, which suspends Schrodinger dynamics in measurement contexts. Contending that the fundamental dynamical law of quantum theory breaks down every time we test the theory empirically, the collapse postulate is unsatisfactory. Recently philosophers (e.g., van Fraassen and Healey) and physicists (e.g., Kochen and Dieks) have proposed a less violent solution to the measurement problem. Their modal interpretations of quantum mechanics advocate unusual ways of thinking about the situations under which quantum systems exhibit determinate observable values, semantics which reconcile determinate measurement outcomes with universal Schrodinger dynamics. Thus modal interpretations hold out hope that quantum theory is complete and exceptionless. This dissertation tempers that hope. I consider the modal approach to the neglected problem of state preparation. A promising modal account exploits standard quantum transition probabilities. But, I claim, modal interpretations must subject these transition probabilities to a consistency constraint which they can be shown to violate. Non-standard transition probabilities might avoid this inconsistency, but they would also introduce novel dynamics, and so undo the modal triumph of taking Schrodinger dynamics to be complete and universal. Next I consider Albert and Loewer's assault on modal accounts of "error-prone" measurements. I argue that the Albert-Loewer problem is more general than Albert, Loewer, or their critics appreciate, and that the Araki-Yanase theorem implies the existence of a class of observables whose error-free measurements succumb to the Albert-Loewer problem. I review modal responses to Albert and Loewer which appeal to the
Insights into Teaching Quantum Mechanics in Secondary and Lower Undergraduate Education
ERIC Educational Resources Information Center
Krijtenburg-Lewerissa, K.; Pol, H. J.; Brinkman, A.; van Joolingen, W. R.
2017-01-01
This study presents a review of the current state of research on teaching quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantum mechanics and…
Photons and evolution: quantum mechanical processes modulate sexual differentiation.
Davis, George E; Lowell, Walter E
2009-09-01
This paper will show that the fractional difference in the human gender ratio (GR) between the GR(at death) for those born in solar cycle peak years (maxima) and the GR(at death) in those born in solar cycle non-peak years (minima), e.g., 0.023, divided by Pi, yields a reasonable approximation of the quantum mechanical constant, alpha, or the fine structure constant (FSC) approximately 0.007297... or approximately 1/137. This finding is based on a sample of approximately 50 million cases using common, readily available demographic data, e.g., state of birth, birth date, death date, and gender. Physicists Nair, Geim et al. had found precisely the same fractional difference, 0.023, in the absorption of white light (sunlight) by a single-atom thick layer of graphene, a carbon skeleton resembling chicken wire fencing. This absorption fraction, when divided by Pi, yielded the FSC and was the first time this constant could "so directly be assessed practically by the naked eye". As the GR is a reflection of sexual differentiation, this paper reveals that a quantum mechanical process, as manifested by the FSC, is playing a role in the primordial process of replication, a necessary requirement of life. Successful replication is the primary engine driving evolution, which at a biochemical level, is a quantum mechanical process dependent upon photonic energy from the Sun. We propose that a quantum-mechanical, photon-driven chemical evolution preceded natural selection in biology and the mechanisms of mitosis and meiosis are manifestations of this chemical evolution in ancient seas over 3 billion years ago. Evolutionary processes became extant first in self-replicating molecules forced to adapt to high energy photons, mostly likely in the ultraviolet spectrum. These events led to evolution by natural selection as complex mixing of genetic material within species creating the variety needed to match changing environments reflecting the same process initiated at the dawn of life
Quantum mechanical calculations and mineral spectroscopy
NASA Astrophysics Data System (ADS)
Kubicki, J. D.
2006-05-01
Interpretation of spectra in systems of environmental interest is not generally straightforward due to the lack of close analogs and a clear structure of some components of the system. Computational chemistry can be used as an objective method to test interpretations of spectra. This talk will focus on applying ab initio methods to complement vibrational, NMR, and EXAFS spectroscopic information. Examples of systems studied include phosphate/Fe-hydroxides, arsenate/Al- and Fe-hydroxide, fractured silica surfaces. Phosphate interactions with Fe-hydroxides are important in controlling nutrient availability in soils and transport within streams. In addition, organo-phosphate bonding may be a key attachment mechanism for bacteria at Fe-oxide surfaces. Interpretation of IR spectra is enhanced by model predictions of vibrational frequencies for various surface complexes. Ab initio calculations were used to help explain As(V) and As(III) adsorption behavior onto amorphous Al- and Fe-hydroxides in conjunction with EXAFS measurements. Fractured silica surfaces have been implicated in silicosis. These calculations test structures that could give rise to radical formation on silica surfaces. Calculations to simulate the creation of Si and SiO radical species on sufaces and their subsequent production of OH radicals will be discussed.
Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano
2016-09-13
We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.
Functional integral approach: a third formulation of quantum statistical mechanics.
Dai, Xian Xi; Evenson, William E
2002-02-01
Quantum statistical mechanics has developed primarily through two approaches, pioneered by Gibbs and Feynman, respectively. In Gibbs' method one calculates partition functions from phase-space integrations or sums over stationary states. Alternatively, in Feynman's approach, the focus is on the path-integral formulation. The Hubbard-Stratonovich transformation leads to a functional-integral formulation for calculating partition functions. We outline here the functional integral approach to quantum statistical mechanics, including generalizations and improvements to Hubbard's formulation. We show how the dimensionality of the integrals is reduced exactly, how the problem of assuming an unknown canonical transformation is avoided, how the reality of the partition function in the complex representation is guaranteed, and how the extremum conditions are simplified. This formulation can be applied to general systems, including superconductors.
Some theoretical aspects of quantum mechanical equations in Rindler space
NASA Astrophysics Data System (ADS)
Mitra, Soma; Chakrabarty, Somenath
2017-03-01
In this article we have investigated theoretical aspects of the solutions of some of the quantum mechanical problems in Rindler space. We have developed formalisms for the exact analytical solutions for the relativistic equations, along with the approximate form of solutions for the Schrödinger equation. The Hamiltonian operator in Rindler space is found to be non-Hermitian in nature, whereas the energy eigen values are observed to be real in nature. We have noticed that the sole reason behind such real behavior is the PT -symmetric form of the Hamiltonian operator. We have also observed that the energy eigen values are negative, lineraly quantized and the quantum mechanical system becomes more and more bound with the increase in the strength of gravitational field strength produced by the strongly gravitating objects, e.g., black holes, which is classical in nature.
Approaching the standard quantum limit of mechanical torque sensing
NASA Astrophysics Data System (ADS)
Kim, P. H.; Hauer, B. D.; Doolin, C.; Souris, F.; Davis, J. P.
2016-10-01
Reducing the moment of inertia improves the sensitivity of a mechanically based torque sensor, the parallel of reducing the mass of a force sensor, yet the correspondingly small displacements can be difficult to measure. To resolve this, we incorporate cavity optomechanics, which involves co-localizing an optical and mechanical resonance. With the resulting enhanced readout, cavity-optomechanical torque sensors are now limited only by thermal noise. Further progress requires thermalizing such sensors to low temperatures, where sensitivity limitations are instead imposed by quantum noise. Here, by cooling a cavity-optomechanical torque sensor to 25 mK, we demonstrate a torque sensitivity of 2.9 yNm/. At just over a factor of ten above its quantum-limited sensitivity, such cryogenic optomechanical torque sensors will enable both static and dynamic measurements of integrated samples at the level of a few hundred spins.
A quantum mechanical polarizable force field for biomolecular interactions
Donchev, A. G.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, O. V.; Tarasov, V. I.
2005-01-01
We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs. PMID:15911753
The ZX-calculus is complete for stabilizer quantum mechanics
NASA Astrophysics Data System (ADS)
Backens, Miriam
2014-09-01
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
On the consistent effect histories approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Rudolph, Oliver
1996-11-01
A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of ``history'' is generalized to the notion of ``effect history.'' The space of effect histories carries the structure of a D-poset. Recent results of J. D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnès' logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.
The equivalence principle of quantum mechanics: Uniqueness theorem
Faraggi, A.E.; Matone, M.
1997-10-28
Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.
The black hole S-Matrix from quantum mechanics
NASA Astrophysics Data System (ADS)
Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga
2016-11-01
We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory & c = 1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model — of waves scattering off inverted harmonic oscillator potentials — that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.
Approaching the standard quantum limit of mechanical torque sensing.
Kim, P H; Hauer, B D; Doolin, C; Souris, F; Davis, J P
2016-10-20
Reducing the moment of inertia improves the sensitivity of a mechanically based torque sensor, the parallel of reducing the mass of a force sensor, yet the correspondingly small displacements can be difficult to measure. To resolve this, we incorporate cavity optomechanics, which involves co-localizing an optical and mechanical resonance. With the resulting enhanced readout, cavity-optomechanical torque sensors are now limited only by thermal noise. Further progress requires thermalizing such sensors to low temperatures, where sensitivity limitations are instead imposed by quantum noise. Here, by cooling a cavity-optomechanical torque sensor to 25 mK, we demonstrate a torque sensitivity of 2.9 yNm/. At just over a factor of ten above its quantum-limited sensitivity, such cryogenic optomechanical torque sensors will enable both static and dynamic measurements of integrated samples at the level of a few hundred spins.