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Sample records for quantum mechanical hamiltonian

  1. Quantum mechanical Hamiltonian models of discrete processes

    SciTech Connect

    Benioff, P.

    1981-03-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.

  2. Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

    SciTech Connect

    Al-Hashimi, M.H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

    2013-10-15

    We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.

  3. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

  4. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015

  5. Positive-operator-valued measures in the Hamiltonian formulation of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Arsenović, D.; Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

    2015-06-01

    In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positive-operator-valued measures (POVMs). In the Hamiltonian formulation of quantum mechanics, canonical coordinates are related to PVM. In this paper the results of an analysis of various aspects of applications of POVMs in the Hamiltonian formulation are reported. Several properties of state parameters and quantum observables given by POVMs or represented in an overcomplete basis, including the general Hamiltonian treatment of the Neumark extension, are presented. An analysis of the phase operator, given by the corresponding POVMs, in the Hilbert space and the Hamiltonian frameworks is also given.

  6. Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.

    PubMed

    Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao

    2013-09-10

    Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.

  7. Laboratory implementation of quantum-control-mechanism identification through Hamiltonian encoding and observable decoding

    SciTech Connect

    Rey-de-Castro, R.; Rabitz, H.

    2010-06-15

    We report on the laboratory implementation of quantum-control-mechanism identification through Hamiltonian encoding and observable decoding (HE-OD). Over a sequence of experiments, HE-OD introduces a special encoded signature into the components of a previously determined control field expressed in a chosen representation. The outcome appears as a modulated signal in the controlled system observable. Decoding the modulated signal identifies the hierarchy of correlations between components of the control field in a particular representation. In cases where the initial quantum state and observable operator are fully known, then HE-OD can also identify the transition amplitudes of the various Dyson expansion orders contributing to the controlled dynamics. The basic principles of HE-OD are illustrated for second harmonic generation when the components of the field representation are simply taken as the pixels in the pulse shaper. The outcome of HE-OD agrees well with simulations, verifying the concept.

  8. Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics

    SciTech Connect

    Caticha, Ariel; Bartolomeo, Daniel; Reginatto, Marcel

    2015-01-13

    Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the 'quantum potential' that leads to the Schrödinger equation follows naturally from information geometry.

  9. Multidimensional supersymmetric quantum mechanics: a scalar Hamiltonian approach to excited states by the imaginary time propagation method.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    Supersymmetric quantum mechanics (SUSY-QM) is shown to provide a novel approach to the construction of the initial states for the imaginary time propagation method to determine the first and second excited state energies and wave functions for a two-dimensional system. In addition, we show that all calculations are carried out in sector one and none are performed with the tensor sector two Hamiltonian. Through our tensorial approach to multidimensional supersymmetric quantum mechanics, we utilize the correspondence between the eigenstates of the sector one and two Hamiltonians to construct appropriate initial sector one states from sector two states for the imaginary time propagation method. The imaginary time version of the time-dependent Schrödinger equation is integrated to obtain the first and second excited state energies and wave functions using the split operator method for a two-dimensional anharmonic oscillator system and a two-dimensional double well potential. The computational results indicate that we can obtain the first two excited state energies and wave functions even when a quantum system does not exhibit any symmetry. Moreover, instead of dealing with the increasing computational complexity resulting from computations in the tensor sector two Hamiltonian, this study presents a new supersymmetric approach to calculations of accurate excited state energies and wave functions by directly using the scalar sector one Hamiltonian.

  10. An eight-dimensional quantum mechanical Hamiltonian for X + YCZ3 system and its applications to H + CH4 reaction

    NASA Astrophysics Data System (ADS)

    Liu, Rui; Xiong, Hongwei; Yang, Minghui

    2012-11-01

    An eight-dimensional quantum mechanical Hamiltonian has been proposed based on Palma and Clary's model in which the non-reacting CZ3 group keeps a C3v symmetry in the X + YCZ3 ↔ XY + CZ3 reaction J. Palma and D. C. Clary [J. Chem. Phys. 112, 1859 (2000), 10.1063/1.480749]. By transforming the original Cartesian coordinate system (x, s) into a scaled polar coordinate system (q, γ), the vibrational Hamiltonian of CZ3 group is expressed in a simple form with a clear physical picture. This Hamiltonian is used to investigate the H + CH4 → H2 + CH3 reaction on the Jordan-Gilbert potential energy surface. The total reaction probabilities are calculated for the initial ground state, and umbrella, bending, symmetric, and asymmetric stretching excited states of CH4 with total angular momentum J = 0. The integral cross sections for the reaction are also studied for these initial vibrational states with a centrifugal-sudden approximation. The total integral cross sections for the asymmetric stretching vibrational excited state are in good agreement with the experimental observations. The results also showed the difference of dynamical behavior between reactions from symmetric and asymmetric stretching excited states. The thermal rate constants are calculated for the temperature range T = 250-2000 K and compared with the experimental and other theoretical results.

  11. Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

    NASA Astrophysics Data System (ADS)

    Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.

    2016-03-01

    Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

  12. From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the 'Stochastic Matrix Form' decomposition

    SciTech Connect

    Castelnovo, Claudio . E-mail: castel@buphy.bu.edu; Chamon, Claudio; Mudry, Christopher; Pujol, Pierre

    2005-08-01

    Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.

  13. Hydration free energies using semiempirical quantum mechanical Hamiltonians and a continuum solvent model with multiple atomic-type parameters.

    PubMed

    Anisimov, Victor M; Cavasotto, Claudio N

    2011-06-23

    To build the foundation for accurate quantum mechanical (QM) simulation of biomacromolecules in an aqueous environment, we undertook the optimization of the COnductor-like Screening MOdel (COSMO) atomic radii and atomic surface tension coefficients for different semiempirical Hamiltonians adhering to the same computational conditions recently followed in the simulation of biomolecular systems. This optimization was achieved by reproducing experimental hydration free energies of a set consisting of 507 neutral and 99 ionic molecules. The calculated hydration free energies were significantly improved by introducing a multiple atomic-type scheme that reflects different chemical environments. The nonpolar contribution was treated according to the scaled particle Claverie-Pierotti formalism. Separate radii and surface tension coefficient sets have been developed for AM1, PM3, PM5, and RM1 semiempirical Hamiltonians, with an average unsigned error for neutral molecules of 0.64, 0.66, 0.73, and 0.71 kcal/mol, respectively. Free energy calculation of each molecule took on average 0.5 s on a single processor. The new sets of parameters will enhance the quality of semiempirical QM calculations using COSMO in biomolecular systems. Overall, these results further extend the utility of QM methods to chemical and biological systems in the condensed phase.

  14. Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics

    SciTech Connect

    Rose, Harald

    2003-12-11

    A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by the charge and the spin of the moving particle are derived. In addition the covariant equations for the dynamics of the components of the spin tensor are obtained. These equations can be transformed to the familiar BMT equation in the case of homogeneous electromagnetic fields. The quantization of the five-dimensional Hamilton-Jacobi equation yields a five-dimensional spinor wave equation, which degenerates to the Dirac equation in the stationary case if we neglect gravitation. The quantity which corresponds to the probability density of standard quantum mechanics is the four-dimensional mass density which has a real physical meaning. By means of the Green method the wave equation is transformed into an integral equation enabling a covariant relativistic path integral formulation. Using this approach a very accurate approximation for the four-dimensional propagator is derived. The proposed formalism makes Dirac's hole theory obsolete and can readily be extended to many particles.

  15. Quantum Hamiltonian Physics with Supercomputers

    NASA Astrophysics Data System (ADS)

    Vary, James P.

    2014-06-01

    The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark-gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

  16. Position-dependent mass quantum Hamiltonians: general approach and duality

    NASA Astrophysics Data System (ADS)

    Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.

    2016-03-01

    We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.

  17. Hamiltonian learning and certification using quantum resources.

    PubMed

    Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D G

    2014-05-16

    In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable.

  18. Hamiltonian learning and certification using quantum resources.

    PubMed

    Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D G

    2014-05-16

    In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable. PMID:24877920

  19. 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)

  20. Generalized quantum Hall projection Hamiltonians

    NASA Astrophysics Data System (ADS)

    Simon, Steven H.; Rezayi, E. H.; Cooper, Nigel R.

    2007-02-01

    Certain well known quantum Hall states—including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states—can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g .

  1. Non-Hermitian quantum Hamiltonians with PT symmetry

    SciTech Connect

    Jones-Smith, Katherine; Mathur, Harsh

    2010-10-15

    We formulate quantum mechanics for non-Hermitian Hamiltonians that are invariant under PT, where P is the parity and T denotes time reversal, for the case that time-reversal symmetry is odd (T{sup 2}=-1), generalizing prior work for the even case (T{sup 2}=1). We discover an analog of Kramer's theorem for PT quantum mechanics, present a prototypical example of a PT quantum system with odd time reversal, and discuss potential applications of the formalism.

  2. PT -symmetric Hamiltonians and their application in quantum information

    NASA Astrophysics Data System (ADS)

    Croke, Sarah

    2015-05-01

    We discuss the prospect of PT -symmetric Hamiltonians finding applications in quantum information science, and conclude that such evolution is unlikely to provide any benefit over existing techniques. Although it has been known for some time that PT -symmetric quantum theory, when viewed as a unitary theory, is exactly equivalent to standard quantum mechanics, proposals continue to be put forward for schemes in which PT -symmetric quantum theory can outperform standard quantum theory. The most recent of these is the suggestion to use PT -symmetric Hamiltonians to perform an exponentially fast database search, a task known to be impossible with a quantum computer. Further, such a scheme has been shown to apparently produce effects in conflict with fundamental information-theoretic principles, such as the impossibility of superluminal information transfer, and the invariance of entanglement under local operations. In this paper we propose three inequivalent experimental implementations of PT -symmetric Hamiltonians, with careful attention to the resources required to realize each such evolution. Such an operational approach allows us to resolve these apparent conflicts, and evaluate fully schemes proposed in the literature for faster time evolution and state discrimination.

  3. Uncertainty relation for non-Hamiltonian quantum systems

    SciTech Connect

    Tarasov, Vasily E.

    2013-01-15

    General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

  4. Hamiltonian mechanics limits microscopic engines

    NASA Astrophysics Data System (ADS)

    Anglin, James; Gilz, Lukas; Thesing, Eike

    2015-05-01

    We propose a definition of fully microscopic engines (micro-engines) in terms of pure mechanics, without reference to thermodynamics, equilibrium, or cycles imposed by external control, and without invoking ergodic theory. This definition is pragmatically based on the observation that what makes engines useful is energy transport across a large ratio of dynamical time scales. We then prove that classical and quantum mechanics set non-trivial limits-of different kinds-on how much of the energy that a micro-engine extracts from its fuel can be converted into work. Our results are not merely formal; they imply manageable design constraints on micro-engines. They also suggest the novel possibility that thermodynamics does not emerge from mechanics in macroscopic regimes, but rather represents the macroscopic limit of a generalized theory, valid on all scales, which governs the important phenomenon of energy transport across large time scale ratios. We propose experimental realizations of the dynamical mechanisms we identify, with trapped ions and in Bose-Einstein condensates (``motorized bright solitons'').

  5. New Hamiltonian constraint operator for loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Yang, Jinsong; Ma, Yongge

    2015-12-01

    A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  6. A geometric Hamiltonian description of composite quantum systems and quantum entanglement

    NASA Astrophysics Data System (ADS)

    Pastorello, Davide

    2015-05-01

    Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

  7. Time and a physical Hamiltonian for quantum gravity.

    PubMed

    Husain, Viqar; Pawłowski, Tomasz

    2012-04-01

    We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach.

  8. 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

  9. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Auletta, Gennaro; Fortunato, Mauro; Parisi, Giorgio

    2014-01-01

    Introduction; Part I. Basic Features of Quantum Mechanics: 1. From classical mechanics to quantum mechanics; 2. Quantum observable and states; 3. Quantum dynamics; 4. Examples of quantum dynamics; 5. Density matrix; Part II. More Advanced Topics: 6. Angular momentum and spin; 7. Identical particles; 8. Symmetries and conservation laws; 9. The measurement problem; Part III. Matter and Light: 10. Perturbations and approximation methods; 11. Hydrogen and helium atoms; 12. Hydrogen molecular ion; 13. Quantum optics; Part IV. Quantum Information: State and Correlations: 14. Quantum theory of open systems; 15. State measurement in quantum mechanics; 16. Entanglement: non-separability; 17. Entanglement: quantum information; References; Index.

  10. Squeezed states from a quantum deformed oscillator Hamiltonian

    NASA Astrophysics Data System (ADS)

    Ramírez, R.; Reboiro, M.

    2016-03-01

    The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions.

  11. Continuous decomposition of quantum measurements via Hamiltonian feedback

    NASA Astrophysics Data System (ADS)

    Florjanczyk, Jan; Brun, Todd A.

    2015-12-01

    We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamiltonian. Each probe in the stream interacts weakly with the target quantum system and then is measured projectively in a standard basis. This measurement result is used in a closed feedback loop to tune the interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process with the structure of a one-dimensional random walk. To maintain this structure and require that at long times the measurement outcomes be independent of the path, the allowed interaction Hamiltonians must lie in a restricted set such that the Hamiltonian terms on the target system form a finite-dimensional Jordan algebra. This algebraic structure of the interaction Hamiltonians yields a large class of generalized measurements that can be continuously performed by our scheme and we fully describe this set.

  12. Effective Hamiltonian for the hybrid double quantum dot qubit

    NASA Astrophysics Data System (ADS)

    Ferraro, E.; De Michielis, M.; Mazzeo, G.; Fanciulli, M.; Prati, E.

    2014-05-01

    Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single-qubit and two-qubits quantum logic ports. We derive the Schrieffer-Wolff effective Hamiltonian that describes in a simple and intuitive way the qubit by combining a Hubbard-like model with a projector operator method. As a result, the Hubbard-like Hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons. The effective Hamiltonian is exploited to derive the dynamical behavior of the system and its eigenstates on the Bloch sphere to generate qubits operation for quantum logic ports. A realistic implementation in silicon and the coupling of the qubit with a detector are discussed.

  13. Phase space quantum mechanics

    NASA Astrophysics Data System (ADS)

    Błaszak, Maciej; Domański, Ziemowit

    2012-02-01

    This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic

  14. The detectability lemma and its applications to quantum Hamiltonian complexity

    NASA Astrophysics Data System (ADS)

    Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph

    2011-11-01

    Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general

  15. Bose-Hubbard Hamiltonian: Quantum chaos approach

    NASA Astrophysics Data System (ADS)

    Kolovsky, Andrey R.

    2016-03-01

    We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.

  16. Noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gamboa, J.; Loewe, M.; Rojas, J. C.

    2001-09-01

    A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

  17. PT quantum mechanics - Recent results

    NASA Astrophysics Data System (ADS)

    Bender, Carl M.

    2012-09-01

    Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H = p2+ix3 has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p2+ix3 is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p2-x4, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric gφ4 quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.

  18. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

    2015-06-01

    We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects.

  19. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians.

    PubMed

    Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

    2015-06-01

    We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects. PMID:26196632

  20. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

    Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

    2010-09-15

    We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

  1. Driver Hamiltonians for constrained optimization in quantum annealing

    NASA Astrophysics Data System (ADS)

    Hen, Itay; Sarandy, Marcelo S.

    2016-06-01

    One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems, the main reason for this being the rigid layout of their quantum bits as well as their sparse connectivity. In particular, the implementation of constraints has become a major bottleneck in the embedding of practical problems, because the latter is typically achieved by adding harmful penalty terms to the problem Hamiltonian, a technique that often requires an all-to-all connectivity between the qubits. Recently, a novel technique designed to obviate the need for penalty terms was suggested; it is based on the construction of driver Hamiltonians that commute with the constraints of the problem, rendering the latter constants of motion. In this work we propose general guidelines for the construction of such driver Hamiltonians given an arbitrary set of constraints. We illustrate the broad applicability of our method by analyzing several diverse examples, namely, graph isomorphism, not-all-equal three-satisfiability, and the so-called Lechner-Hauke-Zoller constraints. We also discuss the significance of our approach in the context of current and future experimental quantum annealers.

  2. Interest rates in quantum finance: the Wilson expansion and Hamiltonian.

    PubMed

    Baaquie, Belal E

    2009-10-01

    Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

  3. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Mandl, F.

    1992-07-01

    The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.

  4. Supersymmetry in quantum mechanics

    SciTech Connect

    Khare, Avinash

    2004-12-23

    An elementary introduction is given to the subject of supersymmetry in quantum mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct n new exactly solvable Hamiltonians having n - 1, n - 2,..., 0 bound states. The relationship between the eigenvalues, eigenfunctions and scattering matrix of the supersymmetric partner potentials is derived and a class of reflectionless potentials are explicitly constructed. We extend the operator method of solving the one-dimensional harmonic oscillator problem to a class of potentials called shape-invariant potentials. It is worth emphasizing that this class includes almost all the solvable problems that are found in the standard text books on quantum mechanics. Further, we show that given any potential with at least one bound state, one can very easily construct one continuous parameter family of potentials having same eigenvalues and s-matrix. The supersymmetry inspired WKB approximation (SWKB) is also discussed and it is shown that unlike the usual WKB, the lowest order SWKB approximation is exact for the shape-invariant potentials and further, this approximation is not only exact for large quantum numbers but by construction, it is also exact for the ground state. Finally, we also construct new exactly solvable periodic potentials by using the machinery of supersymmetric quantum mechanics.

  5. Participation spectroscopy and entanglement Hamiltonian of quantum spin models

    NASA Astrophysics Data System (ADS)

    Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

    2014-08-01

    Shannon-Rényi entropies and associated participation spectra quantify how much a many-body wave-function is localized in a given configuration basis. Using these tools, we present an analysis of the ground-state wave functions of various quantum spin systems in one and two dimensions. General ideas and a review of the current status of this field are first given, with a particular emphasis on universal subleading terms characterizing different quantum phases of matter, and associated transitions. We highlight the connection with the related entanglement entropies and spectra when this is possible. In a second part, new results are presented for the participation spectra of interacting spin models, mostly based on quantum Monte Carlo simulations, but also using perturbation theory in some cases. For full antiferromagnetic one-dimensional systems, participation spectra are analyzed in terms of ferromagnetic domain walls which experience a pairwise attractive interaction. This confinement potential is either linear for long-range Néel order, or logarithmic for quasi-long-range order. The case of subsystems is also analyzed in great detail for a 2d dimerized Heisenberg model undergoing a quantum phase transition between a gapped paramagnet and a Néel phase. Participation spectra of line shaped (1d) sub-systems are quantitatively compared with finite temperature participation spectra of ansatz effective boundary (1d) entanglement Hamiltonians. While short-range models describe almost perfectly the gapped side, the Néel regime is best compared using long-range effective Hamiltonians. Spectral comparisons performed using Kullback-Leibler divergences, a tool potentially useful for entanglement spectra, provide a quantitative way to identify both the best boundary entanglement Hamiltonian and effective temperature.

  6. Supersymmetric q-deformed quantum mechanics

    SciTech Connect

    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.

  7. Quantum Simulation via Filtered Hamiltonian Engineering: Application to Perfect Quantum Transport in Spin Networks

    NASA Astrophysics Data System (ADS)

    Ajoy, Ashok; Cappellaro, Paola

    2013-05-01

    We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

  8. Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks.

    PubMed

    Ajoy, Ashok; Cappellaro, Paola

    2013-05-31

    We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions. PMID:23767705

  9. 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.

  10. Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems

    NASA Astrophysics Data System (ADS)

    Barth, A. M.; Vagov, A.; Axt, V. M.

    2016-09-01

    We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.

  11. The Hamiltonian Mechanics of Stochastic Acceleration

    SciTech Connect

    Burby, J. W.

    2013-07-17

    We show how to nd the physical Langevin equation describing the trajectories of particles un- dergoing collisionless stochastic acceleration. These stochastic di erential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.

  12. Faster than Hermitian Quantum Mechanics

    SciTech Connect

    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.

  13. Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

    SciTech Connect

    Longhi, Stefano

    2014-06-15

    Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.

  14. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    PubMed

    Dridi, G; Julien, R; Hliwa, M; Joachim, C

    2015-08-28

    The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor. PMID:26234709

  15. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    PubMed

    Dridi, G; Julien, R; Hliwa, M; Joachim, C

    2015-08-28

    The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

  16. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate

    NASA Astrophysics Data System (ADS)

    Dridi, G.; Julien, R.; Hliwa, M.; Joachim, C.

    2015-08-01

    The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

  17. PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Jones, Hugh; Znojil, Miloslav

    2008-06-01

    Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the

  18. A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II

    NASA Astrophysics Data System (ADS)

    Ogata, Yoshiko

    2016-06-01

    We give a characterization of the class of gapped Hamiltonians introduced in Part I (Ogata, A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015). The Hamiltonians in this class are given as MPS (Matrix product state) Hamiltonians. In Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), we list up properties of ground state structures of Hamiltonians in this class. In this Part II, we show the converse. Namely, if a (not necessarily MPS) Hamiltonian H satisfies five of the listed properties, there is a Hamiltonian H' from the class by Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), satisfying the following: The ground state spaces of the two Hamiltonians on the infinite interval coincide. The spectral projections onto the ground state space of H on each finite intervals are approximated by that of H' exponentially well, with respect to the interval size. The latter property has an application to the classification problem with open boundary conditions.

  19. 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.

  20. quantum mechanics

    PubMed Central

    Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.

    2013-01-01

    -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 -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. 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 -synthetic materials are being developed, and the 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 -symmetric quantum mechanics. PMID:23509390

  1. From Classical to Quantum and Back: A Hamiltonian Scheme for Adaptive Multiresolution Classical/Path-Integral Simulations.

    PubMed

    Kreis, Karsten; Tuckerman, Mark E; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello

    2016-07-12

    Quantum delocalization of atomic nuclei affects the physical properties of many hydrogen-rich liquids and biological systems even at room temperature. In computer simulations, quantum nuclei can be modeled via the path-integral formulation of quantum statistical mechanics, which implies a substantial increase in computational overhead. By restricting the quantum description to a small spatial region, this cost can be significantly reduced. Herein, we derive a bottom-up, rigorous, Hamiltonian-based scheme that allows molecules to change from quantum to classical and vice versa on the fly as they diffuse through the system, both reducing overhead and making quantum grand-canonical simulations possible. The method is validated via simulations of low-temperature parahydrogen. Our adaptive resolution approach paves the way to efficient quantum simulations of biomolecules, membranes, and interfaces. PMID:27214610

  2. Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem

    NASA Astrophysics Data System (ADS)

    Ramezanpour, A.

    2016-06-01

    We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.

  3. Quantum Mechanics

    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...

  4. A particle-field Hamiltonian in relativistic quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Arai, Asao

    2000-07-01

    We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F≔[⊕4L2(R3)]⊗Frad, where Frad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a deformation parameter connecting the Hamiltonian with the "dipole approximation" (τ=0) and the original Hamiltonian (τ=1). We first discuss the self-adjointness problem of Hτ(V,g). Then we consider Hτ≔Hτ(0,g), the Hamiltonian without the external potential. It is shown that, under a general condition on g, the closure of Hτ is unitarily equivalent to a direct integral ∫R3⊕Hτ(p)¯dp with a fiber Hamiltonian Hτ(p) acting in the four direct sum ⊕4Frad of Frad, physically the polaron Hamiltonian of the Dirac particle with total momentum p∈R3.

  5. Quantum error suppression with commuting Hamiltonians: two local is too local.

    PubMed

    Marvian, Iman; Lidar, Daniel A

    2014-12-31

    We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

  6. 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)

  7. From Model Hamiltonians to ab Initio Hamiltonians and Back Again: Using Single Excitation Quantum Chemistry Methods To Find Multiexciton States in Singlet Fission Materials.

    PubMed

    Mayhall, Nicholas J

    2016-09-13

    Due to the promise of significantly enhanced photovoltaic efficiencies, significant effort has been directed toward understanding and controlling the singlet fission mechanism. Although accurate quantum chemical calculations would provide a detail-rich view of the singlet fission mechanism, this is complicated by the multiexcitonic nature of one of the key intermediates, the (1)(TT) state. Being described as two simultaneous and singlet-coupled triplet excitations on a pair of nearest neighbor monomers, the (1)(TT) state is inherently a multielectronic excitation. This fact renders most single-reference ab initio quantum chemical methods incapable of providing accurate results. This paper serves two purposes: (1) to demonstrate that the multiexciton states in singlet fission materials can be described using a spin-only Hamiltonian and with each monomer treated as a biradical and (2) to propose a very simple procedure for extracting the values for this Hamiltonian from single-reference calculations. Numerical examples are included for a number of different systems, including dimers, trimers, tetramers, and a cluster comprised of seven chromophores. PMID:27472260

  8. Algebraic expression of the IBM3 hamiltonian in terms of various quantum numbers

    NASA Astrophysics Data System (ADS)

    Hasegawa, M.

    1991-04-01

    The properties of the IBM3 hamiltonian are algebraically studied. The IBM3 hamiltonian determined microscopically has as characteristic that the isospin T, rmrather than the spin J, is essential to classifying the energy spectra. The T-dependence of the two-body boson interactions is expressed in terms of the Casimir operators or quantum numbers of various groups. This algebraic approach makes preparations for phenomenological understanding of light nuclei with definite isospin.

  9. Two-Dimensional Quantum Hamiltonians with Shape Invariance Symmetry

    NASA Astrophysics Data System (ADS)

    Panahi, H.

    2008-10-01

    It is shown that the Casimir operator associated with the U(1) Lie derivative defined on the S 2= SU(2)/ U(1) base manifold, can be interpreted as Hamiltonians of a pair of scalar particle and scalar anti-particle with opposite charges over the S 2 manifold in the presence of a magnetic monopole located at its origin and an external electric field. Using the SU(2) representation, the spectra of these Hamiltonians have been obtained. It is also proved that these Hamiltonians are isospectral and having the shape invariance symmetry, i.e. they are supersymmetric partner of each other. Also the Dirac’s quantization of magnetic charge comes very naturally from the finiteness of the SU(2) representation.

  10. Quantum simulation of pairing Hamiltonians with nearest-neighbor-interacting qubits

    NASA Astrophysics Data System (ADS)

    Wang, Zhixin; Gu, Xiu; Wu, Lian-Ao; Liu, Yu-xi

    2016-06-01

    Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators." Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. The fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.

  11. 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.

  12. Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

    PubMed

    Gosset, David; Terhal, Barbara M; Vershynina, Anna

    2015-04-10

    We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

  13. Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

    PubMed

    Gosset, David; Terhal, Barbara M; Vershynina, Anna

    2015-04-10

    We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice. PMID:25910098

  14. Decomposition of unitary matrices for finding quantum circuits: application to molecular Hamiltonians.

    PubMed

    Daskin, Anmer; Kais, Sabre

    2011-04-14

    Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems. PMID:21495747

  15. Hamiltonian of photons in a single-mode optical fiber for quantum communications protocols

    NASA Astrophysics Data System (ADS)

    Miroshnichenko, G. P.

    2012-05-01

    A phenomenological Hamiltonian of photons in a single-mode stochastic inhomogeneous optical fiber (OF) is derived. Quantization of radiation is performed in the basis of an ideal OF with proper calibration that ensures transversality of the electric-field-displacement vector. Stochastic parameters of the Hamiltonian are determined by using the reciprocal tensor of the dielectric permittivity averaged over the OF segment volume. The Hamiltonian is parametrized by three phenomenological parameters and preserves the number of photons. It is assumed that the segment of the OF is divided into random subsegments with optical parameters defined by the Wiener process with respect to the longitudinal coordinate. The temporal dynamics of the single-photon density matrix is analyzed in the basis of states with orthogonal polarizations. The relative quantum beat error rate in the sifted quantum key distributed according to the BB84 protocol with polarization coding of information averaged over the scatter of the OF parameters is calculated.

  16. Realization of a quantum Hamiltonian Boolean logic gate on the Si(001):H surface.

    PubMed

    Kolmer, Marek; Zuzak, Rafal; Dridi, Ghassen; Godlewski, Szymon; Joachim, Christian; Szymonski, Marek

    2015-08-01

    The design and construction of the first prototypical QHC (Quantum Hamiltonian Computing) atomic scale Boolean logic gate is reported using scanning tunnelling microscope (STM) tip-induced atom manipulation on an Si(001):H surface. The NOR/OR gate truth table was confirmed by dI/dU STS (Scanning Tunnelling Spectroscopy) tracking how the surface states of the QHC quantum circuit on the Si(001):H surface are shifted according to the input logical status. PMID:26144212

  17. Hamiltonian operator for loop quantum gravity coupled to a scalar field

    NASA Astrophysics Data System (ADS)

    Alesci, E.; Assanioussi, M.; Lewandowski, J.; Mäkinen, I.

    2015-06-01

    We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on the idea of so-called special loops. We discuss in detail the regularization procedure and the assignment of the loops, along with the properties of the resulting operator. We compute the action of the squared Hamiltonian operator on spin network states, and close with some comments and outlooks.

  18. Optical-lattice Hamiltonians for relativistic quantum electrodynamics

    SciTech Connect

    Kapit, Eliot; Mueller, Erich

    2011-03-15

    We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1, and 3+1 dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to (2+1)-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

  19. Statistical mechanics based on fractional classical and quantum mechanics

    SciTech Connect

    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.

  20. Facing quantum mechanical reality.

    PubMed

    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.

  1. Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory

    SciTech Connect

    Vary, J.P.; Maris, P.; Shirokov, A.M.; Honkanen, H.; li, J.; Brodsky, S.J.; Harindranath, A.; Teramond, G.F.de; /Costa Rica U.

    2009-08-03

    Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually,we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

  2. Is quantum mechanics exact?

    NASA Astrophysics Data System (ADS)

    Kapustin, Anton

    2013-06-01

    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.

  3. Is quantum mechanics exact?

    SciTech Connect

    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.

  4. Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices

    PubMed Central

    Chandrashekar, C. M.

    2013-01-01

    From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian. PMID:24088731

  5. Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

    SciTech Connect

    Richardson, W.H. . E-mail: whr@stanford.edu

    2006-06-15

    A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.

  6. Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach.

    PubMed

    Lee, Myeong H; Troisi, Alessandro

    2016-06-01

    Vibronic coupling between the electronic and vibrational degrees of freedom has been reported to play an important role in charge and exciton transport in organic photovoltaic materials, molecular aggregates, and light-harvesting complexes. Explicitly accounting for effective vibrational modes rather than treating them as a thermal environment has been shown to be crucial to describe the effect of vibronic coupling. We present a methodology to study dissipative quantum dynamics of vibronically coupled systems based on a surrogate Hamiltonian approach, which is in principle not limited by Markov approximation or weak system-bath interaction, using a vibronic basis. We apply vibronic surrogate Hamiltonian method to a linear chain system and discuss how different types of relaxation process, intramolecular vibrational relaxation and intermolecular vibronic relaxation, influence population dynamics of dissipative vibronic systems. PMID:27276944

  7. A quantum mechanical point of view to perturbative problems in classical mechanics

    NASA Astrophysics Data System (ADS)

    Dattoli, G.; Torre, A.

    1993-11-01

    In this article it is shown that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of noncollisional particles. The method discussed is based on the concepts of an evolution operator and interaction picture, which can be introduced for a classical Hamiltonian in full analogy with quantum mechanics. The usefulness of the developed method to treat the quantum extension of the Liouville equation is also stressed.

  8. An efficient matrix product operator representation of the quantum chemical Hamiltonian.

    PubMed

    Keller, Sebastian; Dolfi, Michele; Troyer, Matthias; Reiher, Markus

    2015-12-28

    We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries - abelian and non-abelian - and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.

  9. An efficient matrix product operator representation of the quantum chemical Hamiltonian

    SciTech Connect

    Keller, Sebastian Reiher, Markus; Dolfi, Michele Troyer, Matthias

    2015-12-28

    We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.

  10. 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)

  11. Quantum mechanics for applied physics and engineering

    NASA Astrophysics Data System (ADS)

    Fromhold, A. T., Jr.

    An introduction to quantum mechanics is provided, taking into account wave-particle duality, classical wave motion, the wave nature of particles the development of the time-dependent and time-independent Schroedinger wave equations, the wave-packet solutions and the uncertainty relation, and the expectation values for quantum-mechanical operators. Many-particle systems and quantum statistics are considered along with a free-electron model and the Boltzmann equation, the Wentzel-Kramers-Brillouin approximation and electron tunneling, perturbation theory, diffraction of valence electrons, and the nearly-free-electron model. The periodicity of crystalline solids is examined, and Bloch's theorem and energy bands for a periodic potential are discussed, giving attention to the periodic potential characteristic of the perfect monocrystal, the Hamiltonian for an electron in a periodic potential, and energy bands from the viewpoint of the one-electron atomic levels.

  12. Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

    SciTech Connect

    Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar

    2015-09-15

    The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

  13. Gravity and Quantum Mechanics

    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

  14. A Transfer Hamiltonian Model for Devices Based on Quantum Dot Arrays

    PubMed Central

    Illera, S.; Prades, J. D.; Cirera, A.; Cornet, A.

    2015-01-01

    We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the system and it is based on the Transfer Hamiltonian approach. A set of noncoherent rate equations can be written and the interaction between the quantum dots and between the quantum dots and the electrodes is introduced by transition rates and capacitive couplings. A realistic modelization of the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents, and the density of states of each quantum dot have been taken into account. The effects of the local potential are computed within the self-consistent field regime. While the description of the theoretical framework is kept as general as possible, two specific prototypical devices, an arbitrary array of quantum dots embedded in a matrix insulator and a transistor device based on quantum dots, are used to illustrate the kind of unique insight that numerical simulations based on the theory are able to provide. PMID:25879055

  15. Grassmann matrix quantum mechanics

    DOE PAGES

    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

  16. Copenhagen 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.

  17. Taming the zoo of supersymmetric quantum mechanical models

    NASA Astrophysics Data System (ADS)

    Smilga, A. V.

    2013-05-01

    We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.

  18. ``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.

  19. Quantum mechanics over sets

    NASA Astrophysics Data System (ADS)

    Ellerman, David

    2014-03-01

    In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

  20. Deformed Conformal and Supersymmetric Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Spiridonov, Vyacheslav

    Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e., the spectrum of one can be obtained from another (with possible exception of the lowest level) by the q2-factor scaling. A special class of the self-similar potentials is shown to obey the dynamical conformal symmetry algebra suq(1,1). These potentials exhibit exponential spectra and corresponding raising and lowering operators satisfy the q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane.

  1. Landau problem in noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Sayipjamal, Dulat; Li, Kang

    2008-02-01

    The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues. Supported by National Natural Science Foundation of China (10465004, 10665001, 10575026) and Abdus Salam ICTP, Trieste, Italy

  2. Supersymmetric quantum mechanics and its applications

    SciTech Connect

    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.

  3. New solutions of the hamiltonian and diffeomorphism constraints of quantum gravity from a highest weight loop representation

    NASA Astrophysics Data System (ADS)

    Aldaya, V.; Navarro-Salas, J.

    1991-04-01

    We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space. On leave of absence from the Departamento de Fisica Teorica, Universidad de Valencia, and IFIC, Centro Mixto Universidad de Valencia - CSIC, Burjassot, Spain.

  4. Contribution from the interaction Hamiltonian to the expectation value of particle number with the non-equilibrium quantum field theory

    SciTech Connect

    Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki

    2012-07-27

    We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.

  5. Epigenetics: Biology's Quantum Mechanics.

    PubMed

    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.

  6. Epigenetics: Biology's Quantum Mechanics.

    PubMed

    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. PMID:22639577

  7. Quantum Mechanics, Volume 1

    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.

  8. Feynman's simple quantum mechanics

    NASA Astrophysics Data System (ADS)

    Taylor, Edwin F.

    1997-03-01

    This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: "Explore all paths." All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.

  9. Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory

    SciTech Connect

    Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Shirokov, A.M.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Ng, E.G.; Yang, C.; Sosonkina, M.; /Ames Lab

    2012-06-22

    Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.

  10. A restricted quantum reaction path Hamiltonian: Theory, discrete variable representation propagation algorithm, and applications

    NASA Astrophysics Data System (ADS)

    González, Javier; Giménez, Xavier; Bofill, Josep Maria

    2009-08-01

    A derivation of a quantum reaction path Hamiltonian is proposed, which is based on a reformulation of the classical version of González et al. [J. Phys. Chem. A 105, 5022 (2001)], and the resulting equations are solved by means of a discrete variable representation approach, leading to a well-suited algorithm for the calculation of quantum dynamics of chemical reactions involving polyatomic molecules. General expressions for any type of reaction path are presented with special interest in the intrinsic reaction coordinate, which have been used to study selected cases, including a one-dimensional Eckart barrier, for which results are shown to be exact, two bidimensional systems, namely, a Müller-Brown potential energy surface, which is characteristic of polyatomic isomerization processes, and the collinear H+H2 chemical reaction, and finally the tridimensional, J =0, F+H2 reaction. Results for the specific chemical systems are shown to be in quite good agreement with exact two- and three-dimensional quantum calculations concerning autocorrelation functions as well as transmission factors as a function of total energy.

  11. Nontrivial systems and the necessity of the scalar quantum mechanics axioms

    SciTech Connect

    Kotulek, Jan

    2009-06-15

    We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric Aharonov-Bohm effect is presented. It illustrates the topological obstructions for the existence of a Hamiltonian.

  12. Stability and Clustering for Lattice Many-Body Quantum Hamiltonians with Multiparticle Potentials

    NASA Astrophysics Data System (ADS)

    Faria da Veiga, Paulo A.; O'Carroll, Michael

    2015-11-01

    We analyze a quantum system of N identical spinless particles of mass m, in the lattice Z^d, given by a Hamiltonian H_N=T_N+V_N, with kinetic energy T_N≥ 0 and potential V_N=V_{N,2}+V_{N,3} composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials V_{N,2} and V_{N,3} on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the H_N spectrum, \\underline{σ }(H_N)≥ -cN, for c>0 independent of N. For V_{N,3}=0, H_N is unstable, and the system collapses. If V_{N,3}not =0, H_N is stable and, for strong enough repulsion, we obtain \\underline{σ }(H_N)≥ -c' N, where c'N is the energy of ( N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [ \\underline{σ }(V_N)/N ] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value N_s of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers N_r and N_s-N_r, with N_r=1,ldots ,N_s-1.

  13. Classical Mechanics as Nonlinear Quantum Mechanics

    SciTech Connect

    Nikolic, Hrvoje

    2007-12-03

    All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.

  14. N=4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking, and superconformal quantum mechanics

    NASA Astrophysics Data System (ADS)

    Donets, E. E.; Pashnev, A.; Juan Rosales, J.; Tsulaia, M. M.

    2000-02-01

    The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with one-quarter, one-half, and three-quarters of unbroken (broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM, while the one-dimensional N=4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N=4 superconformal quantum-mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed.

  15. 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.

  16. Quantum Mechanics as Dualism

    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.

  17. 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.

  18. Hamiltonian formulation of general relativity.

    NASA Astrophysics Data System (ADS)

    Teitelboim, Claudio

    The following sections are included: * INTRODUCTION * HAMILTONIAN FORMULATION OF GAUGE THEORIES (PRE-BRST) * BRST HAMILTONIAN FORMULATION OF GAUGE THEORIES * DYNAMICS OF GRAVITATIONAL FIELD * DOES THE HAMILTONIAN VANISH? GENERAL COVARIANCE AS AN "ORDINARY" GAUGE INVARIANCE * GENERALLY COVARIANT SYSTEMS * TIME AS A CANONICAL VARIABLE. ZERO HAMILTONIAN * Parametrized Systems * Zero Hamiltonian * Parametrization and Explicit Time Dependence * TIME REPARAMETRIZATION INVARIANCE * Form of Gauge Transformations * Must the Hamiltonian be Zero for a Generally Covariant System? * Simple Example of a Generally Covariant System with a Nonzero Hamiltonian * "TRUE DYNAMICS" VERSUS GAUGE TRANSFORMATIONS * Interpretation of the Formalism * Reduced Phase Space * MUST TIME FLOW? * GAUGE INDEPENDENCE OF PATH INTEGRAL FOR A PARAMETRIZED SYSTEM ILLUSTRATED. EQUIVALENCE OF THE GAUGES t = τ AND t = 0 * Reduced Phase Space Transition Amplitude as a Reduced Phase Space Path Integral * Canonical Gauge Conditions * Gauge t = 0 * Gauge t α τ * BRST CHARGE OF GRAVITATIONAL FIELD * ELEMENTS OF BRST THEORY * THE GHOST, YOU'VE COME A LONG WAY BABY * Introduction * Quantum mechanics, the art of finding and combining simple elementary processes * Ghosts necessary to keep elementary processes simple * BRST symmetry: ghosts and matter become different components of single geometrical object * BRST SYMMETRY IN CLASSICAL MECHANICS * Ghosts have role in classical mechanics * Gauge invariance and constraints * Classical mechanics over Grassmann algebra necessary * Higher order structure functions * Rank defined. Open algebras * Ghosts. Ghost number. BRST generator as generating function for structure functions * A belianization of constraints. Existence of Ω * Uniqueness of Ω * Classical BRST cohomology * QUANTUM BRST THEORY * States and operators * Ghost number * BRST invariant states * Quantum BRST cohomology * Equivalence of the BRST physical subspace with the conventional gauge

  19. Hamiltonian purification

    SciTech Connect

    Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo; Pascazio, Saverio; Nakazato, Hiromichi; Yuasa, Kazuya; Giovannetti, Vittorio

    2015-12-15

    The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.

  20. Hamiltonian purification

    NASA Astrophysics Data System (ADS)

    Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya; Giovannetti, Vittorio

    2015-12-01

    The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians {h1, …, hm} operating on a d-dimensional quantum system ℋd, the problem consists in identifying a set of commuting Hamiltonians {H1, …, Hm} operating on a larger dE-dimensional system ℋdE which embeds ℋd as a proper subspace, such that hj = PHjP with P being the projection which allows one to recover ℋd from ℋdE. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for 𝔲(d) are provided.

  1. Effective S =1/2 Hamiltonians and the Quantum Spin Ice Ground State of Yb2Ti2O7

    NASA Astrophysics Data System (ADS)

    Gaulin, Bruce D.

    2013-03-01

    New neutron scattering instrumentation offers unprecedented opportunities for mapping out the full dispersion and dynamic susceptibility of magnetic materials. In turn, these measurements can be exploited to determine their microscopic spin Hamiltonians in great detail. We've used these techniques to examine the exotic quantum spin ice ground state of Yb2Ti2O7, a pyrochlore magnet, which can be thought of in terms of spins decorating a network of corner-sharing tetrahedra. In this environment, Yb3+displays a ground state crystal field doublet which is very well separated from its excited states, resulting in an effective S =1/2 description for the Yb moments. It's positive Curie-Weiss constant of ~ 0.5 K indicates net ferromagnetic interactions and it displays a g-tensor with XY anisotropy. However strong spin orbit effects give rise to an anisotropic exchange Hamiltonian, which can be understood in quantitative detail by modeling time-of-flight neutron scattering in a high field polarized state with spin wave theory using anisotropic exchange. The resulting Hamiltonian shows strong coupling between local z-components of spin, as in spin ice, but also substantial terms that encourage quantum fluctuations. Armed with the microscopic spin Hamiltonian, the mean field phase diagram and a range of physical properties can be calculated and compared with experiment. We see that any possible ordering is strongly suppressed relative to mean field theory by the presence of geometrical frustration, quantum fluctuations, or both; and the low temperature bulk properties are well accounted for by the effective S =1/2 Hamiltonian we determine.

  2. 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.

  3. A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

    NASA Astrophysics Data System (ADS)

    Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

    2015-01-01

    We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

  4. PT quantum mechanics.

    PubMed

    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.

  5. 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.

  6. Probability Interpretation of Quantum Mechanics.

    ERIC Educational Resources Information Center

    Newton, Roger G.

    1980-01-01

    This paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the "paradoxical" aspects of quantum mechanics lose their counterintuitive character.…

  7. 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.

  8. Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces

    SciTech Connect

    Asplund, Erik; Kluener, Thorsten

    2012-03-28

    In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.

  9. Optimal control of open quantum systems: a combined surrogate hamiltonian optimal control theory approach applied to photochemistry on surfaces.

    PubMed

    Asplund, Erik; Klüner, Thorsten

    2012-03-28

    In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated. PMID:22462846

  10. Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces

    NASA Astrophysics Data System (ADS)

    Asplund, Erik; Klüner, Thorsten

    2012-03-01

    In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)], 10.1063/1.473950. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998), 10.1063/1.475576; Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)], 10.1063/1.1650297. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated.

  11. Extended supersymmetry and hidden symmetries in one-dimensional matrix quantum mechanics

    NASA Astrophysics Data System (ADS)

    Andrianov, A. A.; Sokolov, A. V.

    2016-01-01

    We study properties of nonlinear supersymmetry algebras realized in the one-dimensional quantum mechanics of matrix systems. Supercharges of these algebras are differential operators of a finite order in derivatives. In special cases, there exist independent supercharges realizing an (extended) supersymmetry of the same super-Hamiltonian. The extended supersymmetry generates hidden symmetries of the super-Hamiltonian. Such symmetries have been found in models with (2×2)-matrix potentials.

  12. Quantum mechanical study of a generic quadratically coupled optomechanical system

    NASA Astrophysics Data System (ADS)

    Shi, H.; Bhattacharya, M.

    2013-04-01

    Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.

  13. Communication: Quantum mechanics without wavefunctions

    SciTech Connect

    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.

  14. CALL FOR PAPERS: Special issue on Pseudo Hermitian Hamiltonians in Quantum Physics

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Jones, Hugh F.; Znojil, Miloslav

    2007-11-01

    This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of Pseudo Hermitian Hamiltonians in Quantum Physics as featured in the conference '6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics', City University London, UK, July 16--18 2007 (http://www.staff.city.ac.uk/~fring/PT/). Invited speakers at that meeting as well as other researchers working in the field are invited to submit a research paper to this issue. The Editorial Board has invited Andreas Fring, Hugh F Jones and Miloslav Znojil to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows: •The subject of the paper should relate to the subject of the workshop ((see list of topics in the website of the conference http://www.staff.city.ac.uk/~fring/PT/). •Contributions will be refereed and processed according to the usual procedure of the journal. •Conference papers may be based on already published work but should either contain significant additional new results and/or insights or give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems. •Papers submitted by non-participants should be original and contain substantial new results. The guidelines for the preparation of contributions are the following: •The DEADLINE for submission of contributions is 16 November 2007. This deadline will allow the special issue to appear in June 2008. •There is a nominal page limit of 16 printed pages (approximately 9600 words) per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical may be found at www.iop.org/Journals/jphysa. •Contributions to the special issue should, if possible, be submitted electronically by web

  15. Quantum Mechanics in Insulators

    SciTech Connect

    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).

  16. Quantum mechanics from invariance principles

    NASA Astrophysics Data System (ADS)

    Moldoveanu, Florin

    2015-07-01

    Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.

  17. Emergent quantum mechanics without wavefunctions

    NASA Astrophysics Data System (ADS)

    Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.

    2016-03-01

    We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.

  18. Supersymmetric quantum mechanics and paraquantization

    SciTech Connect

    Morchedi, O.; Mebarki, N.

    2012-06-27

    The paraquantum Hamiltonian of a free particle is shown to be supersymmetric. Depending on the space-time dimension, the corresponding N=1 and N=2 supercharges are constructed and the related Hamiltonians are derived.

  19. 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

  20. Quantum mechanical force field for water with explicit electronic polarization

    PubMed Central

    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

  1. Quantum mechanical force field for water with explicit electronic polarization.

    PubMed

    Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali

    2013-08-01

    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 × 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

  2. 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.

  3. Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators

    SciTech Connect

    Shamshutdinova, V. V.

    2012-10-15

    The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.

  4. Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Moussa, Miled H. Y.

    2016-04-01

    It has been argued that it is incompatible to maintain unitary time evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a nonobservable operator as it ceases to be quasi-Hermitian when the metric becomes time dependent.

  5. 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

  6. 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…

  7. Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation

    NASA Astrophysics Data System (ADS)

    Lisitsyn, Ya. V.; Shapovalov, A. V.

    1998-05-01

    A study is made of the possibility of reducing quantum analogs of Hamiltonian systems to Lie algebras. The procedure of reducing classical systems to orbits in a coadjoint representation based on Lie algebra is well-known. An analog of this procedure for quantum systems described by linear differential equations (LDEs) in partial derivatives is proposed here on the basis of the method of noncommutative integration of LDEs. As an example illustrating the procedure, an examination is made of nontrivial systems that cannot be integrated by separation of variables: the Gryachev-Chaplygin hydrostat and the Kovalevskii gyroscope. In both cases, the problem is reduced to a system with a smaller number of variables.

  8. QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

    PubMed

    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.

  9. Quantum mechanics of Drude oscillators with full Coulomb interaction

    NASA Astrophysics Data System (ADS)

    Sadhukhan, M.; Manby, Frederick R.

    2016-09-01

    Drude oscillators provide a harmonic description of charge fluctuations and are widely studied as a model system and for ab initio calculations. In the dipole approximation the Hamiltonian describing the interaction of Drudes is quadratic, so it can be diagonalized exactly, but the energy diverges at short range. Here we consider the quantum mechanics of Drude oscillators interacting through the full Coulombic Hamiltonian for which the interaction energy does not have this defect. This protypical model for interactions between matter includes electrostatics, induction, and dispersion. Potential energy curves for rare-gas dimers are very closely matched by Drude correlation energies plus a single exponential function. The exact and accurate results presented here help to delineate between the basic properties of the physical model and the effects that arise from the dipole approximation.

  10. Effective equations for the quantum pendulum from momentous quantum mechanics

    SciTech Connect

    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.

  11. Hermeneutics, Underdetermination and Quantum Mechanics.

    ERIC Educational Resources Information Center

    Cushing, James T.

    1995-01-01

    States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)

  12. Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets

    NASA Astrophysics Data System (ADS)

    Kienzler, D.; Flühmann, C.; Negnevitsky, V.; Lo, H.-Y.; Marinelli, M.; Nadlinger, D.; Home, J. P.

    2016-04-01

    We directly observe the quantum interference between two well-separated trapped-ion mechanical oscillator wave packets. The superposed state is created from a spin-motion entangled state using a heralded measurement. Wave packet interference is observed through the energy eigenstate populations. We reconstruct the Wigner function of these states by introducing probe Hamiltonians which measure Fock state populations in displaced and squeezed bases. Squeezed-basis measurements with 8 dB squeezing allow the measurement of interference for Δ α =15.6 , corresponding to a distance of 240 nm between the two superposed wave packets.

  13. Equations of motion in general relativity and quantum mechanics

    NASA Astrophysics Data System (ADS)

    O'Hara, Paul

    2011-12-01

    In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. A generalized Dirac equation is derived and shown to be related to the Lie derivative of the momentum along the curve. In addition,the equations of motion are derived from the Hamilton-Jacobi equation associated with the metric and the wave equation associated with the Hamiltonian is then shown not to commute with the Dirac operator. Finally, the Maxwell-Boltzmann distribution is shown to be a consequence of geodesic motion.

  14. Localization properties in one-dimensional disordered supersymmetric quantum mechanics

    SciTech Connect

    Comtet, A.; Desbois, J.; Monthus, C. |

    1995-05-01

    A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential {phi}({ital x}) is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which {phi}({ital x}) is kept constant are distributed according to a broad distribution. Various applications of this model are considered. {copyright} 1995 Academic Press, Inc.

  15. Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets.

    PubMed

    Kienzler, D; Flühmann, C; Negnevitsky, V; Lo, H-Y; Marinelli, M; Nadlinger, D; Home, J P

    2016-04-01

    We directly observe the quantum interference between two well-separated trapped-ion mechanical oscillator wave packets. The superposed state is created from a spin-motion entangled state using a heralded measurement. Wave packet interference is observed through the energy eigenstate populations. We reconstruct the Wigner function of these states by introducing probe Hamiltonians which measure Fock state populations in displaced and squeezed bases. Squeezed-basis measurements with 8 dB squeezing allow the measurement of interference for Δα=15.6, corresponding to a distance of 240 nm between the two superposed wave packets.

  16. Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons

    NASA Astrophysics Data System (ADS)

    Gómez-Rocha, María; Głazek, Stanisław D.

    2015-09-01

    Asymptotic freedom of gluons in pure-gauge QCD is obtained in the leading terms of their renormalized Hamiltonian in the Fock space, instead of considering virtual Green's functions or scattering amplitudes. Namely, we calculate the three-gluon interaction term in the effective front-form Hamiltonian for gluons in the Minkowski space-time using the renormalization group procedure for effective particles (RGPEP), with a new generator. The resulting three-gluon vertex is a function of the scale parameter, s , that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant, gλ, depending on the associated momentum scale λ =1 /s , is calculated in the series expansion in powers of g0=gλ 0 up to the terms of third order, assuming some small value for g0 at some large λ0. The result exhibits the same finite sensitivity to small-x regularization as the one obtained in an earlier RGPEP calculation, but the new calculation is simpler than the earlier one because of a simpler generator. This result establishes a degree of universality for pure-gauge QCD in the RGPEP.

  17. 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.

  18. Improving students' understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha; Zhu, Guangtian

    2010-02-01

    Learning quantum mechanics is challenging. 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. Supported by the National Science Foundation. )

  19. Quantum mechanics of black holes.

    PubMed

    Witten, Edward

    2012-08-01

    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.

  20. Quantum mechanics of black holes.

    PubMed

    Witten, Edward

    2012-08-01

    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. PMID:22859480

  1. Quantum Hamiltonians with Weak Random Abstract Perturbation. I. Initial Length Scale Estimate

    NASA Astrophysics Data System (ADS)

    Borisov, Denis; Golovina, Anastasia; Veselić, Ivan

    2016-09-01

    We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube size, and consequently the number of parameters as well, tends to infinity, we derive deterministic and probabilistic variational bounds on the lowest eigenvalue, i.e. the spectral minimum, as well as exponential off-diagonal decay of the Green function at energies above, but close to the overall spectral bottom.

  2. Three-space from quantum mechanics

    SciTech Connect

    Chew, G.F.; Stapp, H.P.

    1988-08-01

    We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.

  3. An interpretation within philosophy of the relationship between classical mechanics and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Sibelius, Patrick

    1989-11-01

    A mapping of a finite directed graph onto a curve in space-time is considered. The mapping induces the dynamics of a free particle moving along the curve. The distinction between the Lagrangian and the Hamiltonian formulation of particle mechanics is expressed in terms of the distinction between referring to a particle in space and time and referring to the points in space which the particle occupies, respectively. These elements are combined to yield an interpretation of Feynman's path integral formulation of quantum mechanics. Describing a bound state of a system as a particle is discussed.

  4. Facets of contextual realism in quantum mechanics

    SciTech Connect

    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.

  5. Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier

    SciTech Connect

    Chruscinski, Dariusz . E-mail: darch@phys.uni.torun.pl

    2006-04-15

    We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.

  6. Deformation of supersymmetric and conformal quantum mechanics through affine transformations

    NASA Astrophysics Data System (ADS)

    Spiridonov, Vyacheslav

    Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

  7. Deformation of supersymmetric and conformal quantum mechanics through affine transformations

    NASA Technical Reports Server (NTRS)

    Spiridonov, Vyacheslav

    1993-01-01

    Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

  8. 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.

  9. 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 .

  10. 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

  11. 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)

  12. Unified theory of exactly and quasiexactly solvable ''discrete'' quantum mechanics. I. Formalism

    SciTech Connect

    Odake, Satoru; Sasaki, Ryu

    2010-08-15

    We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional ''discrete'' quantum mechanics, in which the Schroedinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey-Wilson algebra is clarified.

  13. Propagators in polymer quantum mechanics

    SciTech Connect

    Flores-González, Ernesto Morales-Técotl, Hugo A. Reyes, Juan D.

    2013-09-15

    Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green’s function character. Furthermore they are also shown to reduce to the usual Schrödinger propagators in the limit of small parameter μ{sub 0}, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity. -- Highlights: •Formulas for propagators of free and particle in a box in polymer quantum mechanics. •Initial conditions, composition and Green’s function character is checked. •Propagators reduce to corresponding Schrödinger ones in an appropriately defined limit. •Results show overall consistency of the polymer framework. •For the particle in a box results are also verified using formula from method of images.

  14. Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

    SciTech Connect

    Balondo Iyela, Daddy; Govaerts, Jan; Hounkonnou, M. Norbert

    2013-09-15

    Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies.

  15. 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.

  16. Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

    SciTech Connect

    Baykara, N. A.

    2015-12-31

    Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

  17. 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

  18. 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).

  19. Quantum mechanics without state vectors

    NASA Astrophysics Data System (ADS)

    Weinberg, Steven

    2014-10-01

    Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

  20. 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.

  1. Tips and Tools for Teaching Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Zhu, Guangtian; Singh, Chandralekha

    2009-03-01

    Learning quantum mechanics is challenging -- students usually struggle to master the basic concepts, even though they may perform well on solving quantitative problems. Our group is investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are designing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the tutorials employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties, share the material we have developed and evaluated to make the quantum mechanics class engaging and useful, and show ways to bridge the gap between quantitative and conceptual aspects of quantum mechanics.

  2. Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

    NASA Astrophysics Data System (ADS)

    Fuji, Yohei; He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank

    2016-05-01

    We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the U (1 ) particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015), 10.1103/PhysRevLett.115.116803]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunnelings that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the (2 +1 ) -dimensional O (4 ) nonlinear sigma model with the topological θ term at θ =π . Finally, we predict a possible fractional quantum Hall state, the Halperin (221 ) state, at 1 /6 filling.

  3. 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.

  4. 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.

  5. 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.

  6. A Bit of Quantum Mechanics

    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.

  7. 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

  8. Bohmian mechanics and quantum field theory.

    PubMed

    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.

  9. 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

  10. Quantum mechanics without potential function

    SciTech Connect

    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.

  11. Comment on ``Adiabatic quantum computation with a one-dimensional projector Hamiltonian''

    NASA Astrophysics Data System (ADS)

    Kay, Alastair

    2013-10-01

    The partial adiabatic search algorithm was introduced in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for a quantum search with the idea that most of the interesting computation only happens over a very short range of the adiabatic path. By focusing on that restricted range, one can potentially gain an advantage by reducing the control requirements on the system, enabling a uniform rate of evolution. In this Comment, we point out an oversight in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] that invalidates its proof. However, the argument can be corrected, and the calculations in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] are then sufficient to show that the scheme still works. Nevertheless, subsequent works [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.034304 82, 034304 (2010), Chin. Phys. BCPBHAJ1674-105610.1088/1674-1056/20/4/040309 20, 040309 (2011), Chin. Phys. BCPBHAJ1674-105610.1088/1674-1056/21/1/010306 21, 010306 (2012), AASRI Procedia 1, 5862 (2012), and Quantum Inf. Process.10.1007/s11128-013-0557-1 12, 2689 (2013)] cannot all be recovered in the same way.

  12. Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified space

    NASA Astrophysics Data System (ADS)

    Reinhardt, H.

    2016-08-01

    The partition function of a relativistic invariant quantum field theory is expressed by its vacuum energy calculated on a spatial manifold with one dimension compactified to a 1-sphere S1(β ), whose circumference β represents the inverse temperature. Explicit expressions for the usual energy density and pressure in terms of the energy density on the partially compactified spatial manifold R2×S1(β ) are derived. To make the resulting expressions mathematically well defined a Poisson resummation of the Matsubara sums as well as an analytic continuation in the chemical potential are required. The new approach to finite-temperature quantum field theories is advantageous in a Hamilton formulation since it does not require the usual thermal averages with the density operator. Instead, the whole finite-temperature behavior is encoded in the vacuum wave functional on the spatial manifold R2×S1(β ). We illustrate this approach by calculating the pressure of a relativistic Bose and Fermi gas and reproduce the known results obtained from the usual grand canonical ensemble. As a first nontrivial application we calculate the pressure of Yang-Mills theory as a function of the temperature in a quasiparticle approximation motivated by variational calculations in Coulomb gauge.

  13. Dynamical supersymmetric Dirac Hamiltonians

    SciTech Connect

    Ginocchio, J.N.

    1986-01-01

    Using the language of quantum electrodynamics, the Dirac Hamiltonian of a neutral fermion interacting with a tensor field is examined. A supersymmetry found for a general Dirac Hamiltonian of this type is discussed, followed by consideration of the special case of a harmonic electric potential. The square of the Dirac Hamiltonian of a neutral fermion interacting via an anomalous magnetic moment in an electric potential is shown to be equivalent to a three-dimensional supersymmetric Schroedinger equation. It is found that for a potential that grows as a power of r, the lowest energy of the Hamiltonian equals the rest mass of the fermion, and the Dirac eigenfunction has only an upper component which is normalizable. It is also found that the higher energy states have upper and lower components which form a supersymmetric doublet. 15 refs. (LEW)

  14. Kindergarten Quantum Mechanics: Lecture Notes

    SciTech Connect

    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.

  15. Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

    NASA Astrophysics Data System (ADS)

    Barletti, Luigi; Ben Abdallah, Naoufel

    2011-11-01

    In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period {ɛ} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.

  16. Thermodynamic integration from classical to quantum mechanics

    SciTech Connect

    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.

  17. 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

  18. Stochastic surrogate Hamiltonian

    SciTech Connect

    Katz, Gil; Kosloff, Ronnie; Gelman, David; Ratner, Mark A.

    2008-07-21

    The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath.

  19. 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…

  20. Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i

    NASA Astrophysics Data System (ADS)

    Palenik, Mark C.

    2014-07-01

    Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=\\frac{dP}{dt}, P=m\\frac{dV}{dt}, and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.

  1. Polymer quantum mechanics and its continuum limit

    SciTech Connect

    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.

  2. A covariant extrapolation of the noncovariant two particle Wheeler-Feynman Hamiltonian from the Todorov equation and Dirac's constraint mechanics

    NASA Astrophysics Data System (ADS)

    Crater, Horace; Yang, Dujiu

    1991-09-01

    A semirelativistic expansion in powers of 1/c2 is canonically matched through order (1/c4) of the two-particle total Hamiltonian of Wheeler-Feynman vector and scalar electrodynamics to a similar expansion of the center of momentum (c.m.) total energy of two interacting particles obtained from covariant generalized mass shell constraints derived with the use of the classical Todorov equation and Dirac's Hamiltonian constraint mechanics. This determines through order 1/c4 the direct interaction used in the covariant Todorov constraint equation. We show that these interactions are momentum independent in spite of the extensive and complicated momentum dependence of the potential energy terms in the Wheeler-Feynman Hamiltonian. The invariant expressions for the relativistic reduced mass and energy of the fictitious particle of relative motion used in the Todorov equation are also dynamically determined through this order by this same procedure. The resultant covariant Todorov equation then not only reproduces the noncovariant Wheeler-Feynman dynamics through order 1/c4 but also implicitly provides a rather simple covariant extrapolation of it to all orders of 1/c2.

  3. Conservation laws in the quantum mechanics of closed systems

    SciTech Connect

    Hartle, J.B. ||; Laflamme, R. |; Marolf, D.

    1995-06-15

    We investigate conservation laws in the quantum mechanics of closed systems and begin by reviewing an argument that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian. However, we also show that decoherence limits the alternatives that can be included in sets of histories that assess the conservation of these quantities. In the case of charge and energy, these limitations would be severe were these quantities not coupled to a gauge field. However, for the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature, we show that when alternative values of charge and mass decohere they always decohere exactly and are exactly conserved. Further, while decohering histories that describe possible changes in time of the total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict {ital physical} alternatives and are therefore not really limitations at all.

  4. Unitary dilation models of Turing machines in quantum mechanics

    SciTech Connect

    Benioff, P.

    1995-05-01

    A goal of quantum-mechanical models of the computation process is the description of operators that model changes in the information-bearing degrees of freedom. Iteration of the operators should correspond to steps in the computation, and the final state of halting computations should be stable under iteration. The problem is that operators constructed directly from the process description do not have these properties. In general these operators annihilate the halted state. If information-erasing steps are present, there are additional problems. These problems are illustrated in this paper by consideration of operators for two simple one-step processes and two simple Turing machines. In general the operators are not unitary and, if erasing steps are present, they are not even contraction operators. Various methods of extension or dilation to unitary operators are discussed. Here unitary power dilations are considered as a solution to these problems. It is seen that these dilations automatically provide a good solution to the initial- and final-state problems. For processes with erasing steps, recording steps must be included prior to the dilation, but only for the steps that erase information. Hamiltonians for these processes are also discussed. It is noted that {ital H}, described by exp({minus}{ital iH}{Delta})={ital U}{sup {ital T}}, where {ital U}{sup {ital T}} is a unitary step operator for the process and {Delta} a time interval, has complexity problems. These problems and those noted above are avoided here by the use of the Feynman approach to constructing Hamiltonians directly from the unitary power dilations of the model operators. It is seen that the Hamiltonians so constructed have some interesting properties.

  5. Born rule in quantum and classical mechanics

    SciTech Connect

    Brumer, Paul; Gong Jiangbin

    2006-05-15

    Considerable effort has been devoted to deriving the Born rule [i.e., that {psi}(x){sup 2}dx is the probability of finding a system, described by {psi}, between x and x+dx] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

  6. Quantum Mechanical Methods for Enzyme Kinetics

    NASA Astrophysics Data System (ADS)

    Gao, Jiali; Truhlar, Donald G.

    2002-10-01

    This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.

  7. ``Simplest Molecule'' Clarifies Modern Physics II. Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Harter, William; Reimer, Tyle

    2015-05-01

    A ``simplest molecule'' consisting of CW- laser beam pairs helps to clarify relativity from poster board - I. In spite of a seemingly massless evanescence, an optical pair also clarifies classical and quantum mechanics of relativistic matter and antimatter. Logical extension of (x,ct) and (ω,ck) geometry gives relativistic action functions of Hamiltonian, Lagrangian, and Poincare that may be constructed in a few ruler-and-compass steps to relate relativistic parameters for group or phase velocity, momentum, energy, rapidity, stellar aberration, Doppler shifts, and DeBroglie wavelength. This exposes hyperbolic and circular trigonometry as two sides of one coin connected by Legendre contact transforms. One is Hamiltonian-like with a longitudinal rapidity parameter ρ (log of Doppler shift). The other is Lagrange-like with a transverse angle parameter σ (stellar aberration). Optical geometry gives recoil in absorption, emission, and resonant Raman-Compton acceleration and distinguishes Einstein rest mass, Galilean momentum mass, and Newtonian effective mass. (Molecular photons appear less bullet-like and more rocket-like.) In conclusion, modern space-time physics appears as a simple result of the more self-evident Evenson's axiom: ``All colors go c.''

  8. "simplest Molecule" Clarifies Modern Physics II. Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Reimer, T. C.; Harter, W. G.

    2014-06-01

    A "simplest molecule" consisting of CW-laser beam pairs helps to clarify relativity in Talk I. In spite of a seemingly massless evanescence, an optical pair also clarifies classical and quantum mechanics of relativistic matter and anti-matter. *Logical extension of (x,ct) and (ω,ck) geometry gives relativistic action functions of Hamiltonian, Lagrangian, and Poincare that may be constructed in a few ruler-and-compass steps to relate relativistic parameters for group or phase velocity, momentum, energy, rapidity, stellar aberration, Doppler shifts, and DeBroglie wavelength. This exposes hyperbolic and circular trigonometry as two sides of one coin connected by Legendre contact transforms. One is Hamiltonian-like with a longitudinal rapidity parameter ρ (log of Doppler shift). The other is Lagrange-like with a transverse angle parameter σ (stellar aberration). Optical geometry gives recoil in absorption, emission, and resonant Raman-Compton acceleration and distinguishes Einstein rest mass, Galilean momentum mass, and Newtonian effective mass. (Molecular photons appear less bullet-like and more rocket-like.) In conclusion, modern space-time physics appears as a simple result of the more self-evident Evenson's axiom: "All colors go c."

  9. Time-dependent {P} {T}-symmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gong, Jiangbin; Wang, Qing-hai

    2013-12-01

    The parity-time-reversal ( {P} {T})-symmetric quantum mechanics (QM) (PTQM) has developed into a noteworthy area of research. However, to date, most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian operators. In this work, we propose an axiom in PTQM in order to study general time-dependent problems in PTQM, e.g., those with a time-dependent {P} {T}-symmetric Hamiltonian and with a time-dependent metric. We illuminate our proposal by examining a proper mapping from a time-dependent Schrödinger-like equation of motion for PTQM to the familiar time-dependent Schrödinger equation in conventional QM. The rich structure of the proper mapping hints that time-dependent PTQM can be a fruitful extension of conventional QM. Under our proposed framework, we further study in detail the Berry-phase generation in a class of {P} {T}-symmetric two-level systems. It is found that a closed path in the parameter space of PTQM is often associated with an open path in a properly mapped problem in conventional QM. In one interesting case, we further interpret the Berry phase as the flux of a continuously tunable fictitious magnetic monopole, thus highlighting the difference between PTQM and conventional QM despite the existence of a proper mapping between them.

  10. Causal structure in categorical quantum mechanics

    NASA Astrophysics Data System (ADS)

    Lal, Raymond Ashwin

    Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on

  11. General quantum-mechanical setting for field–antifield formalism as a hyper-gauge theory

    NASA Astrophysics Data System (ADS)

    Batalin, Igor A.; Lavrov, Peter M.

    2016-09-01

    A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schr\\"odinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schr\\"odinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.

  12. Strange Bedfellows: Quantum Mechanics and Data Mining

    SciTech Connect

    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.

  13. Consecutive Measurements in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Glick, Jennifer R.; Adami, Christoph

    The physics of quantum measurement still continues to puzzle with no resolution in sight between competing interpretations, in particular because no interpretation has so far produced predictions that would be falsifiable via experiment. Here we present an analysis of consecutive projective measurements performed on a quantum state using quantum information theory, where the entanglement between the quantum system and a measuring device is explicitly taken into account, and where the consecutive measurements increase the joint Hilbert space while the wavefunction of the joint system never collapses. Using this relative-state formalism we rederive well-known results for the pairwise correlation between any two measurement devices, but show that considering the joint as well as conditional entropy of three devices reveals a difference between the collapse and no-collapse pictures of quantum measurement that is experimentally testable. This research was funded by a Michigan State University Enrichment Fellowship.

  14. Optimization of a relativistic quantum mechanical engine.

    PubMed

    Peña, Francisco J; Ferré, Michel; Orellana, P A; Rojas, René G; Vargas, P

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.

  15. Optimization of a relativistic quantum mechanical engine

    NASA Astrophysics Data System (ADS)

    Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.

  16. Optimization of a relativistic quantum mechanical engine.

    PubMed

    Peña, Francisco J; Ferré, Michel; Orellana, P A; Rojas, René G; Vargas, P

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power. PMID:27627248

  17. On the complexity of classical and quantum algorithms for numerical problems in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bessen, Arvid J.

    Our understanding of complex quantum mechanical processes is limited by our inability to solve the equations that govern them except for simple cases. Numerical simulation of quantum systems appears to be our best option to understand, design and improve quantum systems. It turns out, however, that computational problems in quantum mechanics are notoriously difficult to treat numerically. The computational time that is required often scales exponentially with the size of the problem. One of the most radical approaches for treating quantum problems was proposed by Feytiman in 1982 [46]: he suggested that quantum mechanics itself showed a promising way to simulate quantum physics. This idea, the so called quantum computer, showed its potential convincingly in one important regime with the development of Shor's integer factorization algorithm which improves exponentially on the best known classical algorithm. In this thesis we explore six different computational problems from quantum mechanics, study their computational complexity and try to find ways to remedy them. In the first problem we investigate the reasons behind the improved performance of Shor's and similar algorithms. We show that the key quantum part in Shor's algorithm, the quantum phase estimation algorithm, achieves its good performance through the use of power queries and we give lower bounds for all phase estimation algorithms that use power queries that match the known upper bounds. Our research indicates that problems that allow the use of power queries will achieve similar exponential improvements over classical algorithms. We then apply our lower bound technique for power queries to the Sturm-Liouville eigenvalue problem and show matching lower bounds to the upper bounds of Papageorgiou and Wozniakowski [85]. It seems to be very difficult, though, to find nontrivial instances of the Sturm-Lionville problem for which power queries can be simulated efficiently. A quantum computer differs from a

  18. Quantum mechanics: The subtle pull of emptiness

    SciTech Connect

    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.

  19. Quantum mechanics and the generalized uncertainty principle

    SciTech Connect

    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.

  20. Mechanical equivalent of quantum heat engines.

    PubMed

    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.

  1. Hamiltonian description of the ideal fluid

    SciTech Connect

    Morrison, P.J.

    1994-01-01

    Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.

  2. A Reconstruction of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Kochen, Simon

    2015-05-01

    We show that exactly the same intuitively plausible definitions of state, observable, symmetry, dynamics, and compound systems of the classical Boolean structure of intrinsic properties of systems lead, when applied to the structure of extrinsic, relational quantum properties, to the standard quantum formalism, including the Schrödinger equation and the von Neumann-Lüders Projection Rule. This approach is then applied to resolving the paradoxes and difficulties of the orthodox interpretation.

  3. Quantum mechanical stabilization of Minkowski signature wormholes

    SciTech Connect

    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.

  4. 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)

  5. Quantum mechanics: Thought experiments made real

    NASA Astrophysics Data System (ADS)

    Martín, Fernando

    2015-02-01

    Elegant experiments performed with X-rays and a double slit formed from molecular oxygen have finally made it possible to realize and test a long-standing and famous gedanken experiment in quantum mechanics.

  6. 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.

  7. Davidson potential and SUSYQM in the Bohr Hamiltonian

    SciTech Connect

    Georgoudis, P. E.

    2013-06-10

    The Bohr Hamiltonian is modified through the Shape Invariance principle of SUper-SYmmetric Quantum Mechanics for the Davidson potential. The modification is equivalent to a conformal transformation of Bohr's metric, generating a different {beta}-dependence of the moments of inertia.

  8. A dynamical time operator in Dirac's relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bauer, M.

    2014-03-01

    A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

  9. Uncertainty in quantum mechanics: faith or fantasy?

    PubMed

    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.

  10. 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.

  11. Relativistic Bohmian interpretation of quantum mechanics

    SciTech Connect

    Nikolic, Hrvoje

    2006-06-27

    I present a relativistic covariant version of the Bohmian interpretation of quantum mechanics and discuss the corresponding measurable predictions. The covariance is incoded in the fact that the nonlocal quantum potential transforms as a scalar, which is a consequence of the fact that the nonlocal wave function transforms as a scalar. The measurable predictions that can be obtained with the deterministic Bohmian interpretation cannot be obtained with the conventional interpretation simply because the conventional probabilistic interpretation does not work in the case of relativistic quantum mechanics.

  12. The canonical Kravchuk basis for discrete quantum mechanics

    NASA Astrophysics Data System (ADS)

    Hakioglu, Tugrul; Wolf, Kurt Bernardo

    2000-04-01

    The well known Kravchuk formalism of the harmonic oscillator obtained from the direct discretization method is shown to be a new way of formulating discrete quantum phase space. It is shown that the Kravchuk oscillator Hamiltonian has a well defined unitary canonical partner which we identify with the quantum phase of the Kravchuk oscillator. The generalized discrete Wigner function formalism based on the action and angle variables is applied to the Kravchuk oscillator and its continuous limit is examined.

  13. Supersymmetric quantum mechanics and solitons of the sine-Gordon and nonlinear Schroedinger equations

    SciTech Connect

    Koller, Andrew; Olshanii, Maxim

    2011-12-15

    We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schroedinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t)=(n({h_bar}/2{pi})/{tau})/cosh(t/{tau}), with n being an integer and {tau} being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.

  14. Quantum Probability Theory and the Foundations of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Fröhlich, Jürg; Schubnel, Baptiste

    By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).

  15. A "Bit" of Quantum Mechanics

    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…

  16. Time-dependent perturbation theory in quantum mechanics and the renormalization group

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, J. K.; Ray, D. S.

    2016-06-01

    Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.

  17. 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.

  18. Including strain in atomistic tight-binding Hamiltonians: An application to self-assembled InAs/GaAs and InAs/InP quantum dots

    NASA Astrophysics Data System (ADS)

    Zieliński, M.

    2012-09-01

    A method for inclusion of strain into the tight-binding Hamiltonian is presented. This approach bridges from bulk strain to the atomistic language of bond lengths and angles, and features a diagonal parameters shift in a form suitable for atomistic calculation of million atom nanosystems with a small number of empirical parameters. I illustrate this method by calculating electronic and optical properties of self-assembled InAs/(InP,GaAs) lens-shaped quantum dots. A very different structure of confined quantum dots states is shown, depending on the matrix material and inclusion of strain effects. Results are compared with the well-established empirical pseudopotential method, and reasonable agreement is found.

  19. Optimal guidance law in quantum mechanics

    SciTech Connect

    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.

  20. 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.

  1. Quantum mechanics as applied mathematical statistics

    SciTech Connect

    Skala, L.; Cizek, J.; Kapsa, V.

    2011-05-15

    Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

  2. Quantum Mechanics with a Momentum-Space Artificial Magnetic Field

    NASA Astrophysics Data System (ADS)

    Price, Hannah M.; Ozawa, Tomoki; Carusotto, Iacopo

    2014-11-01

    The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. Given the exchanged roles of momentum and position, we demonstrate that the global topology of momentum space is crucially important. We propose an experiment to study the Harper-Hofstadter Hamiltonian with a harmonic trap that will illustrate the advantages of this approach and that will also constitute the first realization of magnetism on a torus.

  3. Coherent states in noncommutative quantum mechanics

    SciTech Connect

    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.

  4. Improving students' understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha

    2011-03-01

    Learning quantum mechanics is especially challenging, in part due to the abstract nature of the subject. We have been conducting investigations of the difficulties that students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. They focus on helping students integrate qualitative and quantitative understanding, confront and resolve their misconceptions and difficulties, and discriminate between concepts that are often confused. In this talk, I will give examples from my research in physics education of how students' prior knowledge relevant for quantum mechanics can be assessed, and how learning tools can be designed to help students develop a robust knowledge structure and critical thinking skills. Supported by the National Science Foundation.

  5. Role of intertwined Hamiltonian in two dimensional classical optics

    NASA Astrophysics Data System (ADS)

    Dehdashti, Shahram; Li, Rujiang; Liu, Xu; Raoofi, Mohammadreza; Chen, Hongsheng

    2015-07-01

    Intertwined Hamiltonian formalism originally has its roots in quantum field theory and non-relativistic quantum mechanics. In this work, we develop the non-relativistic two dimensional intertwined Hamiltonian formalism in classical optics. We obtain the properties of the intertwined media in detail and show that the differential part of intertwining operator is a series in Euclidean algebra generators. Also, we investigate quadratic gradient-index medium as an example of this structure, and obtain the intertwining operator and intertwined medium refractive index. Moreover, we study the preservation of quantum properties in the intertwined medium. For this, we consider superposition preservation as the most important property of quantum characters. We show that when a Schrödinger cat state is generated in gradient-index medium, we can construct another Schrödinger cat state in the intertwined one.

  6. Superstrings and the Foundations of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    't Hooft, Gerard

    2014-05-01

    It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.

  7. Multichannel framework for singular quantum mechanics

    SciTech Connect

    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.

  8. 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.

  9. Space and time from quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chew, G. F.

    1992-09-01

    Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

  10. Space and time from quantum mechanics

    SciTech Connect

    Chew, G.F.

    1992-09-16

    Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

  11. 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.

  12. An Axiomatic Basis for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Cassinelli, Gianni; Lahti, Pekka

    2016-06-01

    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.

  13. Two basic Uncertainty Relations in Quantum Mechanics

    SciTech Connect

    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.

  14. 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.

  15. A proof of von Neumann's postulate in Quantum Mechanics

    SciTech Connect

    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.

  16. Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Grössing, Gerhard

    2015-10-01

    A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...

  17. Dispersions and FRÖHLICH Electron-Phonon Interaction Hamiltonian of Propagating Optical Phonon Modes in Quasi-One Wurtzite GaN-BASED Quantum Well Wires

    NASA Astrophysics Data System (ADS)

    Zhang, L.; Xie, Hong-Jing

    Based on the dielectric continuum model and Loudon's uniaxial crystal model, the propagating (PR) optical phonon modes and the Fröhlich-like electron-PR phonon interaction Hamiltonian in a quasi-one-dimensional (Q1D) wurtzite quantum well wire (QWW) structure are deduced and analyzed. Numerical calculations on AlGaN/GaN/AlGaN wurtzite QWW are performed. Results reveal that the dispersive frequencies of PR modes are the continuous functions of free wavenumber kz in z-direction and discrete functions of azimuthal quantum number m. The reduced behavior of the PR modes in wurtzite quantum systems is obviously observed. From the discussion of the electron-PR phonon coupling functions, it is found that the low-order PR modes in the case of small kz and m play a more important role in the electron-PR phonon interactions. Moreover, a detailed comparison of the PR modes in Q1D QWW structures with those in quasi-two-dimensional quantum wells are also carried out. The physical reasons resulting in the relationship and distinction in the two types of systems are also analyzed deeply.

  18. PREFACE: Singular interactions in quantum mechanics: solvable models

    NASA Astrophysics Data System (ADS)

    Dell'Antonio, Gianfausto; Exner, Pavel; Geyler, Vladimir

    2005-06-01

    conditions at vertices directly. Two papers are devoted to inverse problems in this context: M Harmer studies inverse scattering for the matrix Schrödinger operator on the halfline with applications to star graphs, while P Kurasov and M Nowaczyk give a mathematically rigorous version of the known Gutkin-Smilansky result on the inverse spectral problem. The paper by O Post contributes to the question of how graphs can be approximated by more realistic `fat' graphs, and describes a class leading to disconnected quantum graphs. Finally, S Kondej and one of the editors study scattering in the context of `leaky' graphs which takes quantum tunnelling into account. While most results in this field describe one-particle Hamiltonians, more complicated systems have also been studied. In this issue we have three examples. C Cacciapuito, R Carlone, and R Figari discuss decoherence in a simple model of two particles, one heavy and one light, interacting through a δ potential; they give a rigorous meaning to a formula derived by Joos and Zeh. A related model by R Figari and A Teta is used to describe ionization. M Hallnäs, E Langmann, and C Paufler treat a true N-body situation, namely a model of one-dimensional gas of distinguishable particles interacting through generalized point interactions; they write the Bethe ansatz and present the solution of a particular case. The last group is a collection of contributions which in one sense or another are outside quantum mechanics, either modifying its postulates or applying it to a different physical situation. The latter applies to the paper of D Noja and A Posilicano in which they study nonlinear wave equations with point perturbations and show the existence of a solution to the Cauchy problem. F Coutinho et al discuss one-dimensional point interactions with energy-dependent coupling constant, S Albeverio and S Kuzhel examine a class of point interactions which are not symmetric but P-symmetric, where P is the parity operator, and M

  19. 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.

  20. An OpenMP/MPI approach to the parallelization of iterative four-atom quantum mechanics

    NASA Astrophysics Data System (ADS)

    Medvedev, Dmitry M.; Goldfield, Evelyn M.; Gray, Stephen K.

    2005-03-01

    We present an approach to parallel iterative four-atom quantum mechanics calculations in a computing environment of distributed memory nodes, each node consisting of a group of processors with a shared memory. We parallelize the action of the Hamiltonian matrix on a vector, which is the main computational bottleneck in both iterative calculations of eigenvalues and eigenvectors and the iterative determination of quantum dynamics information via, e.g., wavepacket methods. OpenMP is used to facilitate the parallel work within each node, and MPI is used to communicate information between nodes. For a realistic problem the approach is shown to scale very well up to 512 processors at the NERSC computing facility, working at up to 20% of the theoretical peak performance rate. The highest total floating point rate we achieve is 0.16 Tflops, using 768 processors. Our approach should also be applicable to quantum dynamics problems with more than four atoms.

  1. What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

    NASA Astrophysics Data System (ADS)

    Khots, Boris; Khots, Dmitriy

    2014-12-01

    Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

  2. What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

    SciTech Connect

    Khots, Boris; Khots, Dmitriy

    2014-12-10

    Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

  3. When a local Hamiltonian must be frustration-free.

    PubMed

    Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich

    2016-06-01

    A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory. PMID:27199483

  4. When a local Hamiltonian must be frustration-free.

    PubMed

    Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich

    2016-06-01

    A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.

  5. Consistent interpretations of quantum mechanics

    SciTech Connect

    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.

  6. Max Born's Statistical Interpretation of Quantum Mechanics.

    PubMed

    Pais, A

    1982-12-17

    In the summer of 1926, a statistical element was introduced for the first time in the fundamental laws of physics in two papers by Born. After a brief account of Born's earlier involvements with quantum physics, including his bringing the new mechanics to the United States, the motivation for and contents of Born's two papers are discussed. The reaction of his colleagues is described.

  7. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    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.

  8. Quantum Mechanics Studies of Cellobiose Conformations

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...

  9. Quantum mechanics is compatible with realism

    SciTech Connect

    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.

  10. Conditions for nondegeneracy in supersymmetric quantum mechanics

    SciTech Connect

    Imbo, T.D.; Sukhatme, U.P.

    1986-05-15

    It is shown that the positive ''bosonic'' and ''fermionic'' bound-state spectra in spherically symmetric supersymmetric (SUSY) quantum mechanics are degenerate if and only if the superpotential W(r) satisfies deltaequivalentlim/sub r/..-->..0rVertical BarW(r)Vertical Bar> or =0.5. Also, if delta<0.5, then SUSY is broken.

  11. Subjective and objective probabilities in quantum mechanics

    SciTech Connect

    Srednicki, Mark

    2005-05-15

    We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

  12. 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)

  13. 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.

  14. 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.

  15. Can quantum mechanics fool the cosmic censor?

    SciTech Connect

    Matsas, G. E. A.; Silva, A. R. R. da; Richartz, M.; Saa, A.; Vanzella, D. A. T.

    2009-05-15

    We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the 'cosmic censor' may be oblivious to processes involving quantum effects.

  16. Hamiltonian deformations of Gabor frames: First steps

    PubMed Central

    de Gosson, Maurice A.

    2015-01-01

    Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed – as the title suggests – as the very first steps towards a general deformation theory for Gabor frames. PMID:25892903

  17. Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Subasi, Yigit; Jarzynski, Christopher

    The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l < k . This technique works best for Hamiltonians with a few interactions with very large k and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.

  18. 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).

  19. Coulomb problem in non-commutative quantum mechanics

    SciTech Connect

    Galikova, Veronika; Presnajder, Peter

    2013-05-15

    The aim of this paper is to find out how it would be possible for space non-commutativity (NC) to alter the quantum mechanics (QM) solution of the Coulomb problem. The NC parameter {lambda} is to be regarded as a measure of the non-commutativity - setting {lambda}= 0 which means a return to the standard quantum mechanics. As the very first step a rotationally invariant NC space R{sub {lambda}}{sup 3}, an analog of the Coulomb problem configuration space (R{sup 3} with the origin excluded) is introduced. R{sub {lambda}}{sup 3} is generated by NC coordinates realized as operators acting in an auxiliary (Fock) space F. The properly weighted Hilbert-Schmidt operators in F form H{sub {lambda}}, a NC analog of the Hilbert space of the wave functions. We will refer to them as 'wave functions' also in the NC case. The definition of a NC analog of the hamiltonian as a hermitian operator in H{sub {lambda}} is one of the key parts of this paper. The resulting problem is exactly solvable. The full solution is provided, including formulas for the bound states for E < 0 and low-energy scattering for E > 0 (both containing NC corrections analytic in {lambda}) and also formulas for high-energy scattering and unexpected bound states at ultra-high energy (both containing NC corrections singular in {lambda}). All the NC contributions to the known QM solutions either vanish or disappear in the limit {lambda}{yields} 0.

  20. 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.

  1. Quantum mechanical studies of carbon structures

    SciTech Connect

    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.

  2. A Primer on Resonances in Quantum Mechanics

    SciTech Connect

    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.

  3. Quantum mechanics of two relativistic bound fermions

    SciTech Connect

    Giachetti, R.; Sorace, E.

    2006-11-15

    This presentation shows how a joint use of symbolic and numerical programming makes it possible the construction of new quantum mechanical models and the explicit solution for their spectra. Similar methods can be used for investigating quantum systems of different nature with the highest accuracy, as it can be required by the development of new technologies. In particular we deal with the quantization of two relativistic fermions of arbitrary masses interacting by means of a radial potential. The numerical results are given for the Coulomb interaction.

  4. Quantum mechanical coherence, resonance, and mind

    SciTech Connect

    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.

  5. Emergence of quantum mechanics from a sub-quantum statistical mechanics

    NASA Astrophysics Data System (ADS)

    Grössing, Gerhard

    2014-07-01

    A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.

  6. The dissociative chemisorption of methane on Ni(100) and Ni(111): Classical and quantum studies based on the reaction path Hamiltonian

    SciTech Connect

    Mastromatteo, Michael; Jackson, Bret

    2013-11-21

    Electronic structure methods based on density functional theory are used to construct a reaction path Hamiltonian for CH{sub 4} dissociation on the Ni(100) and Ni(111) surfaces. Both quantum and quasi-classical trajectory approaches are used to compute dissociative sticking probabilities, including all molecular degrees of freedom and the effects of lattice motion. Both approaches show a large enhancement in sticking when the incident molecule is vibrationally excited, and both can reproduce the mode specificity observed in experiments. However, the quasi-classical calculations significantly overestimate the ground state dissociative sticking at all energies, and the magnitude of the enhancement in sticking with vibrational excitation is much smaller than that computed using the quantum approach or observed in the experiments. The origin of this behavior is an unphysical flow of zero point energy from the nine normal vibrational modes into the reaction coordinate, giving large values for reaction at energies below the activation energy. Perturbative assumptions made in the quantum studies are shown to be accurate at all energies studied.

  7. Neutrino oscillations: Quantum mechanics vs. quantum field theory

    SciTech Connect

    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.

  8. Reaction-diffusion mechanisms and quantum spin systems

    NASA Astrophysics Data System (ADS)

    Schütz, Gunter M.

    We present a brief tutorial introduction into the quantum Hamiltonian formalism for stochastic many-body systems defined in terms of a master equation for their time evolution. These models describe interacting classical particle systems where particles hop on a lattice and may undergo reactions such as A+A→0. The quantum Hamiltonian formalism for the master equation provides a convenient general framework for the treatment of such models which, by various mappings, are capable of describing a wide variety of phenomena in non-equilibrium physics and in random media. The formalism is particularly useful if the quantum Hamiltonian has continuous global symmetries or if it is integrable, i.e. has an infinite set of conservation laws. This is demonstrated in the case of the exclusion process and for a toy model of tumor growth. Experimental applications of other integrable reaction-diffusion models in various areas of polymer physics (gel electrophoresis of DNA, exciton dynamics on polymers and the kinetics of biopolymerization on RNA) are pointed out.

  9. Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas

    SciTech Connect

    Sakaguchi, Hidetsugu; Malomed, Boris A.

    2011-01-15

    The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -r{sup -2}) is a well-known issue in quantum theory. It is closely related to the quantum anomaly, i.e., breaking of the scaling invariance of the respective Hamiltonian by quantization. We demonstrate that the mean-field repulsive nonlinearity prevents the collapse and thus puts forward a solution to the quantum-anomaly problem that differs from that previously developed in the framework of the linear quantum-field theory. This solution may be realized in the 3D or 2D gas of dipolar bosons attracted by a central charge and in the 2D gas of magnetic dipoles attracted by a current filament. In the 3D setting, the dipole-dipole interactions are also taken into regard, in the mean-field approximation, resulting in a redefinition of the scattering length which accounts for the contact repulsion between the bosons. In lieu of the collapse, the cubic nonlinearity creates a 3D ground state (GS), which does not exist in the respective linear Schroedinger equation. The addition of the harmonic trap gives rise to a tristability, in the case when the Schroedinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it, creating the GS, as well as its counterparts carrying the angular momentum (vorticity). Counterintuitively, such self-trapped 2D modes exist even in the case of a weakly repulsive potential r{sup -2}. The 2D vortical modes avoid the phase singularity at the pivot (r=0) by having the amplitude diverging at r{yields}0 instead of the usual situation with the amplitude of the vortical mode vanishing at r{yields}0 (the norm of the mode converges despite of the singularity of the amplitude at r{yields}0). In the presence of the harmonic trap, the 2D quintic model with a weakly repulsive central potential r{sup -2} gives rise to three confined modes, the middle

  10. Intertwining operators for non-self-adjoint Hamiltonians and bicoherent states

    NASA Astrophysics Data System (ADS)

    Bagarello, F.

    2016-10-01

    This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.

  11. Measurement and Fundamental Processes in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Jaeger, Gregg

    2015-07-01

    In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.

  12. 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

  13. How to Teach the Postulates of Quantum Mechanics without Enigma.

    ERIC Educational Resources Information Center

    Teixeira-Dias, Jose J. C.

    1983-01-01

    Shows how a statistical approach can help students accept postulates of quantum mechanics. The approach, which also makes students aware of the philosophical/humanistic implications of quantum mechanics, involves the following sequence: (1) important experiments in quantum mechanics; (2) conventional statistical interpretation; (3) mathematical…

  14. Elastic tunneling charge transport mechanisms in silicon quantum dots /SiO{sub 2} thin films and superlattices

    SciTech Connect

    Illera, S. Prades, J. D.; Cirera, A.

    2015-05-07

    The role of different charge transport mechanisms in Si/SiO{sub 2} structures has been studied. A theoretical model based on the Transfer Hamiltonian Formalism has been developed to explain experimental current trends in terms of three different elastic tunneling processes: (1) trap assisted tunneling; (2) transport through an intermediate quantum dot; and (3) direct tunneling between leads. In general, at low fields carrier transport is dominated by the quantum dots whereas, for moderate and high fields, transport through deep traps inherent to the SiO{sub 2} is the most relevant process. Besides, current trends in Si/SiO{sub 2} superlattice structure have been properly reproduced.

  15. PREFACE: Singular interactions in quantum mechanics: solvable models

    NASA Astrophysics Data System (ADS)

    Dell'Antonio, Gianfausto; Exner, Pavel; Geyler, Vladimir

    2005-06-01

    This issue comprises two dozen research papers which are all in one sense or another devoted to models in which the interaction is singular and sharply localized; a typical example is a quantum particle interacting with a family of δ-type potentials. Such an idealization usually makes analysis of their properties considerably easier, sometimes allowing us to reduce it to a simple algebraic problem—this is why one speaks about solvable models. The subject can be traced back to the early days of quantum mechanics; however, the progress in this field was slow and uneven until the 1960s, mostly because singular interactions are often difficult to deal with mathematically and intuitive arguments do not work. After overcoming the initial difficulties the `classical' theory of point interactions was developed, and finally summarized in 1988 in a monograph by Albeverio, Gesztesy, Høegh-Krohn, and Holden, which you will find quoted in numerous places within this issue. A reliable way to judge theories is to observe the progress they make within one or two decades. In this case there is no doubt that the field has witnessed a continuous development and covered areas which nobody had thought of when the subject first emerged. The reader may see it in the second edition of the aforementioned book which was published by AMS Chelsea only recently and contained a brief survey of these new achievements. It is no coincidence that this topical issue appears at the same time; it has been conceived as its counterpart and a forum at which fresh results in the field can demonstrated. Let us briefly survey the contents of the issue. While the papers included have in common the basic subject, they represent a broad spectrum philosophically as well as technically, and any attempt to classify them is somewhat futile. Nevertheless, we will divide them into a few groups. The first comprises contributions directly related to the usual point-interaction ideology. M Correggi and one of the

  16. Quantum Mechanics, Gravity, and the Multiverse

    NASA Astrophysics Data System (ADS)

    Nomura, Yasunori

    2012-04-01

    The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.

  17. Beyond relativity and quantum mechanics: space physics

    NASA Astrophysics Data System (ADS)

    Lindner, Henry H.

    2011-09-01

    Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.

  18. Covariant quantum mechanics applied to noncommutative geometry

    NASA Astrophysics Data System (ADS)

    Astuti, Valerio

    2015-08-01

    We here report a result obtained in collaboration with Giovanni Amelino-Camelia, first shown in the paper [1]. Applying the manifestly covariant formalism of quantum mechanics to the much studied Snyder spacetime [2] we show how it is trivial in every physical observables, this meaning that every measure in this spacetime gives the same results that would be obtained in the flat Minkowski spacetime.

  19. A Philosopher's Understanding of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vermaas, Pieter E.

    2005-07-01

    1. Introduction; 2. Quantum mechanics; 3. Modal interpretations; Part I. Formalism: 4. The different versions; 5. The full property ascription; 6. Joint property ascriptions; 7. Discontinuities, instabilities and other bad behaviour; 8. Transition probabilities; 9. Dynamical autonomy and locality; Part II. Physics: 10. The measurement problem; 11. The Born rule; Part III. Philosophy: 12. Properties, states, measurement outcomes and effective states; 13. Holism versus reductionism; 14. Possibilities and impossibilities; 15. Conclusions.

  20. A Philosopher's Understanding of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vermaas, Pieter E.

    2000-02-01

    1. Introduction; 2. Quantum mechanics; 3. Modal interpretations; Part I. Formalism: 4. The different versions; 5. The full property ascription; 6. Joint property ascriptions; 7. Discontinuities, instabilities and other bad behaviour; 8. Transition probabilities; 9. Dynamical autonomy and locality; Part II. Physics: 10. The measurement problem; 11. The Born rule; Part III. Philosophy: 12. Properties, states, measurement outcomes and effective states; 13. Holism versus reductionism; 14. Possibilities and impossibilities; 15. Conclusions.

  1. Quantum mechanics lessons for standard cosmology

    NASA Astrophysics Data System (ADS)

    Reyes, Marco A.

    2012-08-01

    By recalling the relevance of the Sturm-Liouville theory has had on the solutions of quantum mechanics problems, here it is explored the possibility of getting some insight to the solutions for a standard cosmology model for inflation, from a time independent Schrödinger 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.

  2. Collocation method for fractional quantum mechanics

    SciTech Connect

    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.

  3. A Local Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Lopez, Carlos

    2016-04-01

    A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the "virtual" paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.

  4. Time of arrival in quantum mechanics

    SciTech Connect

    Grot, N.; Rovelli, C.; Tate, R.S.

    1996-12-01

    We study the problem of computing the probability for the time of arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle{close_quote}s (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the {open_quote}{open_quote}time-of-arrival{close_quote}{close_quote} operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr{umlt o}dinger current. We derive a well-defined uncertainty relation between time of arrival and energy; this result shows that the well-known arguments against the existence of such a relation can be circumvented. Finally, we define a {open_quote}{open_quote}time representation{close_quote}{close_quote} of the quantum mechanics of a free particle, in which the time of arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics. {copyright} {ital 1996 The American Physical Society.}

  5. Quantum mechanics with coordinate dependent noncommutativity

    SciTech Connect

    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.

  6. A fully 3D atomistic quantum mechanical study on random dopant induced effects in 25nm MOSFETs

    SciTech Connect

    Wang, Lin-Wang; Jiang, Xiang-Wei; Deng, Hui-Xiong; Luo, Jun-Wei; Li, Shu-Shen; Wang, Lin-Wang; Xia, Jian-Bai

    2008-07-11

    We present a fully 3D atomistic quantum mechanical simulation for nanometered MOSFET using a coupled Schroedinger equation and Poisson equation approach. Empirical pseudopotential is used to represent the single particle Hamiltonian and linear combination of bulk band (LCBB) method is used to solve the million atom Schroedinger's equation. We studied gate threshold fluctuations and threshold lowering due to the discrete dopant configurations. We compared our results with semiclassical simulation results. We found quantum mechanical effects increase the threshold fluctuation while decreases the threshold lowering. The increase of threshold fluctuation is in agreement with previous study based on approximated density gradient approach to represent the quantum mechanical effect. However, the decrease in threshold lowering is in contrast with the previous density gradient calculations.

  7. Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

    SciTech Connect

    Angraini, Lily Maysari; Suparmi,; Variani, Viska Inda

    2010-12-23

    SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

  8. Retrocausal quantum mechanics: Maudlin's challenge revisited

    NASA Astrophysics Data System (ADS)

    Lewis, Peter J.

    2013-11-01

    In 1994, Maudlin proposed an objection to retrocausal approaches to quantum mechanics in general, and to the transactional interpretation (TI) in particular, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, is that there are two aspects to Maudlin's objection; the more readily soluble aspect has received all the attention, but the more problematic aspect has gone unnoticed. I consider the prospects for developing a successful retrocausal quantum theory in light of this second aspect of the objection.

  9. When a local Hamiltonian must be frustration-free

    NASA Astrophysics Data System (ADS)

    Sattath, Or; Morampudi, Siddhardh C.; Laumann, Chris R.; Moessner, Roderich

    2016-06-01

    A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.

  10. Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.

    PubMed

    Schmidt, Steffen; Klevansky, S P

    2013-04-28

    This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory.

  11. A quantum mechanics-based algorithm for vessel segmentation in retinal images

    NASA Astrophysics Data System (ADS)

    Youssry, Akram; El-Rafei, Ahmed; Elramly, Salwa

    2016-06-01

    Blood vessel segmentation is an important step in retinal image analysis. It is one of the steps required for computer-aided detection of ophthalmic diseases. In this paper, a novel quantum mechanics-based algorithm for retinal vessel segmentation is presented. The algorithm consists of three major steps. The first step is the preprocessing of the images to prepare the images for further processing. The second step is feature extraction where a set of four features is generated at each image pixel. These features are then combined using a nonlinear transformation for dimensionality reduction. The final step is applying a recently proposed quantum mechanics-based framework for image processing. In this step, pixels are mapped to quantum systems that are allowed to evolve from an initial state to a final state governed by Schrödinger's equation. The evolution is controlled by the Hamiltonian operator which is a function of the extracted features at each pixel. A measurement step is consequently performed to determine whether the pixel belongs to vessel or non-vessel classes. Many functional forms of the Hamiltonian are proposed, and the best performing form was selected. The algorithm is tested on the publicly available DRIVE database. The average results for sensitivity, specificity, and accuracy are 80.29, 97.34, and 95.83 %, respectively. These results are compared to some recently published techniques showing the superior performance of the proposed method. Finally, the implementation of the algorithm on a quantum computer and the challenges facing this implementation are introduced.

  12. Testing Quantum Mechanics on New Ground

    NASA Astrophysics Data System (ADS)

    Ghose, Partha

    2006-11-01

    Preface; Acknowledgements; 1. Wave-particle duality; 2. Cavity quantum electrodynamics; 3. Quantum nondemolition measurements; 4. Topological phases; 5. Macroscopic quantum coherence; 6. The quantum Zeno paradox; 7. Testing collapse; 8. Macroscopic quantum jumps; 9. Nonlocality; 10. Tunneling times; References; Indexes.

  13. Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.

    PubMed

    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.

  14. Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems.

    PubMed

    Hudson, Phillip S; Woodcock, H Lee; Boresch, Stefan

    2015-12-01

    Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches. PMID:26539729

  15. Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems.

    PubMed

    Hudson, Phillip S; Woodcock, H Lee; Boresch, Stefan

    2015-12-01

    Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.

  16. QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.

    PubMed

    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.

  17. The gravity duals of modular Hamiltonians

    NASA Astrophysics Data System (ADS)

    Jafferis, Daniel L.; Suh, S. Josephine

    2016-09-01

    In this work, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.

  18. 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.

  19. Multichannel framework for singular quantum mechanics

    NASA Astrophysics Data System (ADS)

    Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.

    2014-01-01

    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.

  20. Quantum Backaction Evading Measurement of Collective Mechanical Modes

    NASA Astrophysics Data System (ADS)

    Ockeloen-Korppi, C. F.; Damskägg, E.; Pirkkalainen, J.-M.; Clerk, A. A.; Woolley, M. J.; Sillanpää, M. A.

    2016-09-01

    The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.

  1. Quantum mechanical study of solvent effects in a prototype SN2 reaction in solution: Cl− attack on CH3Cl

    PubMed Central

    Kuechler, Erich R.; York, Darrin M.

    2014-01-01

    The nucleophilic attack of a chloride ion on methyl chloride is an important prototype SN2 reaction in organic chemistry that is known to be sensitive to the effects of the surrounding solvent. Herein, we develop a highly accurate Specific Reaction Parameter (SRP) model based on the Austin Model 1 Hamiltonian for chlorine to study the effects of solvation into an aqueous environment on the reaction mechanism. To accomplish this task, we apply high-level quantum mechanical calculations to study the reaction in the gas phase and combined quantum mechanical/molecular mechanical simulations with TIP3P and TIP4P-ew water models and the resulting free energy profiles are compared with those determined from simulations using other fast semi-empirical quantum models. Both gas phase and solution results with the SRP model agree very well with experiment and provide insight into the specific role of solvent on the reaction coordinate. Overall, the newly parameterized SRP Hamiltonian is able to reproduce both the gas phase and solution phase barriers, suggesting it is an accurate and robust model for simulations in the aqueous phase at greatly reduced computational cost relative to comparably accurate ab initio and density functional models. PMID:24511924

  2. Comment on ``Arrival time in quantum mechanics'' and ``Time of arrival in quantum mechanics''

    NASA Astrophysics Data System (ADS)

    Kijowski, Jerzy

    1999-01-01

    Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

  3. Feynman Disentangling of Noncommuting Operators in Quantum Mechanics

    SciTech Connect

    Popov, V.S.

    2005-11-01

    Feynman's disentangling theorem is applied to noncommuting operators in the problem of quantum parametric oscillator, which is mathematically equivalent to the problem of SU(1, 1) pseudospin rotation. The number states of the oscillator correspond to unitary irreducible representations of the SU(1, 1) group. Feynman disentangling is combined with group-theoretic arguments to obtain simple analytical formulas for the matrix elements and transition probabilities between the initial and final states of the oscillator. Feynman disentangling of time evolution operators is also discussed for an atom or ion interacting with a laser field and for a model Hamiltonian possessing the 'hidden' symmetry of the hydrogen atom.

  4. Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Lamb, Willis E.

    2001-04-01

    It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born's probabilistic interpretation of the wave function built in from the start. I call this new theory "super classical quantum mechanics" (SCQM). Using Ehrenfest's theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.

  5. The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

    1994-01-01

    The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

  6. Differentiability of correlations in realistic quantum mechanics

    SciTech Connect

    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.

  7. 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.

  8. An Infinite Order Discrete Variable Representation of an Effective Mass Hamiltonian: Application to Exciton Wave Functions in Quantum Confined Nanostructures.

    PubMed

    Kaledin, Alexey L; Lian, Tianquan; Hill, Craig L; Musaev, Djamaladdin G

    2014-08-12

    We describe an extension of the conventional Fourier grid discrete variable representation (DVR) to the bound state problem of a particle with a position-dependent mass. An infinite order DVR, derived for a variable mass kinetic energy operator, coupled with an efficient grid contraction scheme yields essentially exact eigenvalues for a chosen grid spacing. Implementation of the method is shown to be very practical due to the fact that in a DVR no integral evaluation is necessary and that the resultant kinetic energy matrix is sparse. Numerical calculations are presented for exciton states of spherical, cylindrical, and toric Type I (CdSe/ZnS) core-shell quantum dots. In these examples, electron-hole interaction is treated explicitly by solving a self-consistent Schrödinger-Poisson equation on a contracted DVR grid. Prospective applications of the developed approach to calculating electron transfer rates between adsorbed molecular acceptors and quantum confined nanocrystals of generic shape, dimensionality, and composition are also discussed.

  9. Hamiltonian Structure of the Schrödinger Classical Dynamical System

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Mond, Michael; Batic, Davide

    2016-09-01

    The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of "projections" onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimensional classical dynamical system (CDS), denoted as Schrödinger CDS, which uniquely determines the time-evolution of the underlying quantum state describing a set of N like and mutually interacting quantum particles. In this paper the realization of the same CDS in terms of a coupled set of Hamiltonian systems is established. These are respectively associated with a quantum-hydrodynamic CDS advancing in time the quantum fluid velocity and a further one the RD-CDS, describing the relative dynamics with respect to the quantum fluid.

  10. Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

    SciTech Connect

    Klink, W.H.; Wickramasekara, S.

    2013-09-15

    This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics. -- Highlights: •A formulation of Galilean quantum mechanics in non-inertial reference frames is presented. •The Galilei group is generalized to infinite dimensional Galilean line group. •Loop prolongations of Galilean line group contain central extensions of Galilei group. •Unitary representations of the loops are constructed. •These representations lead to terms in the Hamiltonian corresponding to fictitious forces, including centrifugal and Coriolis

  11. Elements of (Super-)Hamiltonian Formalism

    NASA Astrophysics Data System (ADS)

    Nersessian, A.

    In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard textbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction illustrating it by the examples related to Hopf maps. Then we briefly discuss the supergeneralization(s) of the Hamiltonian formalism and present some simple models of supersymmetric mechanics on Kähler manifolds.

  12. Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy

    SciTech Connect

    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.

  13. 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…

  14. Construction of traveling clusters in the Hamiltonian mean-field model by nonequilibrium statistical mechanics and Bernstein-Greene-Kruskal waves.

    PubMed

    Yamaguchi, Yoshiyuki Y

    2011-07-01

    Traveling clusters are ubiquitously observed in the Hamiltonian mean-field model for a wide class of initial states, which are not predicted to become spatially inhomogeneous states by nonequilibrium statistical mechanics and by nonlinear Landau damping. To predict such a cluster state from a given initial state, we combine nonequilibrium statistical mechanics and a construction method of Bernstein-Greene-Kruskal (BGK) waves with the aid of phenomenological assumptions. The phenomenological theory is partially successful, and the theoretically constructed cluster states are in good agreement with N-body simulations. Robustness of the theory is also discussed for unsuccessful initial states. PMID:21867277

  15. Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.

    PubMed

    Sun, Qiming; Chan, Garnet Kin-Lic

    2014-09-01

    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.

  16. From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics

    NASA Astrophysics Data System (ADS)

    Mugur-Schächter, Mioara

    1993-01-01

    In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie, Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965).

  17. Symmetry as a foundational concept in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Ziaeepour, Houri

    2015-07-01

    Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. Nonetheless its application is not limited to explaining confusing concept and it may be a necessary step toward a consistent model of quantum cosmology and gravity.

  18. Three Attempts at Two Axioms for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Rohrlich, Daniel

    The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field here may act on an electron there. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?

  19. Tampering detection system using quantum-mechanical systems

    DOEpatents

    Humble, Travis S.; Bennink, Ryan S.; Grice, Warren P.

    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.

  20. Causal localizations in relativistic quantum mechanics

    SciTech Connect

    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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Waveform information from quantum mechanical entropy

    NASA Astrophysics Data System (ADS)

    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.

  6. Gauge invariance and reciprocity in quantum mechanics

    SciTech Connect

    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.

  7. 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.

  8. 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.

  9. Theoretical research of the spin-Hamiltonian parameters for two rhombic W5+ centers in KTiOPO4 (KTP) crystal through a two-mechanism model

    NASA Astrophysics Data System (ADS)

    Mei, Yang; Chen, Bo-Wei; Wei, Chen-Fu; Zheng, Wen-Chen

    2016-09-01

    The high-order perturbation formulas based on the two-mechanism model are employed to calculate the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) for two approximately rhombic W5+ centers in KTiOPO4 (KTP) crystal. In the model, both the widely-applied crystal-field (CF) mechanism concerning the interactions of CF excited states with the ground state and the generally-neglected charge-transfer (CT) mechanism concerning the interactions of CT excited states with the ground state are included. The calculated results agree with the experimental values, and the signs of constants Ai are suggested. The calculations indicate that (i) for the high valence state dn ions in crystals, the contributions to spin-Hamiltonian parameters should take into account both the CF and CT mechanisms and (ii) the large g-shifts |Δgi | (=|gi-ge |, where ge≈ 2.0023) for W5+ centers in crystals are due to the large spin-orbit parameter of free W5+ ion.

  10. 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…

  11. 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…

  12. Quantum Mechanics from Periodic Dynamics: the bosonic case

    SciTech Connect

    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.

  13. 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…

  14. 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.

  15. 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.

  16. 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…

  17. 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…

  18. Quantum mechanics in rotating-radio-frequency traps and Penning traps with a quadrupole rotating field

    SciTech Connect

    Abe, K.; Hasegawa, T.

    2010-03-15

    Quantum-mechanical analysis of ion motion in a rotating-radio-frequency (rrf) trap or in a Penning trap with a quadrupole rotating field is carried out. Rrf traps were introduced by Hasegawa and Bollinger [Phys. Rev. A 72, 043404 (2005)]. The classical motion of a single ion in this trap is described by only trigonometric functions, whereas in the conventional linear radio-frequency (rf) traps it is by the Mathieu functions. Because of the simple classical motion in the rrf trap, it is expected that the quantum-mechanical analysis of the rrf traps is also simple compared to that of the linear rf traps. The analysis of Penning traps with a quadrupole rotating field is also possible in a way similar to the rrf traps. As a result, the Hamiltonian in these traps is the same as the two-dimensional harmonic oscillator, and energy levels and wave functions are derived as exact results. In these traps, it is found that one of the vibrational modes in the rotating frame can have negative energy levels, which means that the zero-quantum-number state (''ground'' state) is the highest energy state.

  19. Quartic quantum theory: an extension of the standard quantum mechanics

    NASA Astrophysics Data System (ADS)

    Życzkowski, Karol

    2008-09-01

    We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher-dimensional convex body {\\cal M}_N^Q of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in the N-dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalization of the standard quantum theory for which K = N2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N.

  20. Nonsupersymmetric strong coupling background from the large N quantum mechanics of two matrices coupled via a Yang-Mills interaction

    SciTech Connect

    Rodrigues, Joao P.; Zaidi, Alia

    2010-10-15

    We derive a planar sector of the large N nonsupersymmetric background of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction, in terms of the density of eigenvalues of one of the matrices. This background satisfies an implicit nonlinear integral equation, with a perturbative small coupling expansion and a solvable large coupling solution, which is obtained. The energy of system and the expectation value of several correlators are obtained in this strong coupling limit. They are free of infrared divergences.

  1. RG-Whitham dynamics and complex Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Gorsky, A.; Milekhin, A.

    2015-06-01

    Inspired by the Seiberg-Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG)-like Whitham behavior. We show that at the Argyres-Douglas (AD) point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne-Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.

  2. 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.

  3. Perturbation Theory for Quantum Mechanics in its Hessenberg-Matrix Representation

    NASA Astrophysics Data System (ADS)

    Znojil, Miloslav

    For years, the partial integrability in quantum mechanics [e.g., the exceptional terminating Lanczos solutions or the so called quasi-exactly solvable "next-to-elementary" systems] represented a challenge in perturbation theory. The main difficulty lied in an incompleteness of the available zero-order wavefunctions and in the related impossibility of an easy construction of the necessary zero-order propagators. We describe a solution of this problem, based on an unusual choice of model space. A few examples illustrate the underlying technicalities: Paying detailed attention to the Hessenberg-matrix Hamiltonians, our formalism compensates the incompleteness of integrability by a slightly less elementary (viz., non-diagonal but still triangular) matrix structure of its propagators.

  4. Phase Transformations in CuAu: Morphologies and Kinetics from Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Elder, Ken; Chakraborty, Bulbul; Goldenfeld, Nigel

    1996-03-01

    The existence of a modulated superlattice at intermediate temperatures in CuAu gives rise to a rich and complex set of phase transformations. For example, quenches from high and low temperatures into the modulated region leads respectively to the nucleation of labyrinth and bullseye patterns. In this alloy even the formation of the ordered superlattice from a disordered phase is dramatically different than that which occurs in standard disorder/order transformations. This transformation is strongly influenced by the presence of small metastable droplets that are the size of the modulated wavelength. A theoretical description(Bulbul Chakraborty, Ken Elder and Nigel Goldenfeld, Physica A, in press (1995)) of these kinetics and morphologies will be presented and compared to experiment. This description is based on a time-dependent Ginzburg-Landau equation that was derived from a quantum mechanical Hamiltonian using the embedded atom method(Bulbul Chakraborty and Zhigang Xi, Phys. Rev. Lett 68), 2039 (1992).

  5. Natural star-products on symplectic manifolds and related quantum mechanical operators

    SciTech Connect

    Błaszak, Maciej Domański, Ziemowit

    2014-05-15

    In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration space is given with the use of a sequence of pair-wise commuting vector fields. The connection with a covariant representation of such a star-product is also presented. Then, an extension of the construction to symplectic manifolds over flat and non-flat pseudo-Riemannian configuration spaces is discussed. Finally, a coordinate free construction of related quantum mechanical operators from Hilbert space over respective configuration space is presented. -- Highlights: •Invariant representations of natural star-products on symplectic manifolds are considered. •Star-products induced by flat and non-flat connections are investigated. •Operator representations in Hilbert space of considered star-algebras are constructed.

  6. Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations

    NASA Astrophysics Data System (ADS)

    Brown, Natalie

    In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy.

  7. Quantum mechanical model for J / ψ suppression in the LHC era

    NASA Astrophysics Data System (ADS)

    Peña, C.; Blaschke, D.

    2014-07-01

    We discuss the interplay of screening, absorption and regeneration effects, on the quantum mechanical evolution of quarkonia states, within a time-dependent harmonic oscillator (THO) model with complex oscillator strength. We compare the results with data for RAA /RAA (CNM) from CERN and RHIC experiments. In the absence of a measurement of cold nuclear matter (CNM) effects at LHC we estimate their role and interpret the recent data from the ALICE experiment. We also discuss the temperature dependence of the real and imaginary parts of the oscillator frequency which stand for screening and absorption/regeneration, respectively. We point out that a structure in the J / ψ suppression pattern for In-In collisions at SPS is possibly related to the recently found X (3872) state in the charmonium spectrum. Theoretical support for this hypothesis comes from the cluster expansion of the plasma Hamiltonian for heavy quarkonia in a strongly correlated medium.

  8. PT-symmetric quantum theory

    NASA Astrophysics Data System (ADS)

    Bender, Carl M.

    2015-07-01

    The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.

  9. 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 .

  10. Theory of diatomic molecules in an external electromagnetic field from first quantum mechanical principles.

    PubMed

    Sindelka, Milan; Moiseyev, Nimrod

    2006-04-27

    We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications, such as alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational, and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac-field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian.

  11. Some Novel Thought Experiments Involving Foundations of Quantum Mechanics and Quantum Information

    NASA Astrophysics Data System (ADS)

    Akhavan, Omid

    2004-02-01

    In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two theoretical quantum communication schemes including quantum dense coding and quantum teleportation schemes have been proposed by using entangled spatial states of two EPR particles shared between two parties. It is shown that the rate of classical information gain in our dense coding scheme is greater than some previously proposed multi-qubit protocols by a logarithmic factor dependent on the dimension of Hilbert space. The proposed teleportation scheme can provide a complete wave function teleportation of an object having other degrees of freedom in our three-dimensional space, for the first time. All required unitary operators which are necessary in our state preparation and Bell state measurement processes are designed using symmetric normalized Hadamard matrix, some basic gates and one typical conditional gate, which are introduced here for the first time.

  12. 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.

  13. New Formulation of Statistical Mechanics Using Thermal Pure Quantum States

    NASA Astrophysics Data System (ADS)

    Sugiura, Sho; Shimizu, Akira

    2014-03-01

    We formulate statistical mechanics based on a pure quantum state, which we call a "thermal pure quantum (TPQ) state". A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. In the TPQ formulation of statistical mechanics, thermal fluctuations are completely included in quantum-mechanical fluctuations. As a consequence, TPQ states have much larger quantum entanglement than the equilibrium density operators of the ensemble formulation. We also show that the TPQ formulation is very useful in practical computations, by applying the formulation to a frustrated two-dimensional quantum spin system.

  14. 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.

  15. Accurate Energy Spectrum for the Quantum Yang-Mills Mechanics with Nonlinear Color Oscillations

    NASA Astrophysics Data System (ADS)

    Pedram, Pouria

    2015-01-01

    Yang-Mills theory as the foundation for quantum chromodynamics is a non-Abelian gauge theory with self-interactions between vector particles. Here, we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the absence of external sources corresponding to the group SU(2). In the quantum domain, we diagonalize the Hamiltonian using the optimized trigonometric basis expansion method and find accurate energy eigenvalues and eigenfunctions for one and two degrees of freedom. We also compare our results with the semiclassical solutions.

  16. Quantum mechanical studies of DNA and LNA.

    PubMed

    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.

  17. Quantum Mechanical Studies of DNA and LNA

    PubMed Central

    Shim, Irene; Lindow, Morten; Ørum, Henrik

    2014-01-01

    Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the 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. PMID:24491259

  18. "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…

  19. A fast quantum mechanics based contour extraction algorithm

    NASA Astrophysics Data System (ADS)

    Lan, Tian; Sun, Yangguang; Ding, Mingyue

    2009-02-01

    A fast algorithm was proposed to decrease the computational cost of the contour extraction approach based on quantum mechanics. The contour extraction approach based on quantum mechanics is a novel method proposed recently by us, which will be presented on the same conference by another paper of us titled "a statistical approach to contour extraction based on quantum mechanics". In our approach, contour extraction was modeled as the locus of a moving particle described by quantum mechanics, which is obtained by the most probable locus of the particle simulated in a large number of iterations. In quantum mechanics, the probability that a particle appears at a point is equivalent to the square amplitude of the wave function. Furthermore, the expression of the wave function can be derived from digital images, making the probability of the locus of a particle available. We employed the Markov Chain Monte Carlo (MCMC) method to estimate the square amplitude of the wave function. Finally, our fast quantum mechanics based contour extraction algorithm (referred as our fast algorithm hereafter) was evaluated by a number of different images including synthetic and medical images. It was demonstrated that our fast algorithm can achieve significant improvements in accuracy and robustness compared with the well-known state-of-the-art contour extraction techniques and dramatic reduction of time complexity compared to the statistical approach to contour extraction based on quantum mechanics.

  20. Philosophy and Quantum Mechanics in Science Teaching

    NASA Astrophysics Data System (ADS)

    Pospiech, Gesche

    Research in physics has its impact on world view; physics influences the image of nature. On the other hand philosophy thinks about nature and the role of man. The insight that philosophy might indicate the frontiers of human possibilities of thought makes it highly desirable to teach these aspects in physics education. One of the most exciting examples is quantum theory which v. Weizsäcker called a fundamental philosophical advance. I give some hints to implementing philosophical aspects into a course on quantum theory. For this purpose I designed a dialogue between three philosophers - from the Antique, the Enlightenment and a quantum philosopher - discussing results of quantum theory on the background of important philosophical terms. Especially the views of Aristotle are reviewed. This idea has been carried out in a supplementary course on quantum theory for interested teacher students and for in-service training of teachers.

  1. A Student's Guide to Lagrangians and Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hamill, Patrick

    2013-11-01

    Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.

  2. An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics

    NASA Astrophysics Data System (ADS)

    McLenaghan, Raymond G.; Smirnov, Roman G.; The, Dennis

    2004-03-01

    We develop a new approach to the study of Killing tensors defined in pseudo-Riemannian spaces of constant curvature that is ideologically close to the classical theory of invariants. The main idea, which provides the foundation of the new approach, is to treat a Killing tensor as an algebraic object determined by a set of parameters of the corresponding vector space of Killing tensors under the action of the isometry group. The spaces of group invariants and conformal group invariants of valence two Killing tensors defined in the Minkowski plane are described. The group invariants, which are the generators of the space of invariants, are applied to the problem of classification of orthogonally separable Hamiltonian systems defined in the Minkowski plane. Transformation formulas to separable coordinates expressed in terms of the parameters of the corresponding space of Killing tensors are presented. The results are applied to the problem of orthogonal separability of the Drach superintegrable potentials.

  3. Hamiltonian theory of symmetric optical network transforms

    NASA Astrophysics Data System (ADS)

    Törmä, Päivi; Stenholm, Stig

    1995-12-01

    We discuss the theory of extracting an interaction Hamiltonian from a preassigned unitary transformation of quantum states. Such a procedure is of significance in quantum computations and other optical information processing tasks. We particularize the problem to the construction of totally symmetric 2N ports as introduced by Zeilinger and his collaborators [A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, and D. M. Greenberger, in Fundamental Aspects of Quantum Theory, edited by J. Anandan and J. J. Safko (World Scientific, Singapore, 1994)]. These are realized by the discrete Fourier transform, which simplifies the construction of the Hamiltonian by known methods of linear algebra. The Hamiltonians found are discussed and alternative realizations of the Zeilinger class transformations are presented. We briefly discuss the applicability of the method to more general devices.

  4. Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

    SciTech Connect

    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.

  5. Development and validation of an achievement test in introductory quantum mechanics: The Quantum Mechanics Visualization Instrument (QMVI)

    NASA Astrophysics Data System (ADS)

    Cataloglu, Erdat

    The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate

  6. Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.

    PubMed

    Burger, Steven K; Schofield, Jeremy; Ayers, Paul W

    2013-12-01

    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.

  7. Ruling out multi-order interference in quantum mechanics.

    PubMed

    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.

  8. Predicting crystal structure by merging data mining with quantum mechanics.

    PubMed

    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.

  9. 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.

  10. Nonstationary Quantum Mechanics. III. Quantum Mechanics Does Not Incorporate Classical Physics

    NASA Astrophysics Data System (ADS)

    Todorov, Nickola Stefanov

    1981-01-01

    It is shown that disagreement between the prediction of classical and conventional quantum mechanics about momentum probabilities exists in the case of a quasiclassical motion. The discussion is based on the detailed consideration of two specific potentials: U( x)= x and the oscillatory potential U( x)= mω 2 x 2/2. The results of the present Part III represent a further development of the idea in Todorov (1980) about the possible inefficiency of conventional theory in the case of potentials swiftly varying with time.

  11. 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…

  12. Conservation of information and the foundations of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chiribella, Giulio; Scandolo, Carlo Maria

    2015-05-01

    We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory [1, 2]. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.

  13. 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)

  14. Quantum Mechanics and the Social Sciences: After Hermeneutics.

    ERIC Educational Resources Information Center

    Heelan, Patrick A.

    1995-01-01

    An analysis of the hermeneutical aspect of quantum mechanical measurement reveals close analogs with the hermeneutical social/historical sciences. Suggests that the hermeneutical analysis of science requires the move from the epistemological attitude to an ontological view. (LZ)

  15. Identifying a cooperative control mechanism between an applied field and the environment of open quantum systems

    NASA Astrophysics Data System (ADS)

    Gao, Fang; Rey-de-Castro, Roberto; Wang, Yaoxiong; Rabitz, Herschel; Shuang, Feng

    2016-05-01

    Many systems under control with an applied field also interact with the surrounding environment. Understanding the control mechanisms has remained a challenge, especially the role played by the interaction between the field and the environment. In order to address this need, here we expand the scope of the Hamiltonian-encoding and observable-decoding (HE-OD) technique. HE-OD was originally introduced as a theoretical and experimental tool for revealing the mechanism induced by control fields in closed quantum systems. The results of open-system HE-OD analysis presented here provide quantitative mechanistic insights into the roles played by a Markovian environment. Two model open quantum systems are considered for illustration. In these systems, transitions are induced by either an applied field linked to a dipole operator or Lindblad operators coupled to the system. For modest control yields, the HE-OD results clearly show distinct cooperation between the dynamics induced by the optimal field and the environment. Although the HE-OD methodology introduced here is considered in simulations, it has an analogous direct experimental formulation, which we suggest may be applied to open systems in the laboratory to reveal mechanistic insights.

  16. 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.

  17. 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.

  18. Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.

    PubMed

    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.

  19. $\\cN$-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.

  20. Scattering in the Euclidean formulation of relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Polyzou, Wayne

    2013-10-01

    Euclidean relativistic quantum mechanics is a formulation of relativistic quantum mechanics based on the Osterwalder-Schrader reconstruction theorem that exploits the logical independence of locality from the rest of the axioms of Euclidean field theory. I discuss the properties of Euclidean Green functions necessary for the existence of Møller wave operators and the construction of these wave operators in this formalism. Supported by the US Department of Energy, Grant - DE-AC02-81ER40038.

  1. Interpreting Quantum Mechanics according to a Pragmatist Approach

    NASA Astrophysics Data System (ADS)

    Bächtold, Manuel

    2008-09-01

    The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.

  2. Scalable quantum mechanical simulation of large polymer systems

    SciTech Connect

    Goedecker, S.; Hoisie, A.; Kress, J.; Lubeck, O.; Wasserman, H.

    1997-08-01

    We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.

  3. On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

    SciTech Connect

    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.

  4. An axiomatic formulation of the Montevideo interpretation of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gambini, Rodolfo; García-Pintos, Luis Pedro; Pullin, Jorge

    We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects. Unlike in ordinary quantum mechanics, classical time only plays the role of an unobservable parameter. The formulation eliminates any privileged role of the measurement process giving an objective definition of when an event occurs in a system.

  5. Quantum mechanical effects in plasmonic structures with subnanometre gaps

    NASA Astrophysics Data System (ADS)

    Zhu, Wenqi; Esteban, Ruben; Borisov, Andrei G.; Baumberg, Jeremy J.; Nordlander, Peter; Lezec, Henri J.; Aizpurua, Javier; Crozier, Kenneth B.

    2016-06-01

    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.

  6. Quantum mechanical effects in plasmonic structures with subnanometre gaps

    PubMed Central

    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

  7. Electron exchange-correlation in quantum mechanics

    SciTech Connect

    Ritchie, B

    2009-01-30

    It is shown that Fermi-Dirac statistics is guaranteed by the Dirac current, from which spin-dependent quantum velocity fields and spin-dependent quantum trajectories can be inferred. Pauli's exclusion principle is demonstrated using the spin-dependent quantum trajectories. The Dirac current, unlike the Schroedinger current, is nonzero for stationary bound states due to the permanent magnetic moment of the electron. It is of order c{sup 0} in agreement with observation that Fermi-Dirac statistics is independent of electronic velocity. In summary the physical basis for exchange-correlation is found in Dirac's equation, although Schroedinger's equation may be used to evaluate the Dirac current in the nonrelativistic regime of electronic velocity.

  8. Whitehead's Philosophy and Quantum Mechanics (QM)

    NASA Astrophysics Data System (ADS)

    Malin, Shimon

    This paper is a tribute to Abner Shimony and a continuation of my discussions with him. In the first part some ofWhitehead's concepts, and, in particular, actual entities and atemporal processes, are introduced. These are shown to correspond to the objectivized aspects of the collapse of quantum states. Next we reconcile the entanglement of quantum states with the speed of light barrier for the transmission of information by modifying Whitehead's system: We suggest that events that take place far apart can be aspects if the same actual entity. We show that this takes care of Lovejoy's objection to Whitehead's system.

  9. '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.

  10. Multiple-event probability in general-relativistic quantum mechanics

    SciTech Connect

    Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo

    2007-04-15

    We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

  11. Hamiltonian cosmology of bigravity

    NASA Astrophysics Data System (ADS)

    Soloviev, V. O.

    The purpose of this talk is to give an introduction both to the Hamiltonian formalism and to the cosmological equations of bigravity. In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in addressing cosmological problems.

  12. Nonperturbative embedding for highly nonlocal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Subaşı, Yiǧit; Jarzynski, Christopher

    2016-07-01

    The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l Hamiltonian which is more local than the original one (using an analog device), and finally reverse the unitary transformation. The net effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.

  13. proper versus improper mixtures: Toward a quaternionic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Masillo, F.; Scolarici, G.; Sozzo, S.

    2009-07-01

    The density operators obtained by taking partial traces represent improper mixtures of subsystems of a compound physical system because the coefficients in the convex sums expressing them never bear the ignorance interpretation. Assigning states to these subsystems is consequently problematic in standard quantum mechanics (subentity problem). In the semantic realism interpretation of quantum mechanics, it is instead proposed to consider improper mixtures true nonpure states conceptually distinct from proper mixtures. Based on this proposal, we show that proper and improper mixtures can be represented by different density operators in the quaternionic formulation of quantum mechanics and can hence be distinguished even from a mathematical standpoint. We provide a simple example related to the quantum theory of measurement.

  14. 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.

  15. 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.

  16. The Möbius symmetry of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Faraggi, Alon E.; Matone, Marco

    2015-07-01

    The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under D-dimensional Mobius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global Mobius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the Möbius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

  17. Inflation from quantum geometry.

    PubMed

    Bojowald, Martin

    2002-12-23

    Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.

  18. An approximate approach to quantum mechanical study of biomacromolecules

    NASA Astrophysics Data System (ADS)

    Chen, Xihua

    This thesis summarizes the author's major work in Prof. John Z.H. Zhang's Threoretical Chemistry research group. In Chapter 1, we present a general description of MFCC (molecular fractionation with conjugated caps) method that has been developed in this group to treat biomacromolecules in a divide-and-conquer fashion. Then we give in detail a computational study of MFCC application to peptide/protein that contains disulfide bonds. Continued on the basis of previous MFCC tests, this study provides another numerical support for the accuracy of the MFCC approach to full quantum mechanical calculation of protein/peptide-small molecule interaction. In Chapter 2, we further develop the MFCC scheme for quantum mechanical computation of DNA-ligand interaction energy. We study three oligonuclear acid interaction systems: dinucleotide dCG/water, trinucleotide dCGT/water and a Watson-Crick paired DNA segment dCGT/dGCA. The MFCC interaction energies are found to be in excellent agreement with the corresponding results obtained from the full system ab initio calculations. This study is an exemplification of the application of the general MFCC approach to biomacromolecules. In Chapter 3, firstly, a MFCC-downhill simplex method is proposed to study binding structures of ligands (atoms, ions, or small molecules) in large molecular complex systems. This method employs the MFCC approach to compute the interaction energy-structure relation of the system and implements the downhill simplex algorithm for structural optimization. Secondly, this method is numerically tested on a system of [KCp(18-crown-6)], as a simplest monatomic case study, to optimize the binding position of the potassium cation in a fixed coordination Cp and 18-crown-6 coordinating sphere. The result of the MFCC-downhill simplex optimization shows good agreement with both the crystal structure and with the full-system downhill simplex optimized structure. The effects of the initial structure of the simplex and of the

  19. 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

  20. Foundations of a spacetime path formalism for relativistic quantum mechanics

    SciTech Connect

    Seidewitz, Ed

    2006-11-15

    Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincare invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, 'off-shell' theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to nonrelativistic quantum mechanics.

  1. Comments on continuous observation in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Diósi, L.

    1986-06-01

    It is shown that in open quantum systems the so-called Zeno paradox is not valid. The equations of ideal continuous measurement for Markovian open systems are elaborated and applied to Pauli's simple open system, the actual energy level of which is shown to be monitorable by a continuous nondemolition measurement.

  2. 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…

  3. Quantum mechanics problems in observer's mathematics

    SciTech Connect

    Khots, Boris; Khots, Dmitriy

    2012-11-06

    This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.

  4. PT-Symmetric Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Bender, Carl M.

    2011-09-01

    In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.

  5. Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations

    SciTech Connect

    Ojeda-May, Pedro; Pu, Jingzhi

    2015-11-07

    The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r{sup −1} term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN{sub 2} reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN{sub 2} reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical

  6. Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations

    NASA Astrophysics Data System (ADS)

    Ojeda-May, Pedro; Pu, Jingzhi

    2015-11-01

    The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r-1 term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN2 reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN2 reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical reactions.

  7. 2D Quantum Simulation of MOSFET Using the Non Equilibrium Green's Function Method

    NASA Technical Reports Server (NTRS)

    Svizhenko, Alexel; Anantram, M. P.; Govindan, T. R.; Yan, Jerry (Technical Monitor)

    2000-01-01

    The objectives this viewgraph presentation summarizes include: (1) the development of a quantum mechanical simulator for ultra short channel MOSFET simulation, including theory, physical approximations, and computer code; (2) explore physics that is not accessible by semiclassical methods; (3) benchmarking of semiclassical and classical methods; and (4) study other two-dimensional devices and molecular structure, from discretized Hamiltonian to tight-binding Hamiltonian.

  8. Jets and Metastability in Quantum Mechanics and Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Farhi, David

    I give a high level overview of the state of particle physics in the introduction, accessible without any background in the field. I discuss improvements of theoretical and statistical methods used for collider physics. These include telescoping jets, a statistical method which was claimed to allow jet searches to increase their sensitivity by considering several interpretations of each event. We find that indeed multiple interpretations extend the power of searches, for both simple counting experiments and powerful multivariate fitting experiments, at least for h → bb¯ at the LHC. Then I propose a method for automation of background calculations using SCET by appropriating the technology of Monte Carlo generators such as MadGraph. In the third chapter I change gears and discuss the future of the universe. It has long been known that our pocket of the standard model is unstable; there is a lower-energy configuration in a remote part of the configuration space, to which our universe will, eventually, decay. While the timescales involved are on the order of 10400 years (depending on how exactly one counts) and thus of no immediate worry, I discuss the shortcomings of the standard methods and propose a more physically motivated derivation for the decay rate. I then make various observations about the structure of decays in quantum field theory.

  9. Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'

    SciTech Connect

    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.

  10. 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.

  11. 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.

  12. A modified Lax-Phillips scattering theory for quantum mechanics

    SciTech Connect

    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.

  13. 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.

  14. Quantum mechanics from an equivalence principle

    SciTech Connect

    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.

  15. Multiscale quantum mechanics/electromagnetics simulation for electronic devices.

    PubMed

    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.

  16. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-01

    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.

  17. Some thoughts about consciousness: from a quantum mechanics perspective.

    PubMed

    Gargiulo, Gerald J

    2013-08-01

    The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning.

  18. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-01

    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. PMID:26124246

  19. 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.

  20. 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.

  1. Quantum mechanical study of solvent effects in a prototype S{sub N}2 reaction in solution: Cl{sup −} attack on CH{sub 3}Cl

    SciTech Connect

    Kuechler, Erich R.; York, Darrin M.

    2014-02-07

    The nucleophilic attack of a chloride ion on methyl chloride is an important prototype S{sub N}2 reaction in organic chemistry that is known to be sensitive to the effects of the surrounding solvent. Herein, we develop a highly accurate Specific Reaction Parameter (SRP) model based on the Austin Model 1 Hamiltonian for chlorine to study the effects of solvation into an aqueous environment on the reaction mechanism. To accomplish this task, we apply high-level quantum mechanical calculations to study the reaction in the gas phase and combined quantum mechanical/molecular mechanical simulations with TIP3P and TIP4P-ew water models and the resulting free energy profiles are compared with those determined from simulations using other fast semi-empirical quantum models. Both gas phase and solution results with the SRP model agree very well with experiment and provide insight into the specific role of solvent on the reaction coordinate. Overall, the newly parameterized SRP Hamiltonian is able to reproduce both the gas phase and solution phase barriers, suggesting it is an accurate and robust model for simulations in the aqueous phase at greatly reduced computational cost relative to comparably accurate ab initio and density functional models.

  2. EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT

    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

  3. Universal quantum computation by discontinuous quantum walk

    SciTech Connect

    Underwood, Michael S.; Feder, David L.

    2010-10-15

    Quantum walks are the quantum-mechanical analog of random walks, in which a quantum ''walker'' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This ''discontinuous'' quantum walk employs perfect quantum-state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one time step apart.

  4. Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian

    NASA Astrophysics Data System (ADS)

    Pittman, S. M.; Tannenbaum, E.; Heller, E. J.

    2016-08-01

    This paper attempts to resolve the issue of the nature of the 0.01-0.1 cm-1 peak splittings observed in high-resolution IR spectra of polyatomic molecules. One hypothesis is that these splittings are caused by dynamical tunneling, a quantum-mechanical phenomenon whereby energy flows between two disconnected regions of phase-space across dynamical barriers. However, a competing classical mechanism for energy flow is Arnol'd diffusion, which connects different regions of phase-space by a resonance network known as the Arnol'd web. The speed of diffusion is bounded by the Nekhoroshev theorem, which guarantees stability on exponentially long time scales if the Hamiltonian is steep. Here we consider a non-convex Hamiltonian that contains the characteristics of a molecular Hamiltonian, but does not satisfy the Nekhoroshev theorem. The diffusion along the Arnol'd web is expected to be fast for a non-convex Hamiltonian. While fast diffusion is an unlikely competitor for longtime energy flow in molecules, we show how dynamical tunneling dominates compared to fast diffusion in the nearly integrable regime for a non-convex Hamiltonian, as well as present a new kind of dynamical tunneling.

  5. 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.

  6. Quantum mechanics, gravity and modified quantization relations.

    PubMed

    Calmet, Xavier

    2015-08-01

    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.

  7. Generalized coherent states under deformed quantum mechanics with maximum momentum

    NASA Astrophysics Data System (ADS)

    Ching, Chee Leong; Ng, Wei Khim

    2013-10-01

    Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of γ (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on γ. The equation of motion is studied, and both Ehrenfest’s theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments.

  8. Connection between quantum-mechanical and classical time evolution via a dynamical invariant

    SciTech Connect

    Schuch, Dieter; Moshinsky, Marcos

    2006-06-15

    The time evolution of a quantum system with at most quadratic Hamiltonian is described with the help of different methods, namely the time-dependent Schroedinger equation, the time propagator or Feynman kernel, and the Wigner function. It is shown that all three methods are connected via a dynamical invariant, the so-called Ermakov invariant. This invariant introduces explicitly the quantum aspect via the position uncertainty and its possible time dependence. The importance of this aspect, also for the difference between classical and quantum dynamics, and in particular the role of the initial position uncertainty is investigated.

  9. 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.

  10. The Foundations of Quantum Mechanics and the Evolution of the Cartan-Kähler Calculus

    NASA Astrophysics Data System (ADS)

    Vargas, Jose G.

    2008-07-01

    In 1960 1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons. The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent. A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms.

  11. 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.

  12. A deformation quantization theory for noncommutative quantum mechanics

    SciTech Connect

    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)].

  13. Multilayered model in optics and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Kovalev, M. D.

    2009-08-01

    Three types of dispersion equations are analyzed that describe the eigenvalues of the effective refractive index of a multilayer plane optical waveguide and the energy eigenvalues of a quantum particle placed in a piecewise constant potential field. The first equation (D1) is derived by setting to zero the determinant of the system of linear equations produced by matching the solutions in the layers. The second equation (D2) is obtained using the well-known method of characteristic matrices. The third equation has been obtained in the general case by the author and is known as a multilayer equation. Simple relations between the three equations are established. It is shown that the set of roots of D2 exactly coincides with the set of eigenvalues of the multilayer problem, while the roots of D1 and the multilayer equation contain those equal to the refractive index in the optical case (or to the potential in the quantum case) in internal layers of the system, which may be superfluous. Examples are presented.

  14. Quantum mechanisms of density wave transport.

    PubMed

    Miller, John H; Wijesinghe, Asanga I

    2012-06-01

    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 NbSe(3) and TaS(3), 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

  15. Quantum mechanisms of density wave transport

    PubMed Central

    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

  16. New method for calculating binding energies in quantum mechanics and quantum field theories

    SciTech Connect

    Gat, G.; Rosenstein, B. Institute of Physics, Academia Sinica, Taipei, 11529 )

    1993-01-04

    We propose a systematic perturbative method for calculating the binding energy of threshold bound states---states which exist for arbitrary small coupling. The starting point is a (regularized) free theory. Explicit calculations are performed for quantum mechanics with arbitrary short-range potential in 1D and various (1+1)-dimensional quantum field theories. We check the method by comparing the results with exact formulas available in solvable models.

  17. 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.

  18. 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.

  19. Quantum Magnetomechanics: Ultrahigh-Q-Levitated Mechanical Oscillators

    NASA Astrophysics Data System (ADS)

    Cirio, M.; Brennen, G. K.; Twamley, J.

    2012-10-01

    Engineering nanomechanical quantum systems possessing ultralong motional coherence times allows for applications in precision quantum sensing and quantum interfaces, but to achieve ultrahigh motional Q one must work hard to remove all forms of motional noise and heating. We examine a magneto-meso-mechanical quantum system that consists of a 3D arrangement of miniature superconducting loops which is stably levitated in a static inhomogeneous magnetic field. The motional decoherence is predominantly due to loss from induced eddy currents in the magnetized sphere which provides the trapping field ultimately yielding Q˜109 with motional oscillation frequencies of several hundreds of kilohertz. By inductively coupling this levitating object to a nearby driven flux qubit one can cool its motion very close to the ground state and this may permit the generation of macroscopic entangled motional states of multiple clusters.

  20. 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.

  1. Spacetime alternatives in the quantum mechanics of a relativistic particle

    SciTech Connect

    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.

  2. 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.

  3. The uncertainty principle determines the nonlocality of quantum mechanics.

    PubMed

    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.

  4. Perturbation Theory for Parent Hamiltonians of Matrix Product States

    NASA Astrophysics Data System (ADS)

    Szehr, Oleg; Wolf, Michael M.

    2015-05-01

    This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).

  5. Hilbert space for quantum mechanics on superspace

    NASA Astrophysics Data System (ADS)

    Coulembier, K.; De Bie, H.

    2011-06-01

    In superspace a realization of {sl}_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}_2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

  6. Hilbert space for quantum mechanics on superspace

    SciTech Connect

    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.

  7. Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

    1995-05-01

    The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

  8. 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.

  9. The SCOP-formalism: an Operational Approach to Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    D'Hooghe, Bart

    2010-05-01

    We present the SCOP-formalism, an operational approach to quantum mechanics. If a State—COntext—Property—System (SCOP) satisfies a specific set of `quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.

  10. Hamiltonian gadgets with reduced resource requirements

    NASA Astrophysics Data System (ADS)

    Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre

    2015-01-01

    Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and k -body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a Y Y interaction term using Hamiltonians containing only {X ,Z ,X X ,Z Z } terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.

  11. To Quantum Mechanics Through Projection of Classical Statistical Mechanics on Prespace

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2005-10-01

    We show that in opposite to a common opinion quantum mechanics can be represented as projection of classical statistical model on prequantum space -- prespace. All distinguishing features of the quantum probabilistic model (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, classical model should be considered as a contextual model (in the sense that all probabilities are determined by contexts - complexes of physical conditions). Moreover, the prequantum→quantum map is well defined only for two fundamental physical variables (in quantum mechanics these are position and momentum). Quantum mechanics is a projection of classical statistical model through these two "reference observables". Similarly, ordinary classical statistical mechanics on physical phase space is a projection of classical statistical mechanics on prespace, We also introduce a mental prespace and consider its quantum-like representation. Mental prespace describes subconsciousness and its quantum-like representation gives a model of consciousness.

  12. 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.

  13. Is Quantum Mechanics Incompatible with Newton's First Law?

    NASA Astrophysics Data System (ADS)

    Rabinowitz, Mario

    2008-04-01

    Quantum mechanics (QM) clearly violates Newton’s First Law of Motion (NFLM) in the quantum domain for one of the simplest problems, yielding an effect in a force-free region much like the Aharonov-Bohm effect. In addition, there is an incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. A general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. Alternatives to the Schrödinger equation are considered that might avoid this problem. The meaning of the classical limit is examined. Critical views regarding QM by Schrödinger, Bohm, Bell, Clauser, and others are presented to provide a more complete perspective.

  14. ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations

    NASA Astrophysics Data System (ADS)

    Eburilitu; Alatancang

    2010-03-01

    The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy's principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.

  15. Topics in gravitational-wave science: Macroscopic quantum mechanics and black hole physics

    NASA Astrophysics Data System (ADS)

    Yang, Huan

    The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics. The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities. The second part of this thesis (Chapters 3 -- 7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects --- as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function. The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes --- a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting

  16. EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT

    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

  17. 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?

  18. Estimation of a general time-dependent Hamiltonian for a single qubit

    PubMed Central

    de Clercq, L. E.; Oswald, R.; Flühmann, C.; Keitch, B.; Kienzler, D.; Lo, H. -Y.; Marinelli, M.; Nadlinger, D.; Negnevitsky, V.; Home, J. P.

    2016-01-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control. PMID:27075230

  19. Estimation of a general time-dependent Hamiltonian for a single qubit.

    PubMed

    de Clercq, L E; Oswald, R; Flühmann, C; Keitch, B; Kienzler, D; Lo, H-Y; Marinelli, M; Nadlinger, D; Negnevitsky, V; Home, J P

    2016-04-14

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

  20. Charge-dependent non-bonded interaction methods for use in quantum mechanical modeling of condensed phase reactions

    NASA Astrophysics Data System (ADS)

    Kuechler, Erich R.

    Molecular modeling and computer simulation techniques can provide detailed insight into biochemical phenomena. This dissertation describes the development, implementation and parameterization of two methods for the accurate modeling of chemical reactions in aqueous environments, with a concerted scientific effort towards the inclusion of charge-dependent non-bonded non-electrostatic interactions into currently used computational frameworks. The first of these models, QXD, modifies interactions in a hybrid quantum mechanical/molecular (QM/MM) mechanical framework to overcome the current limitations of 'atom typing' QM atoms; an inaccurate and non-intuitive practice for chemically active species as these static atom types are dictated by the local bonding and electrostatic environment of the atoms they represent, which will change over the course of the simulation. The efficacy QXD model is demonstrated using a specific reaction parameterization (SRP) of the Austin Model 1 (AM1) Hamiltonian by simultaneously capturing the reaction barrier for chloride ion attack on methylchloride in solution and the solvation free energies of a series of compounds including the reagents of the reaction. The second, VRSCOSMO, is an implicit solvation model for use with the DFTB3/3OB Hamiltonian for biochemical reactions; allowing for accurate modeling of ionic compound solvation properties while overcoming the discontinuous nature of conventional PCM models when chemical reaction coordinates. The VRSCOSMO model is shown to accurately model the solvation properties of over 200 chemical compounds while also providing smooth, continuous reaction surfaces for a series of biologically motivated phosphoryl transesterification reactions. Both of these methods incorporate charge-dependent behavior into the non-bonded interactions variationally, allowing the 'size' of atoms to change in meaningful ways with respect to changes in local charge state, as to provide an accurate, predictive and

  1. 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.

  2. 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)

  3. Testing Quantum Mechanics using a Triple slit experiment

    NASA Astrophysics Data System (ADS)

    Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Sorkin, Rafael; Laflamme, Raymond; Weihs, Gregor

    2010-03-01

    As one of the postulates of quantum mechanics, Born's rule tells us how to get probabilities for experimental outcomes from the complex wavefunction of the system. It's quadratic nature entails that interference occurs in pairs of paths. An experiment is in progress in our laboratory that sets out to test the correctness of Born's rule by testing for the presence or absence of genuine three-path interference [1]. This is done using single photons and a three slit aperture. Although the Born rule has been indirectly verified to high accuracy in other experiments, the consequences of a detection of even a small three-way interference in the Quantum mechanical null prediction are tremendous. If a non-zero result were to be obtained, it would mean that Quantum Mechanics is only approximate, in the same way that the double slit experiment proves that classical physics is only an approximation to the true law of nature. This would give us an important hint on how to generalize Quantum Mechanics and open a new window to the world. Some preliminary observations have been reported in reference [2]. In this talk, I will show results that bound the possible violation of the second sum rule and will point out ways to obtain a tighter experimental bound. [1] R. D. Sorkin, Mod. Phys. Lett. A 9, 3119 (1994). [2] U. Sinha et al, in Foundations of Probability and Physics-5, A I P Conference Proceedings, Vol. 1101, pp. 200-207, New-York (2009)

  4. 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)

  5. 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…

  6. Philosophical and metamathematical considerations of quantum mechanical computers

    NASA Astrophysics Data System (ADS)

    Caulfield, H. John; Shamir, Joseph

    1990-07-01

    We ask and give only very preliminary answers to two questions which must arise when we consider quantum mechanical computers with significant quantunt indeterminacy. First, how does this impact our belief in Church's thesis? Second, how does this impact our belief in freedom of thought?

  7. A multiscale quantum mechanics/electromagnetics method for device simulations.

    PubMed

    Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua

    2015-04-01

    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.

  8. 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)

  9. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    SciTech Connect

    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.

  10. 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)

  11. 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…

  12. 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…

  13. 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…

  14. Quasi-Hermitian quantum mechanics in phase space

    SciTech Connect

    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.

  15. 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…

  16. 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

  17. Ruling Out Multi-Order Interference in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Laflamme, Raymond; Weihs, Gregor

    2010-07-01

    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.

  18. Solvable Quantum Macroscopic Motions and Decoherence Mechanisms in Quantum Mechanics on Nonstandard Space

    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.

  19. Superconvergent perturbation method in quantum mechanics

    SciTech Connect

    Scherer, W. )

    1995-02-27

    An analog of Kolmogorov's superconvergent perturbation theory in classical mechanics is constructed for self-adjoint operators. It is different from the usual Rayleigh-Schroedinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter.

  20. 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/.