Concepts Of Quantum Mechanics Research Articles

A Covariant Canonical Quantization of General Relativity

A Hamiltonian formulation of General Relativity within the context of the Nexus Paradigm of quantum gravity is presented. We show that the Ricci flow in a compact matter free manifold serves as the Hamiltonian density of the vacuum as well as a time evolution operator for the vacuum energy density. The metric tensor of GR is expressed in terms of the Bloch energy eigenstate functions of the quantum vacuum allowing an interpretation of GR in terms of the fundamental concepts of quantum mechanics.

Joint Effect of Coherence and Polarization on the Quantification of Visibility and Distinguishability

The wave-particle duality appeared as a quintessential concept in quantum mechanics since the inception of the theory, yet it still attracts attention due to its nonintuitive consequences. In the case of light, this property is known to be manifested in a simplified form in two-way interferometers through the investigation of complementary properties like visibility and distinguishability. Here, we derive two measurable quantifiers of these properties in terms of the entries of the density operator of a general quantum photonic state which encapsulate simultaneously the influence of both coherence and polarization. We observe that these quantifiers fulfill the Englert–Greenberger–Yasin inequality.

Friction as a consistent quantum-mechanical concept

A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant and phenomenological model of dissipation) is known to be in odds with the detailed balance in the thermodynamic limit. We show that this is not the case for quantum systems with internal (e.g. spin) states non-adiabatically coupled to translational dynamics. For such systems, a quantum master equation is derived which phenomenologically accounts for the frictional effect of a uniform zero temperature environment. A simple analytical example is provided. Conjectures regarding the finite temperature case are also formulated. The results are important for efficient simulations of complex molecular dynamics and quantum reservoir engineering applications.

Bohm’s approach to quantum mechanics: Alternative theory or practical picture?

Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm's proposal has caused it more rejection than acceptance. Now, after 65 years of Bohmian mechanics, should still be such an interpretational aspect the prevailing appraisal? Why not favoring a more pragmatic view, as a legitimate picture of quantum mechanics, on equal footing in all respects with any other more conventional quantum picture? These questions are used here to introduce a discussion on an alternative way to deal with Bohmian mechanics at present, enhancing its aspect as an efficient and useful picture or formulation to tackle, explore, describe and explain quantum phenomena where phase and correlation (entanglement) are key elements. This discussion is presented through two complementary blocks. The first block is aimed at briefly revisiting the historical context that gave rise to the appearance of Bohmian mechanics, and how this approach or analogous ones have been used in different physical contexts. This discussion is used to emphasize a more pragmatic view to the detriment of the more conventional hidden-variable (ontological) approach that has been a leitmotif within the quantum foundations. The second block focuses on some particular formal aspects of Bohmian mechanics supporting the view presented here, with special emphasis on the physical meaning of the local phase field and the associated velocity field encoded within the wave function. As an illustration, a simple model of Young's two-slit experiment is considered. The simplicity of this model allows to understand in an easy manner how the information conveyed by the Bohmian formulation relates to other more conventional concepts in quantum mechanics. This sort of pedagogical application is also aimed at ...

USING ANDROID-BASED EQUATION PLOTTERS AS SUPPORTING TOOLS FOR TEACHING AND LEARNING ATOMIC ORBITALS

Chemistry undergraduate students are required to master the theory of quantum mechanics as the basic requirement to study the properties of the submicroscopic particle. However, many studies showed the students’ difficulties to bring the quantum mechanical concept to the macroscopic world and vise-versa. The use of computer visualization tool will very useful for teaching and learning the quantum concept, especially electron and its related atomic orbitals. This technological report paper demonstrates some of the Android-based applications i.e FuncXY, TriPlot 3D Graphing, and Graphing calculator to effectively, quickly, and accurately convert wave functions into various hydrogen atomic orbital visualizations. By selecting spherical coordinate and entering wave equation, these smartphone graphical devices visualize three-dimensional atomic orbitals. Users are also easy to rotate, zoom and manipulate the object. Finally, these user-friendly plotters are very recommended to assist chemistry educators in teaching quantum mechanics.

A Classical Interpretation of the Scrooge Distribution.

The Scrooge distribution is a probability distribution over the set of pure states of a quantum system. Specifically, it is the distribution that, upon measurement, gives up the least information about the identity of the pure state compared with all other distributions that have the same density matrix. The Scrooge distribution has normally been regarded as a purely quantum mechanical concept with no natural classical interpretation. In this paper, we offer a classical interpretation of the Scrooge distribution viewed as a probability distribution over the probability simplex. We begin by considering a real-amplitude version of the Scrooge distribution for which we find that there is a non-trivial but natural classical interpretation. The transition to the complex-amplitude case requires a step that is not particularly natural but that may shed light on the relation between quantum mechanics and classical probability theory.

Five non-volatile memristor enigmas solved

Numerous publications on non-volatile memristors made from disparate materials (from inorganic to organic) share many qualitatively similar memory switching and unique v–i phenomena that have hitherto defied a unified physical explanation. This paper selects five, among many, such unexplained mysteries and presents rigorous mathematical proof of the nonlinear dynamical mechanisms responsible for these mysteries. Since no quantum mechanical or chemical concepts are invoked, our resolution of these enigmas does not depend on the material or structure of the memristors.

A hypothetical dislocation well model for kinematic hardening in cyclic plasticity

Kinematic hardening in metals is widely correlated with various cyclic plastic behaviors. Inspired by the classical dislocation pile-up model and the finite potential well concept in quantum mechanics, a hypothetical dislocation well model is proposed to describe dislocation behavior on a slip plane. In this model, dislocations are also generated in pairs from the source, gliding along opposite directions and interacting with well sides, resulting in impeded dislocations forming kinematic hardening and tunneling dislocations passing through the well. Given the point symmetries of dislocation generation at the source, interaction with the well sides and annihilation in the sink, signed scalars are imported to quantify the impeded and tunneling dislocations and their corresponding shear strains. A common power form rule for tunneling shear strain and a linear hardening law for impeded shear strain are introduced for validation. By assigning additional axisymmetry in the model, the kinematic hardening response is proven to be consistent with the Ohno-Wang models under uniaxial loading. Moreover, the multiple discrete kinematic hardening components are expressed by decomposing the plastic strain into several parts with different tunneling attributes but identical kinematic hardening moduli, and can be further extended into a continuous distribution density form in the total shear strain components. Apart from the path-independent constant density distribution in the total shear strain components, dislocation well sides as stacks in which shear strain components can be stored in order and recovered in the reverse order are also introduced. Shakedown behaviors with constant distribution density in total shear strain components and dislocation well sides or source as stacks, are explored in detail, respectively. In addition, a general non-axisymmetric dislocation well is also proposed and shakedown behavior under the same situations is exploited accordingly. Meanwhile, ratcheting behavior in the non-axisymmetric dislocation well model with varying attributes caused by the tunneling process is compared with that in the usual axisymmetric one. Finally, the cyclic responses of polycrystals in this hypothetical dislocation well model are investigated. Grain boundary effect is also taken into account additionally by associating the impeded shear strain tolerance with the distance to nearest grain boundary.

L-state Solutions of the Relativistic and Non-Relativistic Wave Equations for Modified Hylleraas-Hulthen Potential Using the Nikiforov-Uvarov Quantum Formalism

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

Antilinearity rather than Hermiticity as a guiding principle for quantum theory

Currently there is much interest in Hamiltonians that are not Hermitian but instead possess an antilinear PT symmetry. Here we seek to put such PT symmetric theories into as general a context as possible. After providing a brief overview of the PT symmetry program, we show that having an antilinear symmetry that acts on a well-defined Hilbert space is the most general condition that one can impose on a quantum theory for which one can have a well-defined inner product that is time independent, have a Hamiltonian that is self-adjoint, and have energy eigenvalues that are all real. For each of these properties Hermiticity is only a sufficient condition but not a necessary one, with Hermiticity thus being the special case in which the Hamiltonian has both antilinearity and Hermiticity. As well as being the necessary condition for the reality of energy eigenvalues, antilinearity in addition allows for the physically interesting cases of manifestly non-Hermitian but nonetheless self-adjoint Hamiltonians that have energy eigenvalues that appear in complex conjugate pairs, or that are Jordan block and cannot be diagonalized at all. We show that one can extend these ideas to quantum field theory, with the dual requirements of the existence of time independent inner products and invariance under complex Lorentz transformations forcing the antilinear symmetry to uniquely be CPT. We thus extend the CPT theorem to non-Hermitian Hamiltonians. For theories that are separately charge conjugation invariant, PT symmetry then follows, with the case for the physical relevance of the PT-symmetry program thus being advanced. While CPT symmetry can be defined at the classical level for every classical path in a path integral quantization procedure, in contrast, in such a path integral there is no reference at all to the Hermiticity of the Hamiltonian or the quantum Hilbert space on which it acts, as they are strictly quantum-mechanical concepts that can only be defined after the path integral quantization has been performed and the quantum Hilbert space has been constructed. CPT symmetry thus goes beyond Hermiticity and has primacy over it, with our work raising the question of how Hermiticity ever comes into quantum theory at all. To this end we show that whether or not a CPT-invariant theory has a Hamiltonian that is Hermitian is a property of the solutions to the theory and not of the Hamiltonian itself. Hermiticity thus never needs to be postulated at all.

A Holistic Picture of Physics Student Conceptions of Energy Quantization, the Photon Concept, and Light Quanta Interference

A detailed investigation of student conceptions of quantum phenomena is needed, both to characterize student understanding of quantum concepts and to inform how we might teach quantum mechanics (QM). In this vein, in-depth semi-structured interviews were conducted with 35 students who majored in physics and received university-level QM instructions. Interview protocols were used and based on three quantum contexts: the quantization of energy in explaining the blackbody radiation, the photon concept in explaining the photoelectric effect, and light quanta in explaining the gradual formation of an interference pattern in the cases of low-intensity light beam. By applying a developmental phenomenographic analysis of the interview responses, three description categories (i.e., general patterns behind the conceptual understandings used in explaining each quantum contexts) were identified. These categories of descriptions revealed that most students’ thinking regarding foundational concepts in QM ranged from naive and deficient descriptions based on classical ontologies to simple hybrid and/or mixed models of classical and quantum conceptions. Regarding learning QM, the study found that the perspective of naive and classical ontologies in explaining quantum phenomena influenced students’ responses; they made incorrect generalizations and/or inappropriate links to the concepts learned in classical physics; and patterns of incorrect notions of QM are analogous to those that were documented. Besides, the study confirmed that students’ conceptual difficulties with QM are real, stable over time, and cross-cultural. It seems that the challenge to make QM interesting, effective, and relevant for physics students is a universal concern that knows no boundaries.

Exchange Interaction of Quantum Entities as Interaction of Spin Vortices Created by the Quantum Entities in the Physical Vacuum

The aim of this paper is to show that there is a physical process that underlies the exchange interaction of quantum entities. To this end the features of exchange interaction of quantum entities in the following physical phenomena are discussed: the creation of Cooper pairs in superconductors and superfluids, the covalent (molecular) bond, the interaction of light beams. The explanation of the exchange interaction is based on the concept of quantum mechanics according to which the quantum entity that is a singularity in electric and/or magnetic fields produces in the physical vacuum a pair of oppositely charged virtual particles having precessing spin, that is being essentially a spin vortex in the physical vacuum. The analysis of the above mentioned phenomena allows one to suppose that the exchange interaction of quantum entities in these phenomena may be due to interaction of spin vortices created by these quantum entities in the physical vacuum. It is shown also that the interaction of these vortices may be an electric dipole-dipole interaction. The equations describing the electric dipole-dipole interaction of spin vortices are derived in this work. A possibility of influence of the dipole-dipole interaction of spin vortices created by quantum entities that constitute the medium on viscosity of the medium, that is, on its superconductive and superfluid properties is considered.

A Theoretical Approach to Selection of a Biologically Active Substance in Ultra-Low Doses for Effective Action on a Biological System

An approach is offered to selecting a biologically active substance (BAS) in ultra-low dose for effective action on a biological system (BS). The technique is based on the assumption that BAS in ultra-low doses exerts action on BS by means of spin supercurrent emerging between the spin structure created by BAS, on the one hand, and the spin structure created by BS, on the other hand. According to modern quantum-mechanical concepts, these spin structures may be virtual particles pairs having precessing spin (that is, be essentially spin vortices in the physical vacuum) and created by the quantum entities that BAS and BS consist of. The action is effective provided there is equality of precession frequencies of spins in these spin structures. In this work, some methods are considered for determining the precession frequencies of spins in virtual particles pairs: (1) determination of energy levels of quantum entities that BS and BAS consist of; (2) the use of spin-flip effect of the virtual particles pair spin, the effect being initiated by action of magnetic vector potential (the spin-flip effect takes place when the varied frequency of the magnetic vector potential equals the precession frequency of the spin); (3) determining the frequencies of photons effectively acting on BS. It is shown that the effect of BAS in ultra-low doses on BS can be replaced by the effect of a beam of low-intensity photons, if the frequency of photons equals the precession frequency of spin in spin structures created by BS. Consequently, the color of bodies placed near a biological system is able to exert an effective action on the biological system: that is "color therapy" is possible. It is also supposed that the spin-flip effect may be used not only for determining the precession frequency of spin in spin structures created by BS but also for therapeutic action on biological systems.

Disturbance-Disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance

The Heisenberg uncertainty principle, which underlies many quantum key features, is under close scrutiny regarding its applicability to new scenarios. Using both the Bell-Kochen-Specker theorem establishing that observables do not have predetermined values before measurements and the measurement postulate of quantum mechanics, we propose that in order to describe the disturbance produced by the measurement process, it is convenient to define disturbance by the changes produced on quantum states. Hence, we propose to quantify disturbance in terms of the square root of the Jensen-Shannon entropy distance between the probability distributions before and after the measurement process. Additionally, disturbance and statistical distinguishability of states are fundamental concepts of quantum mechanics that have thus far been unrelated; however, we show that they are intermingled thereupon we enquire into whether the statistical distinguishability of states, caused by statistical fluctuations in the measurement outcomes, is responsible for the disturbance’s magnitude.

Projective measurement onto arbitrary superposition of weak coherent state bases

One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exist. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical states. Recently this highly nontrivial quantum state and its variant have been demonstrated experimentally. Here we demonstrate the superposition of coherent states in quantum measurement which is also a key concept in quantum mechanics. More precisely, we propose and implement a projection measurement onto an arbitrary superposition of two weak coherent states in optical system. The measurement operators are reconstructed experimentally by a novel quantum detector tomography protocol. Our device is realized by combining the displacement operation and photon counting, well established technologies, and thus has implications in various optical quantum information processing applications.

The post-selection operator current

In this paper, we develop the concept of the post-selection operator current and we use it to extend the methodology of quantum mechanics into related fields of science and engineering. We begin by reviewing some results from standard quantum mechanics. We then introduce the post-selection operator current and note that the concept of the operator current provides a common framework for connecting underlying concepts in classical signal theory and quantum mechanics. Next, we explore the geometry of post-selection making use of the Pancharatnam phase. We illustrate the usefulness of the method through a series of simple examples; at each stage we link the results of quantum mechanics to applications in signal processing. We then simplify some results by introducing a density operator. This simplification allows us to present a number of useful observations about weak values. We conclude by using the operator current explore the relationship between post-selection and gauge invariance. The methods developed in this paper enable us to characterize the time evolution of a post-selected operator. The methods can be applied to other evolutionary/transport equations including the Fokker–Planck equation, and the equation of Brownian motion.

Quantum models of cognition and decision

The purpose of this article is to discuss principle ideas of quantum cognition research program, which comprise elements of the formalism of quantum mechanics (mainly Hilbert space theory and quantum probability theory) for modeling human cognition and decision processes. In the opinion of authors of this program, paradox empirical findings in psychological literature may be explained based on concepts of quantum mechanics. Formally, there is described a discrete-time random chain χ which is defined on a finite interval [0, T] and χ(t) can assume only finite number of values. The space H of such processes will be finite-dimensioned. Then some properties and applications of the quantum probability space on H are studied.

Particle in a Box: An Experiential Environment for Learning Introductory Quantum Mechanics

Quantum mechanics (QMs) is a foundational subject in many science and engineering fields. It is difficult to teach, however, as it requires a fundamental revision of the assumptions and laws of classical physics and probability. Furthermore, introductory QM courses and texts predominantly focus on the mathematical formulations of the subject and lay less emphasis on its conceptual understanding. Consequently, students struggle to build robust mental models of the concepts. This paper posits that games can provide an effective platform for an experiential and conceptual understanding of introductory QM. Games are particularly suitable for demonstrating QM characteristics because their repetitive nature is conducive to demonstrating probability concepts that form a core part of QM. Games can also immerse students in an engaging environment that motivates them to learn. This paper presents the design and evaluation of a digital game for learning introductory QM concepts. The evaluation of the game indicates an improvement in students’ conceptual understanding of probability. Students also reported an increase in comfort level with key concepts taught in the game.

High temperature limit of photosynthetic excitons

Excitons in light-harvesting complexes are known to significantly improve solar-energy harnessing. Here we demonstrate photosynthetic excitons at super-physiological temperatures reaching 60–80 °C in different species of mesophilic photosynthetic bacteria. It is shown that the survival of light-harvesting excitons in the peripheral LH2 antennae is restricted by thermal decomposition of the pigment–protein complex rather than by any intrinsic property of excitons. The regular spatial organization of the bacteriochlorophyll a pigments supporting excitons in this complex is lost upon the temperature-induced breakdown of its tertiary structure. Secondary structures of the complexes survive even higher temperatures. The discovered pivotal role of the protein scaffold in the stabilization of excitons comprises an important aspect of structure–function relationship in biology. These results also intimately entangle the fundamental issues of quantum mechanical concepts in biology and in the folding of proteins.

Hoffman’s Interface Theory from a Bio-Psychological Perspective

Hoffman’s interface theory of perception proposes that natural selection is based on icons, which are assessed on the basis of their value for species fitness and have no resemblance to real objects. According to this perspective, perception of truth concerning objects has no value for ensuring the species’ survival. The whole truth can only be grasped if all underlying physical factors creating icons of conscious perception are known. However, knowledge of whole truth as well as partial truth is rejected by the theory. Yet, from a bio-psychological perspective, the theory has some important limitations. Perception limited to partial truth would also be adapted for fitness-based evolutionary selection, as it would result in the enhancement of the existing or the creation of new functions of sense organs. Although Hoffman’s interface theory does not treat sense organs as physical objects, their functions in consciousness are recognized. Symbolic icons on the computer screen lack any veridical representation of the manner in which the data is stored in the computer memory, but are valuable tools in accessing the relevant content. In contrast icons representing images maintain a direct relation to their stored image. Evolutionary selection over many generations is thought to create icons for increasing fitness. However, icons created in the distant past become fixed and cannot be adapted to the rapid changes during an individual learning process necessary for adaption to unexpected new situations. Human inventions of new objects would also be rendered impossible if icons were solely dependent on evolutionary selection in the distant past. The interface theory is based on quantum mechanical concepts, which are extrapolated from the atomocosm to the macrocosm, but do not consider the Heisenberg cut. The interface approach may be adequate for lower-level organisms, but results in oversimplification when applied to the highly complex human perception.