Application Of Quantum Mechanics Research Articles

Colloquium: Non-Markovian dynamics in open quantum systems

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry and quantum information. In close analogy to a classical Markov process, the interaction of an open quantum system with a noisy environment is often modelled by a dynamical semigroup with a generator in Lindblad form, which describes a memoryless dynamics leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence and correlations. Here, recent results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of memory effects. The general theory is illustrated by a series of examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This article further explores the various physical sources of non-Markovian quantum dynamics, such as structured spectral densities, nonlocal correlations between environmental degrees of freedom and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments on the detection, quantification and control of non-Markovian quantum dynamics are also discussed.

Extended optical theorem for scalar monochromatic acoustical beams of arbitrary wavefront in cylindrical coordinates

One of the fundamental theorems in (optical, acoustical, quantum, gravitational) wave scattering is the optical theorem for plane waves, which relates the extinction cross-section to the forward scattering complex amplitude function. In this analysis, the optical theorem is extended for the case of 3D-beams of arbitrary character in a cylindrical coordinates system for any angle of incidence and any scattering angle. Generalized analytical expressions for the extinction, absorption, scattering cross-sections and efficiency factors are derived in the framework of the scalar resonance scattering theory for an object of arbitrary shape. The analysis reveals the presence of an interference scattering cross-section term, which describes interference between the diffracted or specularly reflected inelastic (Franz) waves with the resonance elastic waves. Moreover, an alternate expression for the extinction cross-section, which relates the resonance cross-section with the scattering cross-section for an impenetrable object, is obtained, suggesting an improved method for particle characterization. Cross-section expressions are also derived for known acoustical wavefronts centered on the object, defined as the on-axis case. The extended optical theorem in cylindrical coordinates can be applied to evaluate the extinction efficiency from any object of arbitrary geometry placed on or off the axis of the incident beam. Applications in acoustics, optics, and quantum mechanics should benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by many particles, as well as the radiation force and torque.

Journal of Theoretical and Computational Science: Open Access, A Bridge to Link Knowledge from Chemistry, Physics, Biology and More

Copyright: © 2013 Chelli R. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Welcome to the Journal of Theoretical and Computational Science: Open Access (JTCO). This new open access journal is being introduced to provide a focal point for publication of articles, letters, and reviews (see Ref. [1] for detailed information about publication formats) reporting advances in chemical and physico-chemical theories, computational methods, and important applications to problems in chemistry, physics and biology. The Journal will also dedicate special attention to computational aspects of biomedical sciences, including pharmaceutics, bioinformatics and drug discovery. Applications of high performance computing to the scientific advancement and human therapeutics will be object of publication as well. Though the contents will evolve, some specific topics in the chemical and physical frameworks that are appropriate today for JTCO include advances in or applications of ab initio quantum mechanics, density functional theory, statistical mechanics, design and properties of new materials, surface science, Monte Carlo simulations, solvation models, QM/ MM calculations, biomolecular structure prediction, and molecular dynamics in the broadest sense including gas-phase dynamics, ab initio dynamics, biomolecular dynamics, and protein folding. No less important is the intention of attracting audience from diverse other fields which traditionally are not part of the orthodoxy of theoretical and computational sciences. These fields include software development, information science, network theory, chemical informatics, clinical informatics, medicinal chemistry, bioinformatics, computational neuroscience, synthetic biology, and toxicology (additional information about the fields of interest to JTCO can be found in Ref. [1]).

Survey on nonlocal games and operator space theory

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

Experimental detection of polarization-frequency quantum correlations in a photonic quantum channel by local operations

The measurement of correlations between different degrees of freedom is an important, but in general extremely difficult task in many applications of quantum mechanics. Here, we report an all-optical experimental detection and quantification of quantum correlations between the polarization and the frequency degrees of freedom of single photons by means of local operations acting only on the polarization degree of freedom. These operations only require experimental control over an easily accessible two-dimensional subsystem, despite handling strongly mixed quantum states comprised of a continuum of orthogonal frequency states. Our experiment thus represents a photonic realization of a scheme for the local detection of quantum correlations in a truly infinite-dimensional continuous-variable system, which excludes an efficient finite-dimensional truncation.

Science Academies’ Refresher Course on Applications of Quantum Mechanics: Atoms, Molecules and Radiation

Science Academies’ Refresher Course on Applications of Quantum Mechanics: Atoms, Molecules and Radiation

Subsequent and Subsidiary? Rethinking the Role of Applications in Establishing Quantum Mechanics

As part of an attempt to establish a new understanding of the earliest applications of quantum mechanics and their importance to the overall development of quantum theory, this paper reexamines the role of research on molecular structure in the transition from the so-called old quantum theory to quantum mechanics and in the two years immediately following this shift (1926–1928). We argue on two bases against the common tendency to marginalize the contribution of these researches. First, because these applications addressed issues of longstanding interest to physicists, which they hoped, if not expected, a complete quantum theory to address, and for which they had already developed methods under the old quantum theory that would remain valid under the new mechanics. Second, because generating these applications was one of, if not the, principal means by which physicists clarified the unity, generality, and physical meaning of quantum mechanics, thereby reworking the theory into its now commonly recognized form, as well as developing an understanding of the kinds of predictions it generated and the ways in which these differed from those of the earlier classical mechanics. More broadly, we hope with this article to provide a new viewpoint on the importance of problem solving to scientific research and theory construction, one that might complement recent work on its role in science pedagogy.

Solvable potentials with exceptional orthogonal polynomials

Classes of solvable potentials are presented within an standard application of supersymmetric quantum mechanics. Sets of exceptional orthogonal polynomials generated by these solvable potentials are introduced and examined in detail. Several properties of these polynomials including orthogonality conditions, weight functions, differential equations, the Wronskains, possible recurrence relations are also investigated. image

Algebra of Complex Vectors and Applications in Electromagnetic Theory and Quantum Mechanics

A complex vector is a sum of a vector and a bivector and forms a natural extension of a vector. The complex vectors have certain special geometric properties and considered as algebraic entities. These represent rotations along with specified orientation and direction in space. It has been shown that the association of complex vector with its conjugate generates complex vector space and the corresponding basis elements defined from the complex vector and its conjugate form a closed complex four dimensional linear space. The complexification process in complex vector space allows the generation of higher n-dimensional geometric algebra from (n — 1)-dimensional algebra by considering the unit pseudoscalar identification with square root of minus one. The spacetime algebra can be generated from the geometric algebra by considering a vector equal to square root of plus one. The applications of complex vector algebra are discussed mainly in the electromagnetic theory and in the dynamics of an elementary particle with extended structure. Complex vector formalism simplifies the expressions and elucidates geometrical understanding of the basic concepts. The analysis shows that the existence of spin transforms a classical oscillator into a quantum oscillator. In conclusion the classical mechanics combined with zeropoint field leads to quantum mechanics.

Properties of the Katugampola fractional derivative with potential application in quantum mechanics

Katugampola [e-print arXiv:1410.6535] recently introduced a limit based fractional derivative, Dα (referred to in this work as the Katugampola fractional derivative) that maintains many of the familiar properties of standard derivatives such as the product, quotient, and chain rules. Typically, fractional derivatives are handled using an integral representation and, as such, are non-local in character. The current work starts with a key property of the Katugampola fractional derivative, Dα[y]=t1−αdydt, and the associated differential operator, Dα = t1−αD1. These operators, their inverses, commutators, anti-commutators, and several important differential equations are studied. The anti-commutator serves as a basis for the development of a self-adjoint operator which could potentially be useful in quantum mechanics. A Hamiltonian is constructed from this operator and applied to the particle in a box model.

Bessel Sequences and Its F-Scalability

AbstractFrame theory, which contains wavelet analysis and Gabor analysis, has become a powerful tool for many applications of mathematics, engineering and quantum mechanics. The study of extension principles of Bessel sequences to frames is important in frame theory. This paper studies transformations on Bessel sequences to generate frames and Riesz bases in terms of operators and scalability. Some characterizations of operators that mapping Bessel sequences to frames and Riesz bases are given. We introduce the definitions of F-scalable and P-scalable Bessel sequences. F-scalability and P-scalability of Bessel sequences are discussed in this paper, then characterizations of scalings of F-scalable or P-scalable Bessel sequences are established. Finally, a perturbation result on F-scalable Bessel sequences is derived.

Quantum-Everted Meta-Scientific Lensing as an Arbiter of the Hard Problem

A specific modification of metascientific epistemological standards is developed for the purpose of assessing the putative applicability of quantum mechanics to a physical understanding of consciousness. Formal properties of this epistemic alteration are summarized in a virtual construct called the quantum-everted meta-scientific (QuEMS) Lens. The feasibility of programming a digital approximation of the QuEMS Lens, inputting well accepted data from mainstream neurocognitive research, and inferring the relevance of quantum constructs from the output, is proposed.

Preferential orientation of NV defects in CVD diamond films grown on (113)-oriented substrates

Thick CVD diamond layers were successfully grown on (113)-oriented substrates. They exhibited smooth surface morphologies and a crystalline quality comparable to (100) electronic grade material, and much better than (111)-grown layers. High growth rates (15–50μm/h) were obtained while nitrogen doping could be achieved in a fairly wide range without seriously imparting crystalline quality. Electron spin resonance measurements were carried out to determine NV centers orientation and concluded that one specific orientation has an occurrence probability of 73% when (100)-grown layers show an equal distribution in the 4 possible directions. A spin coherence time of around 270μs was measured which is equivalent to that reported for material with similar isotopic purity. Although a higher degree of preferential orientation was achieved with (111)-grown layers (almost 100%), the ease of growth and post-processing of the (113) orientation make it a potentially useful material for magnetometry or other quantum mechanical applications.

Application of Fractional Classical and Quantum Mechanics to Statistical Physics System

Application of Fractional Classical and Quantum Mechanics to Statistical Physics System

Associative Space-Time Sedenions and Their Application in Relativistic Quantum Mechanics and Field Theory

We present an alternative sixteen-component hypercomplex scalar-vector values named “space-time sedenions”, generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quantum mechanics and field theory equations based on sedenionic wave function and space-time operators is discussed.

Nicholas Charles Handy. 17 June 1941 — 2 October 2012

Nicholas Handy made significant contributions in the applications of quantum mechanics to molecules. In an academic career at Cambridge University he was involved with many advances in the computational methods that have turned quantum chemistry into a central tool for understanding modern molecular science.

The Grand Challenge of Quantum Computing: Bridging the Capacity Gap

The fabrication and control of macroscopic artificial quantum structures, such as qubits (Mooij et al., 1999; Nakamura et al., 1999; Friedman et al., 2000), qubit arrays (Johnson et al., 2011; Barends et al., 2014), quantum annealers (Boixo et al., 2013) and, recently, quantum metamaterials (Macha et al., 2014), have witnessed significant progress over the last 15 years. This was a surprisingly quick evolution from theoretical musings to what can now be called quantum engineering [the observation of such phenomena even in a single superconducting device was considered a truly challenging task in 1980 (Leggett, 1980)]. And today, we stand at the point where existing theoretical and computational tools become inadequate for predicting, analyzing, and simulating the behavior of such structures, in which quantum superposition and entanglement play the key role (Zagoskin et al., 2014). The long-known fundamental impossibility of simulating large enough quantum systems by classical means (Feynman, 1982), unfortunately, manifests itself already at the level of systems containing as few as several hundreds of qubits. Such a system is still too small to be used as an efficient quantum simulator of comparable systems, but already too large for us to tell with certainty, using the existing classical tools, whether it behaves as a quantum system should (Smolin and Smith, 2014). Furthermore, the complexity of already existing quantum processor prototypes confronts us with an engineering problem designing a reliable quantum device and testing its reliability. What is even worse, if there are fundamental corrections to the laws of quantum mechanics for large enough systems, we will be unable to discover them because of our inability to tell what exactly quantum mechanics would predict. Let us take the optimistic view that quantum computing is not fundamentally restricted by, for example, the size of a system capable of demonstrating quantum behavior (Penrose, 1999). In this scenario, it would be possible to create quantum computing devices that will allow us to design and fabricate ever bigger and better quantum computers, as well as other macroscopic quantum devices, of a character and use of which we cannot even imagine at the moment. Alternatively, we may find fundamental limits to the applicability of quantum mechanics. Nevertheless, this can happen only if the gap between our current ability to characterize large quantum systems and the capacities of the smallest workable quantum computers is bridged. Bridging this capacity gap is thus the immediate grand challenge for the field: a challenge that must be met if we hope to make further progress in quantum computing and quantum engineering or if we hope to discover fundamentally new physics, or both. While it is impossible to efficiently simulate a large quantum system by classical means by directly solving the appropriate equations of motion, it is feasible that essential quantum properties of an ensemble of such systems will be reflected in certain higher-level, global characteristics. These properties should be insensitive to details of a particular instance, computable by classical tools and accessible to experimental investigation. This view of a system of qubits as a quantum many-body system should be amenable to the approaches that have proven to work very well in numerous applications in condensed matter physics and quantum statistical mechanics. Therefore, with such earlier breakthroughs in mind, the task at hand will be difficult yet not impossible, and more than worth the effort.

Commonly asked questions in physics

Classical Mechanics What Is Physics? What Is the SI System of Units? What Are Velocity and Acceleration? What Is a Force? What Are Work and Energy? What Is Momentum Conservation? What Is Simple Harmonic Motion? What Are Torque and Angular Momentum? What Is Newton's Law of Universal Gravitation? Can Classical Mechanics Explain Everything? Electromagnetism and Electronics What Are Electric Charges, and How Do They Affect Each Other? What Is an Electric Field? What Is Electric Potential? What Is a Capacitor? What Are Electric Current and Resistance? What Are Semiconductors? What Are Superconductors? What Are Magnetic Dipoles and Magnetic Fields? What Is Electromagnetism? What Are Direct Current and Alternating Current? How Do Electric Motors Work? What Is an Electromagnetic Wave? Solids and Fluids What Are the States of Matter? What Is a Fluid? What Are Transverse and Longitudinal Waves? How Is Sound Generated? How Are Music and Musical Harmonies Made? What Is the Doppler Effect? What Makes a Sonic Boom? Quantum Mechanics What Is Quantization? What Is WaveParticle Duality? What Is the Heisenberg Uncertainty Principle? What Does Quantum Mechanics Tell Us about Hydrogen Atoms? What Is Quantum Tunneling? What Is a Quantum Computer? What Are Some Other Applications of Quantum Mechanics? Light and Optics What Is Light? What Is the Law of Reflection? What Is Refraction? How Do Lenses Work? What Are Some Common Refractive Vision Disorders, and How Are They Corrected with Lenses? How Do Microscopes Work? How Do Telescopes Work? How Does Interference Reveal Light's Wave Properties? What Is Diffraction? What Is Polarization, and Why Is It Useful? Why Is the Sky Blue? How Do Lasers Work, and What Makes Them Different from Other Light Sources? What Is a Light-Emitting Diode? What Is a Solar (Photovoltaic) Cell? Thermodynamics What Is Temperature? What Is the Kinetic Theory of Gases? What Is Thermal Expansion? What Are the Units for Thermal Energy, Heat, and Food Energy? What Are Heat Capacity and Specific Heat? What Are Phase Changes? What Is the First Law of Thermodynamics? What Is the Second Law of Thermodynamics? What Is a Heat Engine? What Are Quantum Statistics? How Cold Can You Get? Atoms and Nuclei Atoms and ElementsWhat Are They? What Is the RutherfordBohr Model of the Atom? What Are Atomic Orbitals and Shells? How Are X-Rays Produced? What Are the Basic Properties of Nuclei? What Is the Strong (Nuclear) Force? How Are Nuclei Bound by the Nuclear Force? What Is Nuclear Binding Energy? What Are the Benefits and Dangers of Radioactive Nuclei? What Is Fission? What Is Fusion? Fundamental Particles and Forces What Are Fundamental and Composite Particles? What Are the Historical Roots of the Search for Fundamental Particles? What Is Antimatter? What Is the Particle Zoo? How Do Particles Mediate Forces? What Are Quarks? What Are Leptons? What Is the Weak Force? What Is a Feynman Diagram? What Conservation Laws Are Associated with Hadrons and Leptons? What Is the Higgs Boson? What Is Unification? Relativity What's the Difference between Special Relativity and General Relativity? How Was Special Relativity Developed? What Are the Two Principles (or Postulates) of Special Relativity? How Are Time and Distance Measurements Affected in Relativity? What Is Spacetime? How Are Velocity Measurements Affected by High Speeds? What Is the Doppler Effect? What Is Relativistic Energy? How Is Relativity Connected to Electromagnetism? What Is the Principle of Equivalence? How Does General Relativity Describe Gravity? What Are Some Consequences of General Relativity? What Is a Black Hole? What Are Gravitational Waves? How Do We Use Relativity? So Is Everything Really Relative? Astrophysics and Cosmology What Are Astronomy, Astrophysics, and Cosmology? How Was Our Solar System Formed? What Are the Orbits of the Planets? What Other Objects Are in the Solar System? What Are Stars? What Is a Supernova? What Are Galaxies? How Has the Universe Evolved in Time? What Are Dark Matter and Dark Energy? Where Do We Go from Here? Index Further Readings appear at the end of each chapter.

Development of Security WLAN Protocol Based on Quantum GHZ Stats

This paper addresses the security WLAN protocol based on Quantum Greenberger---Horne---Zeilinger stats to overcome the flaws of wired equivalent privacy, temporal key integrity protocol, counter mode with CBC-MAC protocol, IEEE802.11i protocol, and ensure wireless communication information security. Our main theorem have two important corollaries. The first is an ingenious application of quantum mechanics to apply in wireless communication theorem. The second is the proof of the protocol that Eve invariably introduces errors within communication network if it wants to gain useful information. Here the novel idea is that quantum cryptography guarantees the security of wireless communication information.

Асимптотика решений неавтономных систем и приложений в квантовой механике

Асимптотика решений неавтономных систем и приложений в квантовой механике