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Sample records for bloch equations

  1. On unorthodox solutions of the Bloch equations

    CERN Document Server

    Moroz, Alexander

    2012-01-01

    A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number field, which makes it possible to find and classify all analytic solutions. Torrey's analytic solution in the form of exponentially damped harmonic oscillations [Phys. Rev. {\\bf 76}, 1059 (1949)] is found to dominate the parameter space, which justifies its use at numerous occasions in magnetic resonance and in quantum optics of atoms, molecules, and quantum dots. The unorthodox solutions of the Bloch equations, which do not have the form of exponentially damped harmonic oscillations, are confined to rather small detunings $\\delta^2\\lesssim (\\gamma-\\gamma_t)^2/27$ and small field strengths $\\Omega^2\\lesssim 8 (\\gamma-\\gamma_t)^2/27$, where $\\gamma$ and $\\gamma_t$ describe decay rates of the excited state (the total population relaxation rate) and of the coherence, respectiv...

  2. Continuity, the Bloch-Torrey equation, and Diffusion MRI

    CERN Document Server

    Hall, Matt G

    2016-01-01

    The Bloch equation describes the evolution of classical particles tagged with a magnetisation vector in a strong magnetic field and is fundamental to many NMR and MRI contrast methods. The equation can be generalised to include the effects of spin motion by including a spin flux, which typically contains a Fickian diffusive term and/or a coherent velocity term. This form is known as the Bloch-Torrey equation, and is fundamental to MR modalities which are sensitive to spin dynamics such as diffusion MRI. Such modalities have received a great deal of interest in the research literature over the last few years, resulting in a huge range of models and methods. In this work we make make use of a more general Bloch-Torrey equation with a generalised flux term. We show that many commonly employed approaches in Diffusion MRI may be viewed as different choices for the flux terms in this equation. This viewpoint, although obvious theoretically, is not usually emphasised in the diffusion MR literature and points to inte...

  3. Bloch-Redfield equations for modeling light-harvesting complexes

    CERN Document Server

    Jeske, Jan; Plenio, Martin B; Huelga, Susana F; Cole, Jared H

    2014-01-01

    We challenge the commonly held view that Bloch-Redfield equations are a less powerful tool than phenomenological Lindblad equations for modeling exciton transport in photosynthetic complexes. This view predominantly originates from the misuse of the secular approximation. We provide a detailed description of how to model both coherent oscillations and several types of noise, giving explicit examples. All issues with non-positivity are overcome by a consistent straightforward physical noise model. Herein also lies the strength of the Bloch-Redfield approach because it facilitates the analysis of noise-effects by linking them back to physical parameters of the noise environment. This includes temporal and spatial correlations and the strength and type of interaction between the noise and the system of interest. Finally we analyze a prototypical dimer system as well as a 7-site Fenna-Matthews-Olson (FMO) complex in regards to spatial correlation length of the noise, noise strength, temperature and their connecti...

  4. Bloch-Redfield equations for modeling light-harvesting complexes.

    Science.gov (United States)

    Jeske, Jan; Ing, David J; Plenio, Martin B; Huelga, Susana F; Cole, Jared H

    2015-02-14

    We challenge the misconception that Bloch-Redfield equations are a less powerful tool than phenomenological Lindblad equations for modeling exciton transport in photosynthetic complexes. This view predominantly originates from an indiscriminate use of the secular approximation. We provide a detailed description of how to model both coherent oscillations and several types of noise, giving explicit examples. All issues with non-positivity are overcome by a consistent straightforward physical noise model. Herein also lies the strength of the Bloch-Redfield approach because it facilitates the analysis of noise-effects by linking them back to physical parameters of the noise environment. This includes temporal and spatial correlations and the strength and type of interaction between the noise and the system of interest. Finally, we analyze a prototypical dimer system as well as a 7-site Fenna-Matthews-Olson complex in regards to spatial correlation length of the noise, noise strength, temperature, and their connection to the transfer time and transfer probability.

  5. Landau-Lifhsitz-Bloch equation for exchange coupled grains

    CERN Document Server

    Vogler, Christoph; Bruckner, Florian; Suess, Dieter

    2014-01-01

    Heat assisted recording is a promising technique to further increase the storage density in hard disks. Multilayer recording grains with graded Curie temperature is discussed to further assist the write process. Describing the correct magnetization dynamics of these grains, from room temperature to far above the Curie point, during a write process is required for the calculation of bit error rates. We present a coarse grained approach based on the Landau-Lifshitz-Bloch (LLB) equation to model exchange coupled grains with low computational effort. The required temperature dependent material properties such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities are obtained by atomistic Landau-Lifshitz-Gilbert (LLB) simulations. Each grain is described with one magnetization vector. In order to mimic the atomistic exchange interaction between the grains a special treatment of the exchange field in the coarse grained approach is presented.

  6. Non-Hermitian wave packet approximation of Bloch optical equations

    Energy Technology Data Exchange (ETDEWEB)

    Charron, Eric [Universite Paris-Sud, Institut des Sciences Moleculaires d' Orsay, ISMO, CNRS, F-91405 Orsay (France); Sukharev, Maxim [Department of Applied Sciences and Mathematics, Arizona State University, Mesa, Arizona 85212 (United States)

    2013-01-14

    We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation, and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method, one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schroedinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure, and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville-von Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.

  7. Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems

    OpenAIRE

    Tscherbul, Timur V.; Brumer, Paul

    2014-01-01

    We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an un...

  8. Derivation of a time dependent Schrödinger equation as the quantum mechanical Landau-Lifshitz-Bloch equation

    Science.gov (United States)

    Wieser, R.

    2016-10-01

    The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation.

  9. Derivation of a time dependent Schrödinger equation as the quantum mechanical Landau-Lifshitz-Bloch equation.

    Science.gov (United States)

    Wieser, R

    2016-10-01

    The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation. PMID:27494599

  10. Quantum Maxwell-Bloch equations for spontaneous emission in optical semiconductor devices

    OpenAIRE

    Hess, Ortwin; Hofmann, Holger F.

    1998-01-01

    We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous optical semiconductor devices taking into account the quantum noise effects which cause spontaneous emission and amplified spontaneous emission. Analytical expressions derived from the QMBE are presented for the spontaneous emission factor beta and the far field pattern of amplified spontaneous emission in broad area quantum well lasers.

  11. Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field

    OpenAIRE

    Hatsugai, Yasuhiro; Kohmoto, Mahito; Wu, Yong-Shi

    1994-01-01

    For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations of Wiegmann and Zabrodin. When the magnetic flux per plaquette is 1 / Q with Q an odd integer, distribution of the roots of the Bethe ansatz equation is uniform except at two points on the unit circle in the complex plane. For the semiclassical limit Q→∞, the wave function is

  12. Circularly polarized few-cycle optical rogue waves: rotating reduced Maxwell-Bloch equations.

    Science.gov (United States)

    Xu, Shuwei; Porsezian, K; He, Jingsong; Cheng, Yi

    2013-12-01

    The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.

  13. Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems

    CERN Document Server

    Tscherbul, Timur V

    2014-01-01

    We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis, and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a fi...

  14. Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron

    CERN Document Server

    Fujita, Shigeji

    2007-01-01

    Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron targets scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and material sciences. It is important that the reader have an understanding of dynamics, quantum mechanics, thermodynamics, statistical mechanics, electromagnetism and solid-state physics. Many worked-out problems are included in the book to aid the reader's comprehension of the subject. The Bloch electron (wave packet) moves by following the Newtonian equation of motion. Under an applied magnetic field B the electron circulates around the field B counterclockwise or clockwise depending on the curvature of the Fermi surface. The signs of the Hall coefficient and the Seebeck coefficient are known to give the sign of the major carrier charge. For alkali metals, both are negative, indicating that the carriers are "electrons." These features arise from the Fermi surface difference...

  15. Ising and Bloch domain walls in a two-dimensional parametrically driven Ginzburg-Landau equation model with nonlinearity management

    DEFF Research Database (Denmark)

    Gaididei, Yu. B.; Christiansen, Peter Leth

    2008-01-01

    We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered...... and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under...

  16. Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes

    OpenAIRE

    Bidégaray-Fesquet, Brigitte

    2010-01-01

    International audience The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies...

  17. Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes

    Science.gov (United States)

    Bidégaray-Fesquet, Brigitte

    2010-10-01

    The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature, we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena.

  18. Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes

    International Nuclear Information System (INIS)

    The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature, we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena.

  19. Maxwell-Bloch Equations Modeling of Ultrashort Optical Pulse Propagation in Semiconductor Materials

    Science.gov (United States)

    Goorjian, Peter M.; Agrawal, Govind, P.

    1997-01-01

    An algorithm has been developed that solves the semiconductor Maxwell-Bloch equations, without making the standard slowly-varying envelope (SVEA) and rotating-wave (RWA) approximations. It is applied to study the propagation of ultrashort pulses in semiconductor materials. The results include many-body effects due to the Coulomb interaction among the charge carriers as well as the nonlinear effects resulting from spectral hole-burning.

  20. Nonlinear waves of the Hirota and the Maxwell-Bloch equations in nonlinear optics

    Institute of Scientific and Technical Information of China (English)

    Li Chuan-Zhong; He Jing-Song; K.Porseizan

    2013-01-01

    In this paper,considering the Hirota and the Maxwell-Bloch (H-MB) equations which are governed by femtosecond pulse propagation through a two-level doped fiber system,we construct the Darboux transformation of this system through a linear eigenvalue problem.Using this Daurboux transformation,we generate multi-soliton,positon,and breather solutions (both bright and dark breathers) of the H-MB equations.Finally,we also construct the rogue wave solutions of the above system.

  1. High tip angle approximation based on a modified Bloch-Riccati equation.

    Science.gov (United States)

    Boulant, Nicolas; Hoult, David I

    2012-02-01

    When designing a radio-frequency pulse to produce a desired dependence of magnetization on frequency or position, the small flip angle approximation is often used as a first step, and a Fourier relation between pulse and transverse magnetization is then invoked. However, common intuition often leads to linear scaling of the resulting pulse so as to produce a larger flip angle than the approximation warrants--with surprisingly good results. Starting from a modified version of the Bloch-Riccati equation, a differential equation in the flip angle itself, rather than in magnetization, is derived. As this equation has a substantial linear component that is an instance of Fourier's equation, the intuitive approach is seen to be justified. Examples of the accuracy of this higher tip angle approximation are given for both constant- and variable-phase pulses.

  2. Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field

    OpenAIRE

    Hatsugai, Yasuhiro; Kohmoto, Mahito; Wu, Yong-Shi

    1994-01-01

    For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations recently proposed by Wiegmann and Zabrodin. When the magnetic flux per plaquette is $1/Q$ where $Q$ is an odd integer, distribution of the roots is uniform on the unit circle in the complex plane. For the semi-classical limit, $ Q\\rightarrow\\infty$, the wavefunction obeys the power low and is given by $|\\psi(x)|^2=(2/ \\sin \\pi x)$ which is critical and unnormal...

  3. Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Tscherbul, Timur V., E-mail: ttscherb@chem.utoronto.ca; Brumer, Paul [Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)

    2015-03-14

    We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.

  4. Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems

    Science.gov (United States)

    Tscherbul, Timur V.; Brumer, Paul

    2015-03-01

    We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.

  5. Modified-Bloch-equation description of EPR transient nutations and free induction decay in solids

    Energy Technology Data Exchange (ETDEWEB)

    Asadullina, N.Ya.; Asadullin, Ya.Ya. [Kazan State Technical University, Department of General Physics, Kazan (Russian Federation); Asadullin, T.Ya. [Kazan State Technical University, Department of General Physics, Kazan (Russian Federation). E-mail: atimur@physics.ktsu-kai.ru

    2001-04-09

    Based on the experimental work by Boscaino et al on the EPR transient nutations (TNs) and free induction decay (FID) in solids, we propose the modified Bloch equations (MBEs). In addition to the Tomita expression for power-dependent parameter T{sub 2u}, we give an original phenomenological expression for power-dependent parameter T{sub 2v} and tuning {delta}. Both analytical (in the form of a Torrey solution with these parameters) and numerical solutions of MBE are obtained for TN and for different FID regimes with very good agreement between theory and experiment. We also discuss the meaning and role of the instantaneous diffusion mechanism in the transient pulse experiments. (author)

  6. A Bloch-Torrey Equation for Diffusion in a Deforming Media

    Energy Technology Data Exchange (ETDEWEB)

    Rohmer, Damien; Gullberg, Grant T.

    2006-12-29

    Diffusion Tensor Magnetic Resonance Imaging (DTMRI)technique enables the measurement of diffusion parameters and therefore,informs on the structure of the biological tissue. This technique isapplied with success to the static organs such as brain. However, thediffusion measurement on the dynamically deformable organs such as thein-vivo heart is a complex problem that has however a great potential inthe measurement of cardiac health. In order to understand the behavior ofthe Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torreyequation that leads the MR behavior is expressed in general curvilinearcoordinates. These coordinates enable to follow the heart geometry anddeformations through time. The equation is finally discretized andpresented in a numerical formulation using implicit methods, in order toget a stable scheme that can be applied to any smooth deformations.Diffusion process enables the link between the macroscopic behavior ofmolecules and themicroscopic structure in which they evolve. Themeasurement of diffusion in biological tissues is therefore of majorimportance in understanding the complex underlying structure that cannotbe studied directly. The Diffusion Tensor Magnetic ResonanceImaging(DTMRI) technique enables the measurement of diffusion parametersand therefore provides information on the structure of the biologicaltissue. This technique has been applied with success to static organssuch as the brain. However, diffusion measurement of dynamicallydeformable organs such as the in-vivo heart remains a complex problem,which holds great potential in determining cardiac health. In order tounderstand the behavior of the magnetic resonance (MR) signal in adeforming media, the Bloch-Torrey equation that defines the MR behavioris expressed in general curvilinear coordinates. These coordinates enableus to follow the heart geometry and deformations through time. Theequation is finally discretized and presented in a numerical formulationusing

  7. Analytical solution of the Bloch NMR flow equations: A quantum mechanical model for general fluid flow analysis

    International Nuclear Information System (INIS)

    The equations of fluid mechanics, coupled with those that describe matter transportation at the molecular level must be handled effectively. Putting the fluid into equations, we model the Bloch NMR flow equations into the harmonic wave equation for the analysis of general fluid flow. We derived the solution of the modelled harmonic equation in non relativistic quantum mechanics and discuss its semi classical application to illustrate its potential wide-ranging usefulness in the search for the best possible data obtainable for general fluid flow analysis. Representing the solution of the derived harmonic wave equation by a normalized state function is quite useful in generating the properly normalized wave functions and in the efficient evaluation of expectation values of many operators that can be fundamental to the analysis of fluid flow especially at the microscopic level. (author)

  8. Light-Matter Interaction and Lasing in Semiconductor Nanowires: A combined FDTD and Semiconductor Bloch Equation Approach

    CERN Document Server

    Buschlinger, Robert; Peschel, Ulf

    2014-01-01

    We present a time-domain model for the simulation of light-matter interaction in semiconductors in arbitrary geometries and across a wide range of excitation conditions. The electromagnetic field is treated classically using the finite-difference time-domain method. The polarization and occupation numbers of the semiconductor material are described using the semiconductor Bloch equations including many-body effects in the screened Hartree-Fock approximation. Spontaneous emission noise is introduced using stochastic driving terms. As an application of the model, we present simulations of the dynamics of a nanowire laser including optical pumping, seeding by spontaneous emission and the selection of lasing modes.

  9. Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.

    Science.gov (United States)

    Cao, F J

    2004-09-01

    The dynamics in a nonlinear Schrödinger chain in a homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomena.

  10. QED-based Optical Bloch Equations without electric dipole approximation: A model for a two-level atom interacting with a monochromatic X-ray laser beam

    CERN Document Server

    Zhang, Wen-Zhuo

    2012-01-01

    We derive a set of optical Bloch equations (OBEs) directly from the minimal-coupling Hamiltonian density of the bound-state quantum electrodynamics (bound-state QED). Such optical Bloch equations are beyond the former widely-used ones due to that there is no electric dipole approximation (EDA) on the minimal-coupling Hamiltonian density of the bound-state QED. Then our optical Bloch equations can describe a two-level atom interacting with a monochromatic light of arbitrary wavelength, which are suitable to study the spectroscopy and the Rabi oscillations of two-level atoms in X-ray laser beams since that the wavelength of X-ray is close to an atom to make the electric dipole approximation (EDA) invalid.

  11. Quantum-Kinetic Approach to Deriving Optical Bloch Equations for Light Emitters in a Weakly Absorbing Dielectric

    Directory of Open Access Journals (Sweden)

    Gladush M.G.

    2015-01-01

    Full Text Available We obtained the system of Maxwell-Bloch equations (MB that describe the interaction of cw laser with optically active impurity centers (particles embedded in a dielectric material. The dielectric material is considered as a continuous medium with sufficient laser detuning from its absorption lines. The model takes into account the effects associated with both the real and the imaginary part of the dielectric constant of the material. MB equations were derived within a many-particle quantum-kinetic formalism, which is based on Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY hierarchy for reduced density matrices and correlation operators of material particles and the quantized radiation field modes. It is shown that this method is beneficial to describe the effects of individual and collective behavior of the light emitters and requires no phenomenological procedures. It automatically takes into account the characteristics associated with the presence of non-resonant and resonant particles filling the space between the optical centers.

  12. Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

    Science.gov (United States)

    Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

    2016-04-01

    Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it

  13. Optical Bloch Equations Modified with Phonon-Induced Intensity-Dependent Dephasing

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    We extend the exciton population equations of a two-level quantum dot system with weak excitation to the ones with strong excitations, in which, the phonon-induced intensity-dependent dephasing time and decay rate are involved. The straightforward calculated populations from the modified population equations demonstrate the damping behavior of Rabi oscillation as the external field increasing. The effect of the intensity-dependent dephasing time and the intensity-dependent decay rate are also discussed.

  14. Dynamics of the time dependent Bloch NMR equations for complex rFB1(t) magnetic field

    International Nuclear Information System (INIS)

    This study examines the dynamical changes produced by a complex time-dependent rFB1(t) magnetic field in an initially unperturbed magnetic resonance system. The analysis uses the Green's function algorithm as a tool to solve the transverse component of the time-dependent Bloch NMR equations with complex rFB1(t) field. The time development of the system is studied in the Hersenberg picture in which the operators are subject to unitary transformation as the applied rFB1(t) field changes the state of the NMR system from its initial ground state into another coherent state. The detailed features of the rFB1(t) field essentially affect the evolution of the state during its application. The state of the system after the complete cessation of the radio-frequency field is determined exclusively by a Fourier component which is in resonance with the NMR system. The unitary operator allows us to determine all the physically relevant information about the system in terms of a NMR relaxation parameter. (author)

  15. Numerical solution to the Bloch equations: paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field

    Science.gov (United States)

    Chen, Wen-Jun; Ma, Hong; Yu, De; Zeng, Xiao-Hu

    2016-08-01

    A novel nuclear magnetic resonance (NMR) experimental scheme, called wideband continuous wave NMR (WB-CW-NMR), is presented in this article. This experimental scheme has promising applications in pulsed magnetic fields, and can dramatically improve the utilization of the pulsed field. The feasibility of WB-CW-NMR scheme is verified by numerically solving modified Bloch equations. In the numerical simulation, the applied magnetic field is a pulsed magnetic field up to 80 T, and the wideband continuous radio frequency (RF) excitation is a band-limited (0.68-3.40 GHz) white noise. Furthermore, the influences of some experimental parameters, such as relaxation time, applied magnetic field strength and wideband continuous RF power, on the WB-CW-NMR signal are analyzed briefly. Finally, a multi-channel system framework for transmitting and receiving ultra wideband signals is proposed, and the basic requirements of this experimental system are discussed. Meanwhile, the amplitude of the NMR signal, the level of noise and RF interference in WB-CW-NMR experiments are estimated, and a preliminary adaptive cancellation plan is given for detecting WB-CW-NMR signal from large background interference. Supported by National Natural Science Foundation of China (11475067), the Innovative Research Foundation of Huazhong University of Science and Technology (2015 ZDTD017) and the Experimental Apparatus Research Project of Wuhan Pulsed High Magnetic Field Center (2015KF17)

  16. Numerical solution to the Bloch equations: paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field

    Science.gov (United States)

    Chen, Wen-Jun; Ma, Hong; Yu, De; Zeng, Xiao-Hu

    2016-08-01

    A novel nuclear magnetic resonance (NMR) experimental scheme, called wideband continuous wave NMR (WB-CW-NMR), is presented in this article. This experimental scheme has promising applications in pulsed magnetic fields, and can dramatically improve the utilization of the pulsed field. The feasibility of WB-CW-NMR scheme is verified by numerically solving modified Bloch equations. In the numerical simulation, the applied magnetic field is a pulsed magnetic field up to 80 T, and the wideband continuous radio frequency (RF) excitation is a band-limited (0.68–3.40 GHz) white noise. Furthermore, the influences of some experimental parameters, such as relaxation time, applied magnetic field strength and wideband continuous RF power, on the WB-CW-NMR signal are analyzed briefly. Finally, a multi-channel system framework for transmitting and receiving ultra wideband signals is proposed, and the basic requirements of this experimental system are discussed. Meanwhile, the amplitude of the NMR signal, the level of noise and RF interference in WB-CW-NMR experiments are estimated, and a preliminary adaptive cancellation plan is given for detecting WB-CW-NMR signal from large background interference. Supported by National Natural Science Foundation of China (11475067), the Innovative Research Foundation of Huazhong University of Science and Technology (2015 ZDTD017) and the Experimental Apparatus Research Project of Wuhan Pulsed High Magnetic Field Center (2015KF17)

  17. A Bloch equation approach to intensity dependent optical spectra of light harvesting complex II: excitation dependence of light harvesting complex II pump-probe spectra.

    Science.gov (United States)

    Richter, Marten; Renger, Thomas; Knorr, Andreas

    2008-01-01

    On the basis of the recent progress in the resolution of the structure of the antenna light harvesting complex II (LHC II) of the photosystem II, we propose a microscopically motivated theory to predict excitation intensity-dependent spectra. We show that optical Bloch equations provide the means to include all 2( N ) excited states of an oligomer complex of N coupled two-level systems and analyze the effects of Pauli Blocking and exciton-exciton annihilation on pump-probe spectra. We use LHC Bloch equations for 14 Coulomb coupled two-level systems, which describe the S (0) and S (1) level of every chlorophyll molecule. All parameter introduced into the Hamiltonian are based on microscopic structure and a quantum chemical model. The derived Bloch equations describe not only linear absorption but also the intensity dependence of optical spectra in a regime where the interplay of Pauli Blocking effects as well as exciton-exciton annihilation effects are important. As an example, pump-probe spectra are discussed. The observed saturation of the spectra for high intensities can be viewed as a relaxation channel blockade on short time scales due to Pauli blocking. The theoretical investigation is useful for the interpretation of the experimental data, if the experimental conditions exceed the low intensity pump limit and effects like strong Pauli Blocking and exciton-exciton annihilation need to be considered. These effects become important when multiple excitations are generated by the pump pulse in the complex. PMID:17924202

  18. Resonant Bloch-wave beatings.

    Science.gov (United States)

    Kartashov, Yaroslav V; Vysloukh, Victor A; Torner, Lluis

    2014-07-01

    We introduce Bloch-wave beatings in arrays of multimode periodically bent waveguides with a transverse refractive index gradient. The new phenomenon manifests itself in the periodic drastic increase of the amplitude of the Bloch oscillations that accompanies resonant conversion of modes guided by the individual waveguides. The Bloch-wave beatings are found to be most pronounced when the length of the resonant mode conversion substantially exceeds the longitudinal period of the Bloch oscillations. The beating frequency decreases when the amplitude of waveguide bending decreases, while the beating amplitude is restricted by the amplitude of the Bloch oscillations that emerge from the second allowed band of the Floquet-Bloch lattice spectrum.

  19. Resonant Bloch-wave beatings

    CERN Document Server

    Kartashov, Yaroslav V; Torner, Lluis

    2014-01-01

    We introduce Bloch-wave beatings in arrays of multimode periodically bent waveguides with a transverse refractive index gradient. The new phenomenon manifests itself in the periodic drastic increase of the amplitude of the Bloch oscillations that accompanies resonant conversion of modes guided by the individual waveguides. The Bloch-wave beatings are found to be most pronounced when the length of the resonant mode conversion substantially exceeds the longitudinal period of the Bloch oscillations. The beating frequency decreases when the amplitude of waveguide bending decreases, while the beating amplitude is restricted by the amplitude of the Bloch oscillations that emerge from the second allowed band of the Floquet-Bloch lattice spectrum.

  20. Polychromatic optical Bloch oscillations.

    Science.gov (United States)

    Longhi, Stefano

    2009-07-15

    Bloch oscillations (BOs) of polychromatic beams in circularly curved optical waveguide arrays are smeared out owing to the dependence of the BO spatial period on the wavelength. Here it is shown that restoring of the self-imaging property of the array and approximate BOs over relatively broad spectral ranges can be achieved by the insertion of suitable lumped phase slips uniformly applied across the array.

  1. A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures

    OpenAIRE

    Allaire, Grégoire; Briane, Marc; Vanninathan, Muthusamy

    2016-01-01

    in press International audience In this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is well-known that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogenized equation [5] where the homogenized equation can be improve...

  2. Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Bloch Electrons in a Magnetic Field

    OpenAIRE

    Wiegmann, P. B.; Zabrodin, A. V.

    1993-01-01

    We present a new approach to the problem of Bloch electrons in magnetic field,\\\\ by making explicit a natural relation between magnetic translations and the\\\\quantum group $U_{q}(sl_2)$. The approach allows to express the spectrum and\\\\\\ the Bloch function as solutions of the Bethe-Ansatz equations typical for com\\\\pletely integrable quantum systems

  3. Bloch vectors for qudits

    Energy Technology Data Exchange (ETDEWEB)

    Bertlmann, Reinhold A; Krammer, Philipp [Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)], E-mail: reinhold.bertlmann@univie.ac.at, E-mail: philipp.krammer@univie.ac.at

    2008-06-13

    We present three different matrix bases that can be used to decompose density matrices of d-dimensional quantum systems, so-called qudits: the generalized Gell-Mann matrix basis, the polarization operator basis and the Weyl operator basis. Such a decomposition can be identified with a vector-the Bloch vector, i.e. a generalization of the well-known qubit case-and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We present a new method to decompose density matrices via so-called standard matrices, consider the important case of an isotropic two-qudit state and decompose it according to each basis. In the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin-1 measurements, which is appropriate for an experimental realization.

  4. A theory of generalized Bloch oscillations.

    Science.gov (United States)

    Duggen, Lars; Lew Yan Voon, L C; Lassen, Benny; Willatzen, Morten

    2016-04-20

    Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact calculation is given to confirm this phenomenon. Our results allow for a greater freedom of design for experimentally observing Bloch oscillations. For strongly coupled oscillator systems displaying Bloch oscillations, it is further demonstrated that reordering of oscillators leads to destruction of Bloch oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics.

  5. A theory of generalized Bloch oscillations

    DEFF Research Database (Denmark)

    Duggen, Lars; Lew Yan Voon, L. C.; Lassen, Benny;

    2016-01-01

    Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact...... calculation is given to confirm this phenomenon. Our results allow for a greater freedom of design for experimentally observing Bloch oscillations. For strongly coupled oscillator systems displaying Bloch oscillations, it is further demonstrated that reordering of oscillators leads to destruction of Bloch...... oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics....

  6. An extended q-deformed su(2) algebra and the Bloch electron problem

    OpenAIRE

    Fujikawa, Kazuo; KUBO, HARUNOBU

    1997-01-01

    It is shown that an extended q-deformed $su(2)$ algebra with an extra (``Schwinger '') term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory of this q-deformed algebra, we obtain functional Bethe ansatz equations whose solutions should be functions of finite degree. It is also shown that the zero energy solution is expressed in t...

  7. Observation of anharmonic Bloch oscillations.

    Science.gov (United States)

    Dreisow, Felix; Wang, Gang; Heinrich, Matthias; Keil, Robert; Tünnermann, Andreas; Nolte, Stefan; Szameit, Alexander

    2011-10-15

    We report on the experimental observation of Bloch oscillations of an optical wave packet in a lattice with second-order coupling. To this end, we employ zigzag waveguide arrays, in which the second-order coupling can be precisely tuned.

  8. Unit quaternions and the Bloch sphere

    Science.gov (United States)

    Wharton, K. B.; Koch, D.

    2015-06-01

    The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to ‘second order qubits’ would imply either a larger gauge freedom or a natural space of hidden variables.

  9. Asymptotic Analysis of Quantum Dynamics in Crystals:the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

    Institute of Scientific and Technical Information of China (English)

    Weinan E; Jian-feng LU; Xu YANG

    2013-01-01

    We study the semi-classical limit of the Schr(o)dinger equation in a crystal in the presence of an external potential and magnetic field.We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting.For the second part,we focus on the appearance of the Berry curvature terms in the asymptotic equations.These terms play a crucial role in many important physical phenomena such as the quantum Hall effect.We give a simple derivation of these terms in different settings using asymptotic analysis.

  10. Bloch oscillations in carbon nanotubes.

    Science.gov (United States)

    Jódar, Esther; Pérez-Garrido, Antonio; Rojas, Fernando

    2009-05-27

    Bloch oscillations arise when electrons are in a one-dimensional linear chain of atoms under a constant electric field. In this paper we show numerically that electrons in different types of carbon nanotubes show oscillations with a Bloch frequency proportional to the constant electric field applied along the nanotube axis. We show these oscillations, calculating the quadratic displacement as a function of the electric field. Because of the double periodicity of the nanotubes' geometry (the lattice constant and the lines of atoms) two frequencies appear, one twice the value of the other. These frequencies coincide perfectly with those predicted for a linear chain of atoms, taking into account the periodicity considered in each case.

  11. Optical analogue of electronic Bloch oscillations.

    Science.gov (United States)

    Sapienza, Riccardo; Costantino, Paola; Wiersma, Diederik; Ghulinyan, Mher; Oton, Claudio J; Pavesi, Lorenzo

    2003-12-31

    We report on the observation of Bloch oscillations in light transport through periodic dielectric systems. By introducing a linear refractive index gradient along the propagation direction the optical equivalent of a Wannier-Stark ladder was obtained. Bloch oscillations were observed as time-resolved oscillations in transmission, in direct analogy to electronic Bloch oscillations in conducting crystals where the Wannier-Stark ladder is obtained via an external electric field. The observed oscillatory behavior is in excellent agreement with transfer matrix calculations.

  12. Hybrid Bloch-Anderson localization of light

    CERN Document Server

    Stutzer, Simon; Vysloukh, Victor A; Konotop, Vladimir V; Nolte, Stefan; Torner, Lluis; Szameit, Alexander

    2013-01-01

    We investigate the interplay of Bloch oscillations and Anderson localization in optics. Gradual washing out of Bloch oscillations and the formation of nearly stationary averaged intensity distributions, which are symmetric for narrow and strongly asymmetric for broad input excitations, are observed experimentally in laser-written waveguide arrays. At large disorder levels Bloch oscillations are completely destroyed and both narrow and wide excitations lead to symmetric stationary averaged intensity distributions with exponentially decaying tails.

  13. Hybrid Bloch-Anderson localization of light.

    Science.gov (United States)

    Stützer, Simon; Kartashov, Yaroslav V; Vysloukh, Victor A; Konotop, Vladimir V; Nolte, Stefan; Torner, Lluis; Szameit, Alexander

    2013-05-01

    We investigate the interplay of Bloch oscillations and Anderson localization in optics. Gradual washing out of Bloch oscillations and the formation of nearly stationary averaged intensity distributions, which are symmetric for narrow and strongly asymmetric for broad input excitations, are observed experimentally in laser-written waveguide arrays. At large disorder levels Bloch oscillations are completely destroyed and both narrow and wide excitations lead to symmetric stationary averaged intensity distributions with exponentially decaying tails.

  14. Wave impedance retrieving via Bloch modes analysis

    DEFF Research Database (Denmark)

    Andryieuski, Andrei; Ha, S.; Sukhorukov, A.;

    2011-01-01

    The main bottleneck in the restoration of electromagnetic effective parameters is connected to the impedance retrieving. The S-parameters method gives the input (Bloch) impedance, which, being then used for permittivity and permeability determination, causes some fundamental physics prin......-ciples violation, like antiresonance behaviour with Im(ε) fundamental) Bloch mode. Then it is possible to determine the Bloch and wave impedances by the surface and volume aver-aging of the electromagnetic field...

  15. The Bloch Vector for N-Level Systems

    OpenAIRE

    Kimura, Gen

    2003-01-01

    We determine the set of the Bloch vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.

  16. Electric dipoles on the Bloch sphere

    CERN Document Server

    Vutha, Amar C

    2014-01-01

    The time evolution of a two-level quantum mechanical system can be geometrically described using the Bloch sphere. By mapping the Bloch sphere evolution onto the dynamics of oscillating electric dipoles, we provide a physically intuitive link between classical electromagnetism and the electric dipole transitions of atomic & molecular physics.

  17. Bloch-Zener oscillations in binary superlattices.

    Science.gov (United States)

    Dreisow, F; Szameit, A; Heinrich, M; Pertsch, T; Nolte, S; Tünnermann, A; Longhi, S

    2009-02-20

    Bloch-Zener oscillations, i.e., the coherent superposition of Bloch oscillations and Zener tunneling between minibands of a binary lattice, are experimentally demonstrated for light waves in curved femtosecond laser-written waveguide arrays. Visualization of double-periodicity breathing and oscillation modes is reported, and synchronous tunneling leading to wave reconstruction is demonstrated.

  18. Bloch oscillations in atom interferometry

    CERN Document Server

    Cladé, Pierre

    2014-01-01

    In Paris, we are using an atom interferometer to precisely measure the recoil velocity of an atom that absorbs a photon. In order to reach a high sensitivity, many recoils are transferred to atoms using the Bloch oscillations technique. In this lecture, I will present in details this technique and its application to high precision measurement. I will especially describe in details how this method allows us to perform an atom recoil measurement at the level of $1.3 \\times 10^{-9}$. This measurement is used in the most precise determination of the fine structure constant that is independent of quantum electrodynamics.

  19. Mathematical design of a magnetic resonance imaging sequence based on bloch NMR lfow equations and bessel functions%基于布洛克磁共振流动方程和贝塞尔函数的磁共振成像序列数学设计

    Institute of Scientific and Technical Information of China (English)

    O.B. Awojoyogbe; O.M. Dada

    2013-01-01

    Bloch方程是NMR/MRI计算、模拟和实验的基础,但通常在不加特定的绝热和非绝热条件的前提下获得Bloch流动方程的解析解是非常困难的。流动方程的一般解析解可以为理解NMR/MRI的基本概念提供额外的信息,而又不需要通常的指数方程。作者的目的是通过贝塞尔函数及其特性得到与时间无关的NMR流动方程的解析解。在不需要主观添加弥散项的前提下利用贝塞尔函数及其特性从NMR流动方程中获得了Stejskal-Tanner公式。这证实了弥散是Bloch流动方程的内在属性并可以通过如贝塞尔函数的适当数学函数提取出来。从解析解得到的非高斯行为的弥散信号在如脑白质的各项异性组织环境中是非常有意义的。发现弥散系数是与T1和T2弛豫参数直接相关的,因此通过对大量已有的贝塞尔函数进行合适利用可以在四个分离的缓存内采集MRI信号(实部和虚部,相位和绝对值)。能够利用MRI监测药物对于不同组织尤其是脑部功能活动的效果。%Bloch NMR equations are fundamental to all NMR/MRI computations, simulations and experiments. It has been very difficult to solve the Bloch NMR flow equations analytically without imposing specific adiabatic and non adiabatic conditions. General analytical solutions of the flow equations can easily provide additional information to understand the basic concept of NMR/MRI without the usual exponential functions. The goal of this report is to present analytical solutions to the time independent NMR lfow equation using the Bessel functions and properties. We derived the Stejskal-Tanner formula from the NMR lfow equations using the Bessel functions and properties without the need to arbitrarily add the diffusion term. This confirms that diffusion is an intrinsic property embedded in the Bloch NMR flow equation and can be extracted by the use of appropriate mathematical functions such as Bessel functions and

  20. First Bloch eigenvalue in high contrast media

    Science.gov (United States)

    Briane, Marc; Vanninathan, Muthusamy

    2014-01-01

    This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast ɛY-periodic conductivity. When the conductivity is bounded in L1 and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ɛ-2, the first Bloch eigenvalue converges as ɛ → 0 to a limit which preserves the second-order expansion with respect to the Bloch parameter. In dimension two the expansion of the limit can be improved until the fourth-order under the same hypotheses. On the contrary, in dimension three a fibers reinforced medium combined with a L1-unbounded conductivity leads us to a discontinuity of the limit first Bloch eigenvalue as the Bloch parameter tends to zero but remains not orthogonal to the direction of the fibers. Therefore, the high contrast conductivity of the microstructure induces an anomalous effect, since for a given low-contrast conductivity the first Bloch eigenvalue is known to be analytic with respect to the Bloch parameter around zero.

  1. First Bloch eigenvalue in high contrast media

    Energy Technology Data Exchange (ETDEWEB)

    Briane, Marc, E-mail: mbriane@insa-rennes.fr [Institut de Recherche Mathématique de Rennes, INSA de Rennes (France); Vanninathan, Muthusamy, E-mail: vanni@math.tifrbng.res.in [TIFR-CAM, Bangalore (India)

    2014-01-15

    This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast εY-periodic conductivity. When the conductivity is bounded in L{sup 1} and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ε{sup −2}, the first Bloch eigenvalue converges as ε → 0 to a limit which preserves the second-order expansion with respect to the Bloch parameter. In dimension two the expansion of the limit can be improved until the fourth-order under the same hypotheses. On the contrary, in dimension three a fibers reinforced medium combined with a L{sup 1}-unbounded conductivity leads us to a discontinuity of the limit first Bloch eigenvalue as the Bloch parameter tends to zero but remains not orthogonal to the direction of the fibers. Therefore, the high contrast conductivity of the microstructure induces an anomalous effect, since for a given low-contrast conductivity the first Bloch eigenvalue is known to be analytic with respect to the Bloch parameter around zero.

  2. Magnetic Bloch oscillations in nanowire superlattice rings.

    Science.gov (United States)

    Citrin, D S

    2004-05-14

    The recent growth of semiconductor nanowire superlattices encourages hope that Bloch-like oscillations in such structures formed into rings may soon be observed in the presence of a time-dependent magnetic flux threading the ring. These magnetic Bloch oscillations are a consequence of Faraday's law; the time-dependent flux produces an electromotive force around the ring, thus leading to the Bloch-like oscillations. In the spectroscopic domain, generalized Wannier-Stark states are found that are manifestations of the emf-induced localization of the states.

  3. Bloch Walls and Macroscopic String States in Bethe's Solution of the Heisenberg Ferromagnetic Linear Chain

    Science.gov (United States)

    Dhar, Abhishek; Sriram Shastry, B.

    2000-09-01

    We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1D for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. They are identified as generalized quantum Bloch wall states, and a simple physical picture is provided for the same.

  4. Bloch Walls and Macroscopic String States in Bethe's solution of the Heisenberg Ferromagnetic Linear Chain

    OpenAIRE

    Dhar, Abhishek; Shastry, B. Sriram

    2000-01-01

    We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1-d for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. These are identified as generalized quantum Bloch wall states, and a simple physical picture provided for the same.

  5. First Bloch eigenvalue in high contrast media

    OpenAIRE

    Briane, Marc; Vanninathan, Muthusamy

    2014-01-01

    16 pages International audience This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast $\\varepsilon Y$-periodic conductivity. When the conductivity is bounded in $L^1$ and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to $\\varepsilon^{-2}$, the first Bloch eigenvalue converges as $\\varepsilon\\to 0$ to a limit which preserves the second-order expansion with respect to the ...

  6. Bloch oscillations in optical dissipative lattices.

    Science.gov (United States)

    Efremidis, Nikolaos K; Christodoulides, Demetrios N

    2004-11-01

    We show that Bloch oscillations are possible in dissipative optical waveguide lattices with a linearly varying propagation constant. These oscillations occur in spite of the fact that the Bloch wave packet experiences coupling gain and (or) loss. Experimentally, this process can be observed in different settings, such as in laser arrays and lattices of semiconductor optical amplifiers. In addition, we demonstrate that these systems can suppress instabilities arising from preferential mode noise growth.

  7. Experimental observation of spectral Bloch oscillations.

    Science.gov (United States)

    Bersch, Christoph; Onishchukov, Georgy; Peschel, Ulf

    2009-08-01

    We report on the first, to our knowledge, experimental observation of spectral Bloch oscillations in an optical fiber employing the interaction between a probe signal and a traveling-wave periodic potential. The spectrum of weak probe pulses is shown to oscillate on account of their group-velocity mismatch to the periodic field. The behavior of a cw probe spectrum reveals the actual discrete nature of the effect. Recurrences of the spectrum after one and two Bloch periods are demonstrated.

  8. SOLITONS: Optimal control of optical soliton parameters: Part 2. Concept of nonlinear Bloch waves in the problem of soliton management

    Science.gov (United States)

    Serkin, Vladimir N.; Belyaeva, T. L.

    2001-11-01

    It is shown that optical solitons in nonlinear fibre-optic communication systems and soliton lasers can be represented as nonlinear Bloch waves in periodic structures. The Bloch theorem is proved for solitons of the nonlinear Schrodinger equation in systems with the dispersion, the nonlinearity, and the gain (absorption coefficient) periodically changing over the length. The dynamics of formation and interaction, as well as stability of the coupled states of nonlinear Bloch waves are investigated. It is shown that soliton Bloch waves exist only under certain self-matching conditions for the basic parameters of the system and reveal a structural instability with respect to the mismatch between the periods of spatial modulation of the dispersion, nonlinearity or gain.

  9. Resonant delocalization and Bloch oscillations in modulated lattices.

    Science.gov (United States)

    El-Ganainy, R; Christodoulides, D N; Rüter, C E; Kip, D

    2011-04-15

    We study the propagation of light in Bloch waveguide arrays exhibiting periodic coupling interactions. Intriguing wave packet revival patterns as well as beating Bloch oscillations are demonstrated. A new resonant delocalization phase transition is also predicted.

  10. Observation of Bloch oscillations in molecular rotation

    CERN Document Server

    Floß, Johannes; Averbukh, Ilya Sh; Bucksbaum, Philip H

    2015-01-01

    The periodically kicked quantum rotor is known for non-classical effects such as quantum localisation in angular momentum space or quantum resonances in rotational excitation. These phenomena have been studied in diverse systems mimicking the kicked rotor, such as cold atoms in optical lattices, or coupled photonic structures. Recently, it was predicted that several solid state quantum localisation phenomena - Anderson localisation, Bloch oscillations, and Tamm-Shockley surface states - may manifest themselves in the rotational dynamics of laser-kicked molecules. Here, we report the first observation of rotational Bloch oscillations in a gas of nitrogen molecules kicked by a periodic train of femtosecond laser pulses. A controllable detuning from the quantum resonance creates an effective accelerating potential in angular momentum space, inducing Bloch-like oscillations of the rotational excitation. These oscillations are measured via the temporal modulation of the refractive index of the gas. Our results int...

  11. Fractional Bloch oscillations in photonic lattices.

    Science.gov (United States)

    Corrielli, Giacomo; Crespi, Andrea; Della Valle, Giuseppe; Longhi, Stefano; Osellame, Roberto

    2013-01-01

    Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.

  12. Fractional Bloch oscillations in photonic lattices

    CERN Document Server

    Corrielli, Giacomo; Della Valle, Giuseppe; Longhi, Stefano; Osellame, Roberto; 10.1038/ncomms2578

    2013-01-01

    Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.

  13. Bloch oscillations in complex crystals with PT symmetry.

    Science.gov (United States)

    Longhi, S

    2009-09-18

    Bloch oscillations in complex lattices with PT symmetry are theoretically investigated with specific reference to optical Bloch oscillations in photonic lattices with gain or loss regions. Novel dynamical phenomena with no counterpart in ordinary lattices, such as nonreciprocal Bloch oscillations related to violation of the Friedel's law of Bragg scattering in complex potentials, are highlighted.

  14. Terahertz Bloch oscillator with a modulated bias.

    Science.gov (United States)

    Hyart, Timo; Alexeeva, Natalia V; Mattas, Jussi; Alekseev, Kirill N

    2009-04-10

    Electrons performing Bloch oscillations in an energy band of a dc-biased superlattice in the presence of weak dissipation can potentially generate THz fields at room temperature. The realization of such a Bloch oscillator is a long-standing problem due to the instability of a homogeneous electric field in conditions of negative differential conductivity. We establish the theoretical feasibility of stable THz gain in a long superlattice device in which the bias is quasistatically modulated by microwave fields. The modulation waveforms must have at least two harmonics in their spectra.

  15. Observation of Bloch Oscillations in Molecular Rotation.

    Science.gov (United States)

    Floß, Johannes; Kamalov, Andrei; Averbukh, Ilya Sh; Bucksbaum, Philip H

    2015-11-13

    We report the observation of rotational Bloch oscillations in a gas of nitrogen molecules kicked by a periodic train of femtosecond laser pulses. A controllable detuning from the quantum resonance creates an effective accelerating potential in angular momentum space, inducing Bloch-like oscillations of the rotational excitation. These oscillations are measured via the temporal modulation of the refractive index of the gas. Our results introduce room-temperature laser-kicked molecules as a new laboratory for studies of localization phenomena in quantum transport.

  16. Electronic Bloch oscillation in bilayer graphene gradient superlattices

    Energy Technology Data Exchange (ETDEWEB)

    Cheng, Hemeng; Li, Changan; Song, Yun [Department of Physics, Beijing Normal University, Beijing 100875 (China); Ma, Tianxing, E-mail: txma@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China); Beijing Computational Science Research Center, Beijing 100084 (China); Wang, Li-Gang, E-mail: sxwlg@yahoo.com [Department of Physics, Zhejiang University, Hangzhou 310027 (China); Lin, Hai-Qing [Beijing Computational Science Research Center, Beijing 100084 (China)

    2014-08-18

    We investigate the electronic Bloch oscillation in bilayer graphene gradient superlattices using transfer matrix method. By introducing two kinds of gradient potentials of square barriers along electrons propagation direction, we find that Bloch oscillations up to terahertz can occur. Wannier-Stark ladders, as the counterpart of Bloch oscillation, are obtained as a series of equidistant transmission peaks, and the localization of the electronic wave function is also signature of Bloch oscillation. Furthermore, the period of Bloch oscillation decreases linearly with increasing gradient of barrier potentials.

  17. Fractional Bloch Oscillations in photonic lattices

    Directory of Open Access Journals (Sweden)

    Corrielli G.

    2013-11-01

    Full Text Available We present the photonic analogy of the Fractional Bloch Oscillations [1]: the oscillatory motion of interacting particles moving in a periodic potential, under the presence of a static force. The analogy is implemented with the propagation of classical light in a specially engineered photonic waveguides lattice, fabricated in fused silica substrate via femtosecond laser micromachining.

  18. Sandwich reactor lattices and Bloch's theorem

    International Nuclear Information System (INIS)

    The study of the neutron flux distribution in repetitive sandwiches of reactor material leads to results analogous to the 1-dimensional form of Bloch's theorem for the electronic structure in crystals. This principle makes it possible to perform analytically accurate homogenisations of sandwich lattices The method has been extended to cover multi group diffusion and transport theory. (author)

  19. Computation and visualization of photonic quasicrystal spectra via Blochs theorem

    CERN Document Server

    Rodriguez, Alejandro W; Avniel, Yehuda; Johnson, Steven G

    2007-01-01

    Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwells equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Blochs theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.

  20. Tunable Bloch Wave Resonances and Bloch Gaps in Uniform Materials with Reconfigurable Boundary Profiles

    Science.gov (United States)

    Pogrebnyak, Victor A.; Furlani, Edward P.

    2016-05-01

    We study wave propagation in uniform materials with periodic boundary profiles and introduce for the first time Bloch resonances and Bloch gaps. Bloch resonances are due to transverse phase matching, i.e., the coupling of two transverse standing waves corresponding to different harmonics. These are distinct from well-known Bragg resonances that result from longitudinal phase matching. We show that Bloch gaps can be engineered over the entire first Brillouin zone up to an infinite wavelength, i.e., kx=0 , where kx is the wave number in the direction of propagation. This is in contrast to Bragg gaps that open at a fixed wavelength, twice the period of the structure. Bloch resonances and gaps can be tuned by reconfiguring the boundary profile and we derive analytical expressions that predict these phenomena when the amplitude of the profile is small. The theory is fundamental as it broadly applies to wave phenomena that span the quantum to continuum scale with applications that range from condensed matter to acoustics. We validate the theory experimentally for the electromagnetic field at GHz frequencies. We also discuss potential photonic and electronic applications of the theory such as a white-light distributed feedback laser and a two-dimensional electron gas transistor.

  1. Tunable Bloch Wave Resonances and Bloch Gaps in Uniform Materials with Reconfigurable Boundary Profiles.

    Science.gov (United States)

    Pogrebnyak, Victor A; Furlani, Edward P

    2016-05-20

    We study wave propagation in uniform materials with periodic boundary profiles and introduce for the first time Bloch resonances and Bloch gaps. Bloch resonances are due to transverse phase matching, i.e., the coupling of two transverse standing waves corresponding to different harmonics. These are distinct from well-known Bragg resonances that result from longitudinal phase matching. We show that Bloch gaps can be engineered over the entire first Brillouin zone up to an infinite wavelength, i.e., k_{x}=0, where k_{x} is the wave number in the direction of propagation. This is in contrast to Bragg gaps that open at a fixed wavelength, twice the period of the structure. Bloch resonances and gaps can be tuned by reconfiguring the boundary profile and we derive analytical expressions that predict these phenomena when the amplitude of the profile is small. The theory is fundamental as it broadly applies to wave phenomena that span the quantum to continuum scale with applications that range from condensed matter to acoustics. We validate the theory experimentally for the electromagnetic field at GHz frequencies. We also discuss potential photonic and electronic applications of the theory such as a white-light distributed feedback laser and a two-dimensional electron gas transistor. PMID:27258880

  2. Bloch oscillations in plasmonic waveguide arrays.

    Science.gov (United States)

    Block, A; Etrich, C; Limboeck, T; Bleckmann, F; Soergel, E; Rockstuhl, C; Linden, S

    2014-05-12

    The combination of modern nanofabrication techniques and advanced computational tools has opened unprecedented opportunities to mold the flow of light. In particular, discrete photonic structures can be designed such that the resulting light dynamics mimics quantum mechanical condensed matter phenomena. By mapping the time-dependent probability distribution of an electronic wave packet to the spatial light intensity distribution in the corresponding photonic structure, the quantum mechanical evolution can be visualized directly in a coherent, yet classical wave environment. On the basis of this approach, several groups have recently observed discrete diffraction, Bloch oscillations and Zener tunnelling in different dielectric structures. Here we report the experimental observation of discrete diffraction and Bloch oscillations of surface plasmon polaritons in evanescently coupled plasmonic waveguide arrays. The effective external potential is tailored by introducing an appropriate transverse index gradient during nanofabrication of the arrays. Our experimental results are in excellent agreement with numerical calculations.

  3. Logarithmic Bloch space and its predual

    CERN Document Server

    Pavlović, Miroslav

    2011-01-01

    We consider the space $\\bk^1_{\\log^\\alpha}$, of analytic functions on the unit disk $\\D,$ defined by the requirement $\\int_\\D|f'(z)|\\phi(|z|)\\,dA(z)<\\infty,$ where $\\phi(r)=\\log^\\alpha(1/(1-r))$ and show that it is a predual of the "$\\log^\\alpha$-Bloch" space and the dual of the corresponding little Bloch space. We prove that a function $f(z)=\\sum_{n=0}^\\infty a_nz^n$ with $a_n\\downarrow 0$ is in $\\bk^1_{\\log^\\alpha}$ iff $\\sum_{n=0}^\\infty \\log^\\alpha(n+2)/(n+1)<\\infty$ and apply this to obtain a criterion for membership of the Libera transform of a function with positive coefficients in $\\bk^1_{\\log^\\alpha}.$ Some properties of the Ces\\'aro and the Libera operator are considered as well.

  4. Bloch oscillations of path-entangled photons.

    Science.gov (United States)

    Bromberg, Yaron; Lahini, Yoav; Silberberg, Yaron

    2010-12-31

    We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.

  5. Photonic Bloch oscillations of correlated particles.

    Science.gov (United States)

    Longhi, Stefano

    2011-08-15

    A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed. The signature of correlated BOs, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.

  6. Quantum state transfer via Bloch oscillations.

    Science.gov (United States)

    Tamascelli, Dario; Olivares, Stefano; Rossotti, Stefano; Osellame, Roberto; Paris, Matteo G A

    2016-05-18

    The realization of reliable quantum channels, able to transfer a quantum state with high fidelity, is a fundamental step in the construction of scalable quantum devices. In this paper we describe a transmission scheme based on the genuinely quantum effect known as Bloch oscillations. The proposed protocol makes it possible to carry a quantum state over different distances with a minimal engineering of the transmission medium and can be implemented and verified on current quantum technology hardware.

  7. A Refresher of the Original Bloch's Law Paper (Bloch, July 1885).

    Science.gov (United States)

    Gorea, Andrei

    2015-08-01

    In 1885, Adolphe-Moïse Bloch asked the following simple question "Is there a law describing the relationship between the duration of a light and its perceived intensity?" Based on a series of experiments using a Foucault regulator and a candle, Bloch concluded that "when the lighting duration varies from 0.00173 to 0.0518 seconds (…) the [visible] light is markedly in inverse proportion to its duration"-his famous law. As this law pertains to the more general and hotly debated question of accumulation of sensory information over time, it is timely to offer the public a full translation of Bloch's original paper (from French) and to present it within the context of contemporary research. PMID:27433317

  8. Inverse Bloch-oscillator: Strong Thz-photocurrent resonances at the Bloch frequency

    Energy Technology Data Exchange (ETDEWEB)

    Unterrainer, K.; Keay, B.J.; Wanke, M.C. [Univ. of California, Santa Barbara, CA (United States)] [and others

    1995-12-31

    We have observed resonant changes in the current-voltage characteristics of miniband semiconductor superlattices when the Bloch frequency is resonant with a terahertz field and its harmonics: the inverse Bloch oscillator effect. The resonant feature consists of a peak in the current which grows with increasing laser intensity accompanied by a decrease of the current at the low bias side. The peak position moves linearly with the laser frequency. When the intensity is increased further the first peak starts to decrease and a second peak at about twice the voltage of the first peak is observed due to a two photon resonance. At the highest intensities we observe up to a four photon resonance. A superlattice is expected to show negative differential conductance due to the strong nonparabolicity of the miniband. In this situation the carriers should undergo Bloch oscillations with a frequency {omega}{sub B} = eEd/h. Transient Bloch oscillations of photo excited carriers have been observed in time resolved Thz emission measurements. However, the possibility of Thz generation form a DC voltage biased superlattice is still under discussion. We have approached this problem by exploring the inverse Bloch oscillator effect in a superlattice excited by the Thz radiation form the UCSB FEL. The superlattice consists of 40 periods of 80{angstrom} GaAs wells and 20{angstrom} Al{sub 0.3}Ga{sub 0.7}As barriers. To couple the electric field of the Terahertz radiation parallel to the growth direction a coplanar bowtie antenna has been employed. Our results show clearly that the external radiation couples to Bloch oscillations in contrary to theoretical suggestions that Thz radiation would not couple to a uniform Wannier Stark ladder. We conclude that this result is intimately related to dissipation and line broadening of the otherwise identical states in the ladder: absorption appears above the Wannier Stark splitting ({omega}{sub B}<{omega}) and gain below ({omega}{sub B}>{omega}).

  9. Bloch's Theorem in the Context of Quaternion Analysis

    CERN Document Server

    Gürlebeck, K

    2012-01-01

    The classical theorem of Bloch (1924) asserts that if $f$ is a holomorphic function on a region that contains the closed unit disk $|z|\\leq 1$ such that $f(0) = 0$ and $|f'(0)| = 1$, then the image domain contains discs of radius $3/2-\\sqrt{2} > 1/12$. The optimal value is known as Bloch's constant and 1/12 is not the best possible. In this paper we give a direct generalization of Bloch's theorem to the three-dimensional Euclidean space in the framework of quaternion analysis. We compute explicitly a lower bound for the Bloch constant.

  10. Bloch oscillations in the presence of plasmons and phonons

    Science.gov (United States)

    Ghosh; Jonsson; Wilkins

    2000-07-31

    The coupling between Bloch oscillating electrons and longitudinal optical phonons in a superlattice leads to resonant phonon excitation but no gap in the Bloch-phonon spectrum. In addition, we predict a sharp transition from plasma to Bloch oscillations at nu(B) = 2nu(P). From a microscopic description with phenomenological dampings, we numerically map out the behavior of coupled Bloch-plasmon-phonon modes for a wide range of parameters, and mimic experimental conditions. Our results are in good agreement with recent experiments by Dekorsy et al. [Phys. Rev. Lett. 85, 1080 (2000)].

  11. Simulação de sinais de RMN através das equações de Bloch

    Directory of Open Access Journals (Sweden)

    Tiago Bueno Moraes

    2014-01-01

    Full Text Available The aim of this paper was to present a simple and fast way of simulating Nuclear Magnetic Resonance signals using the Bloch equations. These phenomenological equations describe the classical behavior of macroscopic magnetization and are easily simulated using rotation matrices. Many NMR pulse sequences can be simulated with this formalism, allowing a quantitative description of the influence of many experimental parameters. Finally, the paper presents simulations of conventional sequences such as Single Pulse, Inversion Recovery, Spin Echo and CPMG.

  12. The Bloch wave operator: generalizations and applications: Part I. The time-independent case

    CERN Document Server

    Killingbeck, J P

    2003-01-01

    This is part 1 of a two-part review on wave operator theory and methods. The basic theory of the time-independent wave operator is presented in terms of partitioned matrix theory for the benefit of general readers, with a discussion of the links between the matrix and projection operator approaches. The matrix approach is shown to lead to simple derivations of the wave operators and effective Hamiltonians of Loewdin, Bloch, Des Cloizeaux and Kato as well as to some associated variational forms. The principal approach used throughout stresses the solution of the nonlinear equation for the reduced wave operator, leading to the construction of the effective Hamiltonians of Bloch and of Des Cloizeaux. Several mathematical techniques which are useful in implementing this approach are explained, some of them being relatively little known in the area of wave operator calculations. The theoretical discussion is accompanied by several specimen numerical calculations which apply the described techniques to a selection ...

  13. Ernst Bloch:repensar la utopia

    Directory of Open Access Journals (Sweden)

    Enric Gil

    2003-07-01

    Full Text Available Aquest article, fruit del treball final de carrera de l'autor per a obtenir la llicenciatura en Humanitats de la UOC, presenta la figura i el pensament d'Ernst Bloch. Considerat el filòsof de la utopia, Bloch aborda aquest tema en totes les seves obres, d'una manera o d'una altra; a més, en la seva trajectòria intel·lectual hi ha una obsessió recurrent pels somnis d'una vida millor en les seves diferents perspectives. Pensador de primera línia, sovint ha estat oblidat i malentès, pel fet de ser considerat un irracionalista que convertia el marxisme en una religió o un marxista heterodox que s'allunyava del materialisme dialèctic per les seves reflexions sobre l'escatologia. La crítica postmodernista dels grans relats i el fracàs dels règims comunistes de l'Est provocaren l'abandó del marxisme i, per extensió, dels seus autors més rellevants.L'article comença amb una exposició general i sintètica dels conceptes de Bloch que apareixen a "El Principi Esperança", comprova el lligam amb la qüestió central de la utopia i desemboca en una reflexió sobre dues utopies del nostre temps que, tot i divergir dels continguts blochians, es troben en diàleg amb l'estructura general dels somnis somiats despert.

  14. Algorithm for generating goldstone and Bloch--Brandow diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Kaldor, U.

    1976-04-01

    An algorithm for the automatic generation of Goldstone and Bloch--Brandow diagrams, needed for diagrammatic perturbation expansions, is described (the Bloch--Brandow diagrams are required for degenerate perturbations). Diagrams are produced in sets, each set consisting of members related by exchanges about interaction lines. Only distinct connected diagrams are generated. Applications are described. 5 figures, 1 table.

  15. Improved Separability Criteria Based on Bloch Representation of Density Matrices.

    Science.gov (United States)

    Shen, Shu-Qian; Yu, Juan; Li, Ming; Fei, Shao-Ming

    2016-01-01

    The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. Theoretical analysis and some examples show that the proposed criteria can be more efficient than the previous related criteria. PMID:27350031

  16. Bloch spaces on bounded symmetric domains in complex Banach spaces

    Institute of Scientific and Technical Information of China (English)

    DENG; Fangwen

    2006-01-01

    We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.

  17. Synchronization of Bloch oscillations by a ring cavity.

    Science.gov (United States)

    Samoylova, M; Piovella, N; Robb, G R M; Bachelard, R; Courteille, Ph W

    2015-06-01

    We consider Bloch oscillations of ultracold atoms stored in a one-dimensional vertical optical lattice and simultaneously interacting with a unidirectionally pumped optical ring cavity whose vertical arm is collinear with the optical lattice. We find that the feedback provided by the cavity field on the atomic motion synchronizes Bloch oscillations via a mode-locking mechanism, steering the atoms to the lowest Bloch band. It also stabilizes Bloch oscillations against noise, and even suppresses dephasing due to atom-atom interactions. Furthermore, it generates periodic bursts of light emitted into the counter-propagating cavity mode, providing a non-destructive monitor of the atomic dynamics. All these features may be crucial for future improvements of the design of atomic gravimeters based on recording Bloch oscillations.

  18. Experimental observation of N00N state Bloch oscillations.

    Science.gov (United States)

    Lebugle, Maxime; Gräfe, Markus; Heilmann, René; Perez-Leija, Armando; Nolte, Stefan; Szameit, Alexander

    2015-09-22

    Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation.

  19. Bloch-Like Oscillations in Finite Quantum Structures

    DEFF Research Database (Denmark)

    Duggen, Lars; Willatzen, Morten; Lassen, Benny;

    Inspired by several attempts to generate Bloch-like oscillations in different fields of physics [1,2], we examine a multitude of oscillator systems and interactions that lead to Bloch oscillations in finite quantum structures. A general requirement is the existence of a common period in the time...... of individual quantum wells and changing the coupling strength as a function of position. It is, furthermore, demonstrated that the application of a magnetic field to a structure of quantum wells may lead to the observation of Bloch oscillations (similar to Bloch oscillations stemming from the Stark effect......) and derive rather general mathematical relations between quantum systems that allow the existence of Bloch oscillations. References: [1]: G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, and R. Osellame, Nature Communications 4, 1555 (2013) [2]: H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez...

  20. Bloch inductance in small-capacitance Josephson junctions.

    Science.gov (United States)

    Zorin, A B

    2006-04-28

    We show that the electrical impedance of a small-capacitance Josephson junction also includes, in addition to the capacitive term -i/(omega)CB, an inductive term i(omega)LB. Similar to the known Bloch capacitance CB(q), the Bloch inductance LB(q) also depends periodically on the quasicharge, q, and its maximum value achieved at q=e(mod 2e) always exceeds the value of the Josephson inductance of this junction LJ(phi) at fixed phi=0. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described.

  1. Bloch-mode analysis for effective parameters restoration

    DEFF Research Database (Denmark)

    Lavrinenko, Andrei; Andryieuski, Andrei; Ha, Sangwoo;

    2012-01-01

    We utilize the Bloch-mode analysis of periodic composite structures to introduce an approach for retrieving effective parameters of homogenized metamaterials. In the case of single-mode propagation we can restore a complex effective refractive index with a high accuracy. By further employing...... surface or volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes we are able to determine the Bloch and wave impedances, leading to wave and material effective parameters, respectively. The approach is demonstrated on several examples. We focus our discussion...

  2. Bloch oscillations in chirped layered structures with metamaterials.

    Science.gov (United States)

    Davoyan, Arthur R; Shadrivov, Ilya V; Sukhorukov, Andrey A; Kivshar, Yuri S

    2008-03-01

    We analyze the Bloch oscillations of electromagnetic waves in chirped layered structures with alternating layers of negative-index metamaterial and conventional dielectric under the condition of the zero average refractive index. We consider the case when the chirp is introduced by varying the thickness of the layers linearly across the structure. We demonstrate that such structures can support three different types of the Bloch oscillations for electromagnetic waves associated with either propagating or evanescent guided modes. In particular, we predict a novel type of the Bloch oscillations associated with coupling between surface waves excited at the interfaces separating the layers of negative-index metamaterial and the layers of the conventional dielectric.

  3. Bloch oscillations of THz acoustic phonons in coupled nanocavity structures.

    Science.gov (United States)

    Lanzillotti-Kimura, N D; Fainstein, A; Perrin, B; Jusserand, B; Mauguin, O; Largeau, L; Lemaître, A

    2010-05-14

    Nanophononic Bloch oscillations and Wannier-Stark ladders have been recently predicted to exist in specifically tailored structures formed by coupled nanocavities. Using pump-probe coherent phonon generation techniques we demonstrate that Bloch oscillations of terahertz acoustic phonons can be directly generated and probed in these complex nanostructures. In addition, by Fourier transforming the time traces we had access to the proper eigenmodes in the frequency domain, thus evidencing the related Wannier-Stark ladder. The observed Bloch oscillation dynamics are compared with simulations based on a model description of the coherent phonon generation and photoelastic detection processes.

  4. Bloch oscillations in a one-dimensional spinor gas.

    Science.gov (United States)

    Gangardt, D M; Kamenev, A

    2009-02-20

    A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of the particle's position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as an SU(2) symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations.

  5. Bloch state tomography using Wilson lines.

    Science.gov (United States)

    Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; Bloch, Immanuel; Schneider, Ulrich

    2016-05-27

    Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z₂ numbers. PMID:27230376

  6. Bloch state tomography using Wilson lines

    Science.gov (United States)

    Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; Bloch, Immanuel; Schneider, Ulrich

    2016-05-01

    Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z2 numbers.

  7. Large momentum beam splitter using Bloch oscillations.

    Science.gov (United States)

    Cladé, Pierre; Guellati-Khélifa, Saïda; Nez, François; Biraben, François

    2009-06-19

    The sensitivity of an inertial sensor based on an atomic interferometer is proportional to the velocity separation of atoms in the two arms of the interferometer. In this Letter we describe how Bloch oscillations can be used to increase this separation and to create a large momentum transfer (LMT) beam splitter. We experimentally demonstrate a separation of 10 recoil velocities. Light shifts during the acceleration introduce phase fluctuations which can reduce the fringes contrast. We precisely calculate this effect and demonstrate that it can be significantly reduced by using a suitable combination of LMT pulses. We finally show that this method seems to be very promising to realize a LMT beam splitter with several tens of recoils and a very good efficiency.

  8. Bloch vector, disclination and exotic quantum holonomy

    Energy Technology Data Exchange (ETDEWEB)

    Tanaka, Atushi, E-mail: tanaka-atushi@tmu.ac.jp [Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397 (Japan); Cheon, Taksu [Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502 (Japan)

    2015-09-04

    A topological formulation of the eigenspace anholonomy, where eigenspaces are interchanged by adiabatic cycles, is introduced. The anholonomy in two-level systems is identified with a disclination of the director (headless vector) of a Bloch vector, which characterizes eigenprojectors. The covering map structure behind the exotic quantum holonomy and the role of the homotopy classification of adiabatic cycles are elucidated. The extensions of this formulation to nonadiabatic cycles and N-level systems are outlined. - Highlights: • A topological formulation of the eigenspace anholonomy is proposed. • The covering map structure behind the anholonomy is identified. • The role of homotopy classification of adiabatic cycles is explained. • The anholonomy in two-level systems is associated with disclinations. • The present formulation offers an extension to nonadiabatic cycles.

  9. Long-living BLOCH oscillations of matter waves in periodic potentials.

    Science.gov (United States)

    Salerno, M; Konotop, V V; Bludov, Yu V

    2008-07-18

    The dynamics of matter waves in linear and nonlinear optical lattices subject to a spatially uniform linear force is studied both analytically and numerically. It is shown that by properly designing the spatial dependence of the scattering length it is possible to induce long-living Bloch oscillations of gap-soliton matter waves in optical lattices. This occurs when the effective nonlinearity and the effective mass of the soliton have opposite signs for all values of the crystal momentum in the Brillouin zone. The results apply to all systems modeled by the periodic nonlinear Schrödinger equation, including propagation of light in photonic and photorefractive crystals with tilted band structures.

  10. Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

    OpenAIRE

    Hatsugai, Y.; Kohmoto, M.; Wu, Y.-S.

    1995-01-01

    The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on the basis of above observation. The semi-classical case with the flux per plaquette $\\phi=1/Q$ is ...

  11. Estimates on Bloch constants for planar harmonic mappings

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan.

  12. Coupled bloch-phonon oscillations in semiconductor superlattices

    Science.gov (United States)

    Dekorsy; Bartels; Kurz; Kohler; Hey; Ploog

    2000-07-31

    We investigate coherent Bloch oscillations in GaAs/AlxGa1-xAs superlattices with electronic miniband widths larger than the optical phonon energy. In these superlattices the Bloch frequency can be tuned into resonance with the optical phonon. Close to resonance a direct coupling of Bloch oscillations to LO phonons is observed which gives rise to the coherent excitation of LO phonons. The density necessary for driving coherent LO phonons via Bloch oscillations is about 2 orders of magnitude smaller than the density necessary to drive coherent LO phonons in bulk GaAs. The experimental observations are confirmed by the theoretical description of this phenomenon [A.W. Ghosh et al., Phys. Rev. Lett. 85, 1084 (2000)].

  13. Calculation of the relativistic Bloch correction to stopping power

    Science.gov (United States)

    Ahlen, S. P.

    1982-01-01

    Bloch's technique of joining the nonrelativistic Bethe and Bohr stopping-power expressions by taking into account wave-packet effects for close collisions is extended to the relativistic case. It is found that Bloch's nonrelativistic correction term must be modified and that charge asymmetric terms appear. Excellent agreement is observed by comparing the results of these calculations to recent data on the stopping power of relativistic heavy ions.

  14. Bloch spin waves and emergent structure in protein folding with HIV envelope glycoprotein as an example

    Science.gov (United States)

    Dai, Jin; Niemi, Antti J.; He, Jianfeng; Sieradzan, Adam; Ilieva, Nevena

    2016-03-01

    We inquire how structure emerges during the process of protein folding. For this we scrutinize collective many-atom motions during all-atom molecular dynamics simulations. We introduce, develop, and employ various topological techniques, in combination with analytic tools that we deduce from the concept of integrable models and structure of discrete nonlinear Schrödinger equation. The example we consider is an α -helical subunit of the HIV envelope glycoprotein gp41. The helical structure is stable when the subunit is part of the biological oligomer. But in isolation, the helix becomes unstable, and the monomer starts deforming. We follow the process computationally. We interpret the evolving structure both in terms of a backbone based Heisenberg spin chain and in terms of a side chain based XY spin chain. We find that in both cases the formation of protein supersecondary structure is akin the formation of a topological Bloch domain wall along a spin chain. During the process we identify three individual Bloch walls and we show that each of them can be modelled with a precision of tenths to several angstroms in terms of a soliton solution to a discrete nonlinear Schrödinger equation.

  15. Bloch Oscillations of Einstein-Podolsky-Rosen States

    CERN Document Server

    Lebugle, Maxime; Heilmann, René; Perez-Leija, Armando; Nolte, Stefan; Szameit, Alexander

    2015-01-01

    Bloch Oscillations (BOs) of quantum particles manifest themselves as periodic spreading and re-localization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit BOs are deeply rooted into the very foundations of quantum mechanics, all experimental observations of this phenomenon so far have only contemplated dynamics of one or two particles initially prepared in separable local states, which is well described by classical wave physics. Evidently, a more general description of genuinely quantum BOs will be achieved upon excitation of a Bloch-oscillator lattice system by nonlocal states, that is, containing correlations in contradiction with local realism. Here we report the first experimental observation of BOs of two-particle Einstein-Podolsky-Rosen states (EPR), whose associated N-particle wave functions are nonlocal by nature. The time evolution of two-photon EPR states in Bloch-oscillators, whether symmetric, antisymmetric or partially symmetric, r...

  16. Landau-Zener Bloch Oscillations with Perturbed Flat Bands.

    Science.gov (United States)

    Khomeriki, Ramaz; Flach, Sergej

    2016-06-17

    Sinusoidal Bloch oscillations appear in band structures exposed to external fields. Landau-Zener (LZ) tunneling between different bands is usually a counteracting effect limiting Bloch oscillations. Here we consider a flat band network with two dispersive and one flat band, e.g., for ultracold atoms and optical waveguide networks. Using external synthetic gauge and gravitational fields we obtain a perturbed yet gapless band structure with almost flat parts. The resulting Bloch oscillations consist of two parts-a fast scan through the nonflat part of the dispersion structure, and an almost complete halt for substantial time when the atomic or photonic wave packet is trapped in the original flat band part of the unperturbed spectrum, made possible due to LZ tunneling.

  17. Mechanical Properties of Laminate Materials: From Surface Waves to Bloch Oscillations

    DEFF Research Database (Denmark)

    Liang, Z.; Willatzen, Morten; Christensen, Johan

    2015-01-01

    for designing Bloch oscillations in classical plate structures and show how mechanical Bloch oscillations can be generated in arrays of solid plates when the modal wavelength is gradually reduced. The design recipe describes how Bloch oscillations in classical structures of arbitrary dimensions can be generated...

  18. COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

    Institute of Scientific and Technical Information of China (English)

    Zhou Zehua; Zhu Min; Shi Jihuai

    2005-01-01

    Let Un be the unit polydisc of Cn and φ = (φ1,…,φn) a holomorphic self map of Un. This paper shows that the composition operator Cφ induced by φ is bounded on the little Bloch space β0*(Un) if and only if φ∈β0*(Un) for every l=1,2,…,n, and also gives a sufficient and necessary condition for the composition operator Cφ to be compact on the little Bloch spaceβ0* (Un).

  19. Surface optical Bloch oscillations in semi-infinite waveguide arrays.

    Science.gov (United States)

    Chremmos, I D; Efremidis, N K

    2012-06-01

    We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a "matched" termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries.

  20. Control of interaction-induced dephasing of Bloch oscillations.

    Science.gov (United States)

    Gustavsson, M; Haller, E; Mark, M J; Danzl, J G; Rojas-Kopeinig, G; Nägerl, H-C

    2008-02-29

    We report on the control of interaction-induced dephasing of Bloch oscillations for an atomic Bose-Einstein condensate in an optical lattice. We quantify the dephasing in terms of the width of the quasimomentum distribution and measure its dependence on time for different interaction strengths which we control by means of a Feshbach resonance. For minimal interaction, the dephasing time is increased from a few to more than 20 thousand Bloch oscillation periods, allowing us to realize a BEC-based atom interferometer in the noninteracting limit.

  1. Optical BLOCH oscillations and Zener tunneling with nonclassical light.

    Science.gov (United States)

    Longhi, Stefano

    2008-11-01

    A quantum theory of optical Bloch oscillations and Zener tunneling (ZT) in arrays of coupled waveguides is theoretically presented, and the particlelike behavior of photons undergoing ZT is highlighted. In singly-periodic arrays excited by a photon-number-state input beam, each photon behaves as a classical particle which independently undergoes a coin-toss ZT event with a probability described by classical Zener theory. In binary arrays, excitation with two tilted beams enables us to observe the Hong-Ou-Mandel interference for two photons undergoing Bloch-Zener oscillations.

  2. Unidirectional optical Bloch oscillations in asymmetric waveguide arrays.

    Science.gov (United States)

    Kumar, Pradeep; Levy, Miguel

    2011-11-15

    We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. A model system consisting of an array of transversely magnetized asymmetric Si/SiO2 waveguides with a magneto-optic cover layer is presented. Large index contrasts between film and cover are critical for practical realizations.

  3. Superfluidity versus Bloch oscillations in confined atomic gases.

    Science.gov (United States)

    Büchler, H P; Geshkenbein, V B; Blatter, G

    2001-09-01

    We study the superfluid properties of (quasi) one-dimensional bosonic atom gases/liquids in traps with finite geometries in the presence of strong quantum fluctuations. Driving the condensate with a moving defect we find the nucleation rate for phase slips using instanton techniques. While phase slips are quenched in a ring resulting in a superfluid response, they proliferate in a tube geometry where we find Bloch oscillations in the chemical potential. These Bloch oscillations describe the individual tunneling of atoms through the defect and thus are a consequence of particle quantization.

  4. Generation of 1D interference patterns of Bloch surface waves

    Science.gov (United States)

    Kadomina, E. A.; Bezus, E. A.; Doskolovich, L. L.

    2016-09-01

    Interference patterns of Bloch surface waves with a period that is significantly less than the wavelength of incident radiation are formed using dielectric diffraction gratings located on the surface of photonic crystal. The simulation based on electromagnetic diffraction theory is used to demonstrate the possibility of high-quality interference patterns due to resonant enhancement of higher evanescent diffraction orders related to the excitation of the Bloch surface waves. The contrast of the interference patterns is close to unity, and the period is less than the period of the diffraction structure by an order of magnitude.

  5. Compact composition operators on the Bloch space in polydiscs

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Let Un be the unit polydisc of Cn and =(1,…n) a holomorphicself-map of Un. As the main result of the paper, it shows that the composition operator Cφ is compact on the Bloch space β(Un) if and only if for every ε>0, there exists a δ>0, such thatwhenever dist((z),Un)<δ.

  6. Quantum Properties of Bloch Point as Nanosized Soliton in Ferromagnetics

    Directory of Open Access Journals (Sweden)

    M.Yu. Barabash

    2014-11-01

    Full Text Available It is established that magnetic soliton – Bloch point – has quantum properties which are manifested in the effects of tunneling and above-barrier reflection in a subhelium temperature range. The conditions of the given phenomena are determined.

  7. Topological optical Bloch oscillations in a deformed slab waveguide.

    Science.gov (United States)

    Longhi, Stefano

    2007-09-15

    Spatial Bloch oscillations of light waves of purely topological origin are theoretically shown to exist in weakly deformed slab waveguides. As the optical rays trapped in the deformed waveguide can roll freely, wave diffraction is strongly affected by the topology of the deformed surface, which can be tailored to simulate the effect of a tilted periodic refractive index.

  8. Interaction-induced decoherence of atomic BLOCH oscillations.

    Science.gov (United States)

    Buchleitner, Andreas; Kolovsky, Andrey R

    2003-12-19

    We show that the energy spectrum of the Bose-Hubbard model amended by a static field exhibits Wigner-Dyson level statistics. In itself a characteristic signature of quantum chaos, this induces the irreversible decay of Bloch oscillations of cold, interacting atoms loaded into an optical lattice, and provides a Hamiltonian model for interaction-induced decoherence.

  9. N-qubit states as points on the Bloch sphere

    Energy Technology Data Exchange (ETDEWEB)

    Maekelae, H; Messina, A, E-mail: harmak@gmail.co [Dipartimento di Scienze Fisiche ed Astronomiche, Universita di Palermo, via Archirafi 36, 90123 Palermo (Italy)

    2010-09-01

    We show how the Majorana representation can be used to express the pure states of an N-qubit system as points on the Bloch sphere. We compare this geometrical representation of N-qubit states with an alternative one, proposed recently by the present authors.

  10. Generalized Bloch spheres for m-qubit states

    Energy Technology Data Exchange (ETDEWEB)

    Dietz, Klaus [Dipartimento di Scienze Fisiche ed Astronomiche dell' Universita di Palermo, via Archirafi 36, 90123 Palermo (Italy); Sektion Physik, LMU, Muenchen, Theresienstrasse 37, 80333 Munich (Germany)

    2006-02-10

    m-qubit states are embedded in Cl{sub 2m} Clifford algebras. Their probability spectrum then depends on O(2m)- or O(2m + 1)-invariants, respectively. Parameter domains for O(2m(+1))-vector and -tensor configurations, generalizing the notion of a Bloch sphere, are derived.

  11. Lines crossing a tetrahedron and the Bloch group

    CERN Document Server

    Hutchinson, Kevin

    2011-01-01

    We consider a simple modification of the Chow group CH^2(Spec(k),3) using only linear subvarieties in affine spaces and show that it maps surjectively to the Bloch group B(k) for any infinite field k. We also describe the kernel of this map.

  12. A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential

    Science.gov (United States)

    Wu, Zhizhang; Huang, Zhongyi

    2016-07-01

    In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness results from complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalized polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.

  13. Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers

    CERN Document Server

    Schnitzer, Ory

    2016-01-01

    We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions, the scatterers are effectively replaced by asymptotic point constraints. The resulting coarse-grained Bloch-wave dispersion problem is solved by a generalised Fourier series, whose singular asymptotics in the vicinities of scatterers yield the dispersion relation governing modes that are strongly perturbed from plane-wave solutions existing in the absence of the scatterers; there are also empty-lattice waves that are only weakly perturbed. Characterising the latter is useful in interpreting and potentially designing the dispersion diagrams of such lattices. The method presented, that simplifies and expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could be applied in the future to study more sophisticated designs entailing resonant subwavelength elements di...

  14. Anderson wall and Bloch oscillations in molecular rotation

    CERN Document Server

    Floß, Johannes

    2014-01-01

    We describe a universal behavior of linear molecules excited by a periodic train of short laser pulses under quantum resonance conditions. In a rigid rotor the resonance causes an unlimited ballistic growth of the angular momentum. We show that the centrifugal distortion of rotating molecules eventually halts the growth, by causing Anderson localization beyond a critical value of the angular momentum -- the Anderson wall. Its position solely depends on the molecular rotational constants and lies in the range of a few tens of hbar. Below the wall, rotational excitation oscillates with the number of pulses due to a mechanism similar to Bloch oscillations in crystalline solids. We suggest optical experiments capable of observing the rotational Anderson wall and Bloch oscillations at ambient conditions with the help of existing laser technology.

  15. Anderson wall and BLOCH oscillations in molecular rotation.

    Science.gov (United States)

    Floß, Johannes; Averbukh, Ilya Sh

    2014-07-25

    We describe a universal behavior of linear molecules excited by a periodic train of short laser pulses under quantum resonance conditions. In a rigid rotor, the resonance causes an unlimited ballistic growth of the angular momentum. We show that the centrifugal distortion of rotating molecules eventually halts the growth, by causing Anderson localization beyond a critical value of the angular momentum--the Anderson wall. Its position solely depends on the molecular rotational constants and lies in the range of a few tens of ℏ. Below the wall, rotational excitation oscillates with the number of pulses due to a mechanism similar to Bloch oscillations in crystalline solids. We suggest optical experiments capable of observing the rotational Anderson wall and Bloch oscillations at near-ambient conditions with the help of existing laser technology.

  16. Geometry of entangled states, Bloch spheres and Hopf fibrations

    Energy Technology Data Exchange (ETDEWEB)

    Mosseri, Remy [Groupe de Physique des Solides, CNRS UMR 7588, Universites Pierre et Marie Curie et Denis Diderot, Paris (France)]. E-mail: mosseri@gps.jussieu.fr; Dandoloff, Rossen [Laboratoire de Physique Theorique et Modelisation, CNRS-ESA 8089, Universite de Cergy-Pontoise, Cergy-Pontoise (France)]. E-mail: rossen.dandoloff@ptm.u-cergy.fr

    2001-11-30

    We discuss a generalization of the standard Bloch sphere representation for a single qubit to two qubits, in the framework of Hopf fibrations of high-dimensional spheres by lower dimensional spheres. The single-qubit Hilbert space is the three-dimensional sphere S{sup 3}. The S{sup 2} base space of a suitably oriented S{sup 3} Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the overall qubit phase degree of freedom. For the two-qubits case, the Hilbert space is a seven-dimensional sphere S{sup 7}, which also allows for a Hopf fibration, with S{sup 3} fibres and a S{sup 4} base. The most striking result is that suitably oriented S{sup 7} Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussed. (author)

  17. Surface Bloch waves mediated heat transfer between two photonic crystals

    OpenAIRE

    Ben-Abdallah, Philippe; Joulain, Karl; Pryamikov, Andrey

    2010-01-01

    submitted to Applied Physics Letters We theoretically investigate the non-radiative heat transfer between two photonic crystals separated by a small gap in non-equilibrium thermal situation. We predict that the surface Bloch states coupling supported by these media can make heat exchanges larger than those measured at the same separation distance between two massive homogeneous materials made with the elementary components of photonic crystals. These results could find broad applications i...

  18. Experimental reconstruction of Wilson lines in Bloch bands

    OpenAIRE

    Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; Bloch, Immanuel; Schneider, Ulrich

    2015-01-01

    Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multi-band systems. By realizing strong-force dynamics in Bloch bands that are described by Wilson lines, we observe an ev...

  19. Nonreciprocal Bloch oscillations in magneto-optic waveguide arrays.

    Science.gov (United States)

    Levy, Miguel; Kumar, Pradeep

    2010-09-15

    We show that nonreciprocal optical Bloch-like oscillations can emerge in transversely magnetized waveguide arrays in the presence of an effective index step between the waveguides. Normal modes of the system are shown to acquire different wavenumbers in opposite propagation directions. Significant differences in phase coherence and decoherence between these normal modes are presented and discussed. Nonreciprocity is established by imposing unequal vertical refractive index gradients at the substrate/core and core/cover interfaces in the presence of transverse magnetization.

  20. Acoustic Bloch oscillations in a two-dimensional phononic crystal.

    Science.gov (United States)

    He, Zhaojian; Peng, Shasha; Cai, Feiyan; Ke, Manzhu; Liu, Zhengyou

    2007-11-01

    We report the observation of acoustic Bloch oscillations at megahertz frequency in a two-dimensional phononic crystal. By creating periodically arrayed cavities with a decreasing gradient in width along one direction in the phononic crystal, acoustic Wannier-Stark ladders are created in the frequency domain. The oscillatory motion of an incident Gaussian pulse inside the sample is demonstrated by both simulation and experiment.

  1. Super Bloch Oscillation in a PT symmetric system

    CERN Document Server

    Turker, Z

    2016-01-01

    Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.

  2. Bloch oscillations of Bose-Einstein condensates: breakdown and revival.

    Science.gov (United States)

    Witthaut, D; Werder, M; Mossmann, S; Korsch, H J

    2005-03-01

    We investigate the dynamics of Bose-Einstein condensates in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable model constructed by an expansion in Wannier-Stark resonance states. We also briefly discuss the pulsed output of such systems for stronger static fields.

  3. Damping of Bloch oscillations in the Hubbard model.

    Science.gov (United States)

    Eckstein, Martin; Werner, Philipp

    2011-10-28

    Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a critical value, below which the system exhibits an ac-type response with Bloch oscillations. The transition from ac to dc response is defined in terms of the universal long-time behavior of the system, which does not depend on the initial condition.

  4. On history and salvation in Emmanuel Levinas and Ernst Bloch

    Directory of Open Access Journals (Sweden)

    Salomon J. Terreblanche

    2008-01-01

    Full Text Available This article explores the tension between history and salvation as theme in contemporary social and humanist philosophy. Special reference is made to Emmanuel Levinas’ work in order to delineate the scope of the questions involved, and to critically elucidate the position on history, death and hope in new-Marxist philosopher Ernst Bloch. The article then illuminates Levinas’ phenomenological account of fecundity, parenthood, patience and institutional justice as hopeful moments that are contained in his philosophy on history

  5. Bloch-mode analysis for retrieving effective parameters of metamaterials

    DEFF Research Database (Denmark)

    Andryieuski, Andrei; Ha, Sangwoo; Sukhorukov, Andrey A.;

    2012-01-01

    We introduce an approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasiperiodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective refractive index can be assigned to the structure, being restored...... that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials....

  6. Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays

    OpenAIRE

    Beneke, M.; Braun, Vladimir M.; Zakharov, V. I.

    1994-01-01

    We investigate the one-loop radiative corrections to the semileptonic decay of a charged particle at finite gauge boson mass. Extending the Bloch-Nordsieck cancellation of infrared logarithms, the subsequent non-analytic terms are also found to vanish after eliminating the pole mass in favor of a mass defined at short distances. This observation justifies the operator product expansion for inclusive decays of heavy mesons and implies that infrared effects associated with the summation of the ...

  7. Orbital magnetism of Bloch electrons I. General formula

    International Nuclear Information System (INIS)

    We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time. (author)

  8. The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications

    OpenAIRE

    Zhou Zehua; Liu Yan

    2006-01-01

    Let be the unit polydisc of and a holomorphic self-map of . , and denote the -Bloch space, little -Bloch space, and little star -Bloch space in the unit polydisc , respectively, where . This paper gives the estimates of the essential norms of bounded composition operators induced by between ( or ) and ( or ). As their applications, some necessary and sufficient conditions for the (bounded) composition operators to be compact from ( or ) into ( or ) are obtained.

  9. Properties of Floquet-Bloch space harmonics in 1D periodic magneto-dielectric structures

    DEFF Research Database (Denmark)

    Breinbjerg, O.

    2012-01-01

    Recent years have witnessed a significant research interest in Floquet-Bloch analysis for determining the homogenized permittivity and permeability of metamaterials consisting of periodic structures. This work investigates fundamental properties of the Floquet-Bloch space harmonics in a 1-dimensi......-dimensional magneto-dielectric lossless structure supporting a transverse-electric-magnetic Floquet-Bloch wave; in particular, the space harmonic permittivity and permeability, as well as the space harmonic Poynting vector....

  10. Excitation of Bloch-like surface waves in quasi-crystals and aperiodic dielectric multilayers.

    Science.gov (United States)

    Koju, Vijay; Robertson, William M

    2016-07-01

    The existence of Bloch surface waves in periodic dielectric multilayer structures with a surface defect is well known. Not yet recognized is that quasi-crystals and aperiodic dielectric multilayers can also support Bloch-like surface waves. In this work, we numerically show the excitation of Bloch-like surface waves in Fibonacci quasi-crystals and Thue-Morse aperiodic dielectric multilayers using the prism coupling method. We report improved surface electric field intensity and penetration depth of Bloch-like surface waves in the air side in such structures compared to their periodic counterparts. PMID:27367064

  11. Staying positive: going beyond Lindblad with perturbative master equations

    Science.gov (United States)

    Whitney, Robert S.

    2008-05-01

    The perturbative master equation (Bloch-Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima-Zwanzig or Schoeller-Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch-Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.

  12. From Bloch to random lasing in ZnO self-assembled nanostructures

    DEFF Research Database (Denmark)

    Garcia-Fernandez, Pedro David; Cefe, López

    2013-01-01

    In this paper, we present measurements on UV lasing in ZnO ordered and disordered nanostructures. Bloch lasing is achieved in the ordered structures by exploiting very low group-velocity Bloch modes in ZnO photonic crystals. In the second case, random lasing is observed in ZnO photonic glasses. W...

  13. A formula for the Bloch vector of some Lindblad quantum systems

    OpenAIRE

    Salgado, D; Sanchez-Gomez, J. L.

    2003-01-01

    Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.

  14. A formula for the Bloch vector of some Lindblad quantum systems

    International Nuclear Information System (INIS)

    Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators

  15. Nonreciprocal Bloch Oscillations in Magneto-Optic Waveguide Arrays

    CERN Document Server

    Levy, Miguel

    2010-01-01

    We show that nonreciprocal optical Bloch-like oscillations can emerge in transversely magnetized waveguide arrays in the presence of an effective index step between the waveguides. Normal modes of the system are shown to acquire different wavenumbers in opposite propagation directions. Significant differences in phase coherence and decoherence between these normal modes are presented and discussed. Non-reciprocity is established by imposing unequal vertical refractive index gradients at the substrate/core, and core/cover interfaces in the presence of transverse magnetization.

  16. Heisenberg-Weyl Observables: Bloch vectors in phase space

    Science.gov (United States)

    Asadian, Ali; Erker, Paul; Huber, Marcus; Klöckl, Claude

    2016-07-01

    We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anticommuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first nontrivial example beyond the dichotomic case.

  17. Traffic restrictions on Routes Bloch, Maxwell and Bohr

    CERN Multimedia

    IT Department

    2008-01-01

    Excavation and pipework is being carried out in the framework of the transfer of the waste water treatment plant for the effluents from the surface treatment workshops from Building 254 to Building 676, currently under construction. This work may encroach onto Routes Bloch, Maxwell and Bohr and disrupt the flow of traffic. Users are requested to comply with the road signs that will be erected. The work is expected to last until the beginning of December 2008. Thank you for your understanding. TS/CE and TS/FM Groups Tel.7 4188 or 16 4314

  18. Tunable photonic Bloch oscillations in electrically modulated photonic crystals.

    Science.gov (United States)

    Wang, Gang; Huang, Ji Ping; Yu, Kin Wah

    2008-10-01

    We exploit theoretically the occurrence and tunability of photonic Bloch oscillations (PBOs) in one-dimensional photonic crystals (PCs) containing nonlinear composites. Because of the enhanced third-order nonlinearity (Kerr-type nonlinearity) of composites, photons undergo oscillations inside tilted photonic bands, which are achieved by the application of graded external-pump electric fields on such PCs, varying along the direction perpendicular to the surface of layers. The tunability of PBOs (including amplitude and period) is readily achieved by changing the field gradient. With an appropriate graded pump ac or dc electric field, terahertz PBOs can appear and cover a terahertz band in an electromagnetic spectrum.

  19. Localization without recurrence and pseudo-Bloch oscillations in optics.

    Science.gov (United States)

    Longhi, Stefano

    2015-10-15

    Dynamical localization, i.e., the absence of secular spreading of a quantum or classical wave packet, is usually associated with Hamiltonians by the pure point spectrum, i.e., with a normalizable and complete set of eigenstates. Such systems always show quasi-periodic dynamics (recurrence). Here, we show, rather counter-intuitively, that dynamical localization can be observed in Hamiltonians with an absolutely continuous spectrum, where recurrence effects are forbidden. An optical realization of such a Hamiltonian is proposed based on beam propagation in a self-imaging optical resonator with a phase grating. Localization without recurrence in this system is explained in terms of pseudo-Bloch optical oscillations.

  20. Plasmonic Bloch oscillations in cylindrical metal-dielectric waveguide arrays.

    Science.gov (United States)

    Shiu, Ruei-Cheng; Lan, Yung-Chiang; Chen, Chin-Min

    2010-12-01

    This study investigates plasmonic Bloch oscillations (PBOs) in cylindrical metal-dielectric waveguide arrays (MDWAs) by performing numerical simulations and theoretical analyses. Optical conformal mapping is used to transform cylindrical MDWAs into equivalent chirped structures with permittivity and permeability gradients across the waveguide arrays, which is caused by the curvature of the cylindrical waveguide. The PBOs are attributed to the transformed structure. The period of oscillation increases with the wavelength of the incident Gaussian beam. However, the amplitude of oscillation is almost independent of wavelength.

  1. Localization without recurrence and pseudo-Bloch oscillations in optics

    CERN Document Server

    Longhi, Stefano

    2015-01-01

    Dynamical localization, i.e. the absence of secular spreading of a quantum or classical wave packet, is usually associated to Hamiltonians with purely point spectrum, i.e. with a normalizable and complete set of eigenstates, which show quasi-periodic dynamics (recurrence). Here we show rather counter-intuitively that dynamical localization can be observed in Hamiltonians with absolutely continuous spectrum, where recurrence effects are forbidden. An optical realization of such an Hamiltonian is proposed based on beam propagation in a self-imaging optical resonator with a phase grating. Localization without recurrence in this system is explained in terms of pseudo-Bloch optical oscillations.

  2. Quasi-BLOCH oscillations in curved coupled optical waveguides.

    Science.gov (United States)

    Joushaghani, Arash; Iyer, Rajiv; Poon, Joyce K S; Aitchison, J Stewart; de Sterke, C Martijn; Wan, Jun; Dignam, Marc M

    2009-10-01

    We report the observation of quasi-Bloch oscillations, a recently proposed, new type of dynamic localization in the spatial evolution of light in a curved coupled optical waveguide array. By spatially resolving the optical intensity at various propagation distances, we show the delocalization and final relocalization of the beam in the waveguide array. Through comparisons with other structures, we show that this dynamic localization is robust beyond the nearest-neighbor tight-binding approximation and exhibits a wavelength dependence different from conventional dynamic localization.

  3. Photon BLOCH oscillations in porous silicon optical superlattices.

    Science.gov (United States)

    Agarwal, V; del Río, J A; Malpuech, G; Zamfirescu, M; Kavokin, A; Coquillat, D; Scalbert, D; Vladimirova, M; Gil, B

    2004-03-01

    We report the first observation of oscillations of the electromagnetic field in an optical superlattice based on porous silicon. These oscillations are an optical equivalent of well-known electronic Bloch oscillations in crystals. Elementary cells of our structure are composed by microcavities whose coupling gives rise to the extended collective modes forming optical minigaps and minibands. By varying thicknesses of the cavities along the structure axis, we have created an effective electric field for photons. A very high quality factor of the confined optical state of the Wannier-Stark ladder may allow lasing in porous silicon-based superlattices.

  4. Plasmonic Bloch oscillations in monolayer graphene sheet arrays.

    Science.gov (United States)

    Fan, Yang; Wang, Bing; Huang, He; Wang, Kai; Long, Hua; Lu, Peixiang

    2014-12-15

    We investigate the spatial plasmonic Bloch oscillations (BOs) in the monolayer graphene sheet arrays (MGSAs) as the surface plasmon polaritons (SPPs) between graphene in the arrays experience weak coupling. In order to realize BOs, linear gradient of the potential is introduced by changing the chemical potentials of individual graphene sheets or the interlayer space between graphene. Numerical simulations show that the complete plasmonic BOs can be observed in the former MGSAs. However, only harmonic oscillations occur in the latter of varying interlayer space. Theoretical analysis based on the coupled-mode theory agrees well with the numerical simulations.

  5. Truncated-Bloch-wave solitons in optical lattices

    CERN Document Server

    Wang, Jiandong; Alexander, Tristram J; Kivshar, Yuri S

    2009-01-01

    We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized states which differ by the number of intensity peaks. These families do not bifurcate from the band edge, and their power curves exhibit double branches. Linear stability analysis demonstrates that in deep lattice potentials the states corresponding to the lower branches are stable, whereas those corresponding to the upper branches are unstable, independently of the number of peaks.

  6. Landau levels from the Bethe Ansatz equations

    OpenAIRE

    Hoshi, K.; Hatsugai, Y.

    2000-01-01

    The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak-field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.

  7. Landau Levels from the Bethe Ansatz Equations

    OpenAIRE

    Hoshi, K.; Hatsugai, Y.

    1999-01-01

    The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.

  8. Shear Bloch waves and coupled phonon-polariton in periodic piezoelectric waveguides.

    Science.gov (United States)

    Piliposyan, D G; Ghazaryan, K B; Piliposian, G T

    2014-02-01

    Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-width waveguide are considered in the framework of the full system of Maxwell's electrodynamic equations. We investigate Bloch-Floquet waves under homogeneous or alternating boundary conditions for the elastic and electromagnetic fields along the guide walls. Zero frequency stop bands, trapped modes as well as some anomalous features due to piezoelectricity are identified. For mixed boundary conditions, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone. The dispersion equation has been investigated also for phonon-polariton band gaps. It is shown that for waveguides at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell but at optical frequencies polariton resonance occurs at wavelengths comparable with the period of the waveguide. PMID:24139302

  9. Local gravity measurement with the combination of atom interferometry and Bloch oscillations

    CERN Document Server

    Charrière, Renée; Zahzam, Nassim; Bidel, Yannick; Bresson, Alexandre

    2011-01-01

    We present a local measurement of gravity combining Bloch oscillations and atom interferometry. With a falling distance of 0.8 mm, we achieve a sensitivity of 2x10-7 g with an integration time of 300 s. No bias associated with the Bloch oscillations has been measured. A contrast decay with Bloch oscillations has been observed and attributed to the spatial quality of the laser beams. A simple experimental configuration has been adopted where a single retro-reflected laser beam is performing atoms launch, stimulated Raman transitions and Bloch oscillations. The combination of Bloch oscillations and atom interferometry can thus be realized with an apparatus no more complex than a standard atomic gravimeter.

  10. Bloch-Zener oscillations in a tunable optical honeycomb lattice

    Energy Technology Data Exchange (ETDEWEB)

    Uehlinger, Thomas; Greif, Daniel; Jotzu, Gregor; Esslinger, Tilman [Institute for Quantum Electronics, ETH Zurich, 8093 Zurich (Switzerland); Tarruell, Leticia [Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland and LP2N, Universite Bordeaux 1, IOGS, CNRS, 351 cours de la Liberation, 33405 Talence (France)

    2013-12-04

    Ultracold gases in optical lattices have proved to be a flexible tool to simulate many different phenomena of solid state physics [1, 2]. Recently, optical lattices with complex geometries have been realized [3, 4, 5, 6, 7], paving the way to simulating more realistic systems. The honeycomb structure has recently become accessible in an optical lattice composed of mutually perpendicular laser beams. This lattice structure exhibits topological features in its band structure – the Dirac points. At these points, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In optical lattices, Bloch oscillations [8] resolved both in time and in quasi-momentum space can be directly observed. We make use of such Bloch-Zener oscillations to probe the vanishing energy gap at the Dirac points as well as their position in the band structure. In small band gap regions, we observe Landau-Zener tunneling [7, 9] to the second band and the regions of maximum transfer can be identified with the position of the Dirac points.

  11. The Quantum Noise of Ferromagnetic π-Bloch Domain Walls

    Directory of Open Access Journals (Sweden)

    Peter R. Crompton

    2009-09-01

    Full Text Available We quantify the probability per unit Euclidean-time of reversing the magnetization of a π-Bloch vector, which describes the Ferromagnetic Domain Walls of a Ferromagnetic Nanowire at finite-temperatures. Our approach, based on Langer’s Theory, treats the double sine-Gordon model that defines the π-Bloch vectors via a procedure of nonperturbative renormalization, and uses importance sampling methods to minimise the free energy of the system and identify the saddlepoint solution corresponding to the reversal probability. We identify that whilst the general solution for the free energy minima cannot be expressed in closed form, we can obtain a closed expression for the saddlepoint by maximizing the entanglement entropy of the system as a polynomial ring. We use this approach to quantify the geometric and non-geometric contributions to the entanglement entropy of the Ferromagnetic Nanowire, defined between entangled Ferromagnetic Domain Walls, and evaluate the Euclidean-time dependence of the domain wall width and angular momentum transfer at the domain walls, which has been recently proposed as a mechanism for Quantum Memory Storage.

  12. Bloch-wave engineering of quantum dot-micropillars for cavity quantum electrodynamics experiments

    CERN Document Server

    Lermer, Matthias; Dunzer, Florian; Reitzenstein, Stephan; Höfling, Sven; Mørk, Jesper; Worschech, Lukas; Kamp, Martin; Forchel, Alfred

    2011-01-01

    We have employed Bloch-wave engineering to realize submicron diameter ultra-high quality factor GaAs/AlAs micropillars (MPs). The design features a tapered cavity in which the fundamental Bloch mode is subject to an adiabatic transition to match the Bragg mirror Bloch mode. The resulting reduced scattering loss leads to record-high visibility of the strong coupling in MPs with modest oscillator strength quantum dots. A quality factor of 13,600 and a Rabi splitting of 85 \\mueV with an estimated visibility v of 0.38 are observed for a small mode volume MP with a diameter dc of 850 nm.

  13. Acoustic analogue of electronic BLOCH oscillations and resonant Zener tunneling in ultrasonic superlattices.

    Science.gov (United States)

    Sanchis-Alepuz, Helios; Kosevich, Yuriy A; Sánchez-Dehesa, José

    2007-03-30

    We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.

  14. Bloch-wave engineering of quantum dot-micropillars for cavity quantum electrodynamics experiments

    DEFF Research Database (Denmark)

    Lermer, Matthias; Gregersen, Niels; Dunzer, Florian;

    2012-01-01

    We have employed Bloch-wave engineering to realize submicron diameter ultra-high quality factor GaAs/AlAs micropillars (MPs). The design features a tapered cavity in which the fundamental Bloch mode is subject to an adiabatic transition to match the Bragg mirror Bloch mode. The resulting reduced...... scattering loss leads to record-high visibility of the strong coupling in MPs with modest oscillator strength quantum dots. A quality factor of 13,600 and a Rabi splitting of 85 \\mueV with an estimated visibility v of 0.38 are observed for a small mode volume MP with a diameter dc of 850 nm....

  15. Inducing transport in a dissipation-free lattice with super Bloch oscillations.

    Science.gov (United States)

    Haller, Elmar; Hart, Russell; Mark, Manfred J; Danzl, Johann G; Reichsöllner, Lukas; Nägerl, Hanns-Christoph

    2010-05-21

    Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these "super" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice.

  16. Engineering of slow Bloch modes for optical trapping

    Energy Technology Data Exchange (ETDEWEB)

    Milord, L.; Gerelli, E.; Jamois, C.; Harouri, A.; Benyattou, T., E-mail: taha.benyattou@insa-lyon.fr [Institut des Nanotechnologies de Lyon (INL), CNRS UMR5270, Université de Lyon, INSA-Lyon, Bât “Blaise Pascal,” 7 avenue Jean Capelle, Villeurbanne F-69621 (France); Chevalier, C.; Viktorovitch, P.; Letartre, X. [Institut des Nanotechnologies de Lyon (INL), CNRS UMR5270, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, Ecully F-69134 (France)

    2015-03-23

    In the present paper, we propose an approach based on slow Bloch mode microcavity that enables the optical trapping of small nanoparticles over a broad surface. A specific design based on a double-period photonic crystal is presented. It enables an easy coupling using a wide free-space Gaussian beam and the cavity Q factor can be tuned at will. Moreover, the microcavity mode is mainly localized within the photonic crystal holes, meaning that each hole of the microcavity behaves as efficient nanotweezers. Experimental studies have shown that 200 nm and 100 nm particles can be trapped within the microcavity, in a spatial region that corresponds to the size of one hole (200 nm wide). The experimental trap stiffness has been extracted. It shows that this approach is among the most performant ones if we take into account the size of the cavity.

  17. Coulomb blockade and BLOCH oscillations in superconducting Ti nanowires.

    Science.gov (United States)

    Lehtinen, J S; Zakharov, K; Arutyunov, K Yu

    2012-11-01

    Quantum fluctuations in quasi-one-dimensional superconducting channels leading to spontaneous changes of the phase of the order parameter by 2π, alternatively called quantum phase slips (QPS), manifest themselves as the finite resistance well below the critical temperature of thin superconducting nanowires and the suppression of persistent currents in tiny superconducting nanorings. Here we report the experimental evidence that in a current-biased superconducting nanowire the same QPS process is responsible for the insulating state--the Coulomb blockade. When exposed to rf radiation, the internal Bloch oscillations can be synchronized with the external rf drive leading to formation of quantized current steps on the I-V characteristic. The effects originate from the fundamental quantum duality of a Josephson junction and a superconducting nanowire governed by QPS--the QPS junction.

  18. Entanglement and the three-dimensionality of the Bloch ball

    Energy Technology Data Exchange (ETDEWEB)

    Masanes, Ll., E-mail: ll.masanes@gmail.com [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Müller, M. P. [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany); Pérez-García, D. [Departamento de Analisis Matematico and IMI, Universidad Complutense de Madrid, 28040 Madrid (Spain); Augusiak, R. [ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona (Spain)

    2014-12-15

    We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.

  19. Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to Bloch photonic crystal modes

    Energy Technology Data Exchange (ETDEWEB)

    Fountaine, Katherine T., E-mail: kfountai@caltech.edu [Department of Chemistry and Chemical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Whitney, William S. [Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Department of Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Atwater, Harry A. [Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Department of Applied Physics and Materials Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States)

    2014-10-21

    We present a unified framework for resonant absorption in periodic arrays of high index semiconductor nanowires that combines a leaky waveguide theory perspective and that of photonic crystals supporting Bloch modes, as array density transitions from sparse to dense. Full dispersion relations are calculated for each mode at varying illumination angles using the eigenvalue equation for leaky waveguide modes of an infinite dielectric cylinder. The dispersion relations along with symmetry arguments explain the selectivity of mode excitation and spectral red-shifting of absorption for illumination parallel to the nanowire axis in comparison to perpendicular illumination. Analysis of photonic crystal band dispersion for varying array density illustrates that the modes responsible for resonant nanowire absorption emerge from the leaky waveguide modes.

  20. Stable BLOCH oscillations of cold atoms with time-dependent interaction.

    Science.gov (United States)

    Gaul, C; Lima, R P A; Díaz, E; Müller, C A; Domínguez-Adame, F

    2009-06-26

    We investigate Bloch oscillations of interacting cold atoms in a mean-field framework. In general, atom-atom interaction causes dephasing and destroys Bloch oscillations. Here we show that Bloch oscillations are persistent if the interaction is modulated harmonically with suitable frequency and phase. For other modulations, Bloch oscillations are rapidly damped. We explain this behavior in terms of collective coordinates whose Hamiltonian dynamics permits one to predict a whole family of stable solutions. In order to describe also the unstable cases, we carry out a stability analysis for Bogoliubov excitations. Using Floquet theory, we are able to predict the unstable modes as well as their growth rate, found to be in excellent agreement with numerical simulations.

  1. Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers

    DEFF Research Database (Denmark)

    Rasmussen, Per Dalgaard; Sukhorukov, A.A.; Neshev, D.N.;

    2008-01-01

    We study theoretically the dispersion properties of Bloch modes and nonlinearly-induced defect states in two-dimensional waveguide arrays. We define the conditions for achieving anomalous group-velocity dispersion and discuss possibilities for generation of spatiotemporal solitons....

  2. Band structure and Bloch states in birefringent 1D magnetophotonic crystals: An analytical approach

    CERN Document Server

    Lévy, M; Levy, Miguel; Jalali, Amir A

    2007-01-01

    An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin film devices. Full analytical expressions are obtained for the dispersion relation and Bloch modes in a layered stack photonic crystal and their properties are analyzed. It is shown that other models recently discussed in the literature are contained as special limiting cases of the formulation presented herein.

  3. A dorsal fold in Gymnura micrura (Bloch and Scheneider, 1801 (Chondrichthyes: Gymnuridae

    Directory of Open Access Journals (Sweden)

    Jorge Luiz Silva Nunes

    2009-04-01

    Full Text Available This paper reports a dorsal fold which is a membranous structure located on the tail of two juvenile butterfly rays, Gymnura micrura (Bloch & Scheneider, 1801, caught through artisanal fishery in the shallow waters of Maranhão State (Brazil.Neste manuscrito registra-se uma nadadeira dorsal em dois espécimes juvenis de Gymnura micrura (Bloch and Scheneider, 1801 capturadas pela pesca artesanal em águas rasas do estado do Maranhão (Brasil.

  4. Weighted Composition Operators from Bergman-Type Spaces into Bloch Spaces

    Indian Academy of Sciences (India)

    Songxiao Li; Stevo Stević

    2007-08-01

    Let be an analytic self-map and be a fixed analytic function on the open unit disk in the complex plane $\\mathbb{C}$. The weighted composition operator is defined by $$u C_\\varphi f=u\\cdot p (f\\circ\\varphi), f\\in H(D).$$ Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.

  5. Bloch Oscillations of Two-Component Bose-Einstein Condensates in Optical Lattices

    Institute of Scientific and Technical Information of China (English)

    GU Huai-Qiang; WANG Zhi-Cheng; JIN Kang; TAN Lei

    2006-01-01

    @@ We study the Bloch oscillations of two-component Bose-Einstein condensates trapped in spin-dependent optical lattices. The influence of the intercomponent atom interaction on the system is discussed in detail Accelerated breakdown of the Bloch oscillations and revival phenomena are found respectively for the repulsive and attractive case. For both the cases, the system will finally be set in a quantum self-trapping state due to dynamical instability.

  6. Imaging of Bloch oscillations in erbium-doped curved waveguide arrays.

    Science.gov (United States)

    Chiodo, N; Della Valle, G; Osellame, R; Longhi, S; Cerullo, G; Ramponi, R; Laporta, P; Morgner, U

    2006-06-01

    We report a direct observation of Bloch-like dynamics of light in curved waveguide arrays manufactured in Er:Yb-doped phosphate glass by femtosecond laser writing. The green upconversion fluorescence emitted by excited erbium ions is exploited to image the flow of the guided pump light at approximately 980 nm along the array. Direct and clear evidence of periodic light breathing for single-waveguide excitation, closely related to Bloch oscillations, is reported.

  7. Photonic Bloch oscillations and Wannier-Stark ladders in exponentially chirped Bragg gratings.

    Science.gov (United States)

    Wilkinson, P B

    2002-05-01

    The formation of photonic Bloch oscillations and Wannier-Stark ladders is demonstrated in an exponentially chirped one-dimensional Bragg grating. The photonic Bloch oscillations are investigated using Hamiltonian optics, and direct analogies are made with electron dynamics in periodic potentials. The results of transfer matrix calculations are presented, which show the existence of a photonic Wannier-Stark ladder that should be detectable in experiments.

  8. Geometry of the generalized Bloch sphere for qutrit

    CERN Document Server

    Goyal, Sandeep K; Singh, Rajeev; Simon, Sudhavathani

    2011-01-01

    The geometry of the generalized Bloch sphere $\\Omega_3$, the state space of a qutrit is studied. Closed form expressions for $\\Omega_3$, its boundary $\\partial \\Omega_3$, and the set of extremals $\\Omega_3^{\\rm ext}$ are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of $\\Omega_3$ into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group $T_d$ is examined in detail. This symmetry is traced to the reduction of the adjoint representation of SU(3), the symmetry underlying $\\Omega_3$, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional ...

  9. Floquet-Bloch theory for polymers in a periodic

    Science.gov (United States)

    Pablo Pedro, Ricardo; Tempel, David; Alexander-Katz, Alfredo

    2014-03-01

    Anderson localization in disordered systems predicts the localization of electronic wave functions and the resulting absence of diffusion. The phenomenon is much more general and has been observed in a variety of systems. In the case of the polymer, the behavior of it in a periodic potential is equivalent to the behavior of a quantum-machanicial particle in a periodic potential. According to this mapping our results for polymers in a periodic potential ara valid for localization of a quantum-mechanical particle in a periodic potential. Besides, one of our motivations for studying polymers in a periodic potential is because it reveals interesting aspects of a self-organization of the adsorbed polymers onto a surface with periodic potential. In order to describe the properties of time-periodic polymer system, we consider the potential time dependent which is periodic in time and space and we evaluate the solutions using the powerful nonperturbative Floquet-Bloch theory which is formulated for linear systems. Finally, we also consider a more interesting problem of when disorder is included in the time-periodic system, where localization of the wave function can occur.

  10. Geometry of the generalized Bloch sphere for qutrits

    Science.gov (United States)

    Goyal, Sandeep K.; Neethi Simon, B.; Singh, Rajeev; Simon, Sudhavathani

    2016-04-01

    The geometry of the generalized Bloch sphere Ω3, the state space of a qutrit, is studied. Closed form expressions for Ω3, its boundary ∂Ω3, and the set of extremals {{{Ω }}}3{{ext}} are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU(3), the symmetry underlying Ω3, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .

  11. Philippe Bloch: Reducing distance between experiments and CERN

    CERN Multimedia

    2009-01-01

    With its unique combination of several hundred staff members and thousands of users from around the world sharing offices and physics data and profiting from mutually beneficial exchanges of know-how and expertise, the PH Department is a good example of a successful worldwide collaboration, set up as it was to construct and run the Laboratory’s physics experiments. The PH Depart-ment has always played host to thousands of users that contribute to CERN experiments and work on them, and whose numbers are set to grow in the years to come. With his long-standing experience as a user and then as the head of the CERN group within the CMS collaboration, Philippe Bloch, the new PH Department Head, is in favour of closer links between the Department and the experiments. "I think that the PH management should have a direct link to the experiments, and to do so we are holding regular management team meetings comprising members of the Department’s management and the e...

  12. Several Growth Characteristics of an Invasive Cyprinid Fish (Carassius gibelio Bloch, 1782

    Directory of Open Access Journals (Sweden)

    Sait BULUT

    2013-05-01

    Full Text Available Age composition, length-weight relationships, growth, and condition factors of the gibel carp (Carassius gibelio Bloch, 1782 were determined using specimens collected from Seyitler Reservoir between July 2005 to June 2006. A total of 149 gibel carp were observed and examined. The age composition of the samples ranged between I and VII years of age. It has been determined than 82.55% of the obtained samples are comprised of females, 16.11% is comprised of males and 1.34% is comprised of immature. The population is dominated by females able to reproduce gynogenetically. The mean fork lengths and mean weights of the population were 14.8-32.5 cm and 43.1-807.3 g respectively. The length-weight relation were calculated as W = 0.0696 L2.132, r=0.838 for females, for males W = 0.2942 L2.6417 r=0.784 and W = 0.0274 L2.9382, r=0.813 for all samples. The mean Fulton Condition Factor was calculated as 2.342 for females, 2.064 for males and 2.276 for all samples. Age-length and age-weight relations were determined according to von Bertalanffy growth equation formula. Growth parameters of the population were Lt = 48.09 [1-e-0.093(t+0.29], and Wt=2323.62 [1-e-0.093(t+0.29]2.9382. The growth performance index value (Ø´ was computed as 5.37 for all specimens.

  13. Bloch Oscillation in a One-Dimensional Array of Small Josephson Junctions

    Science.gov (United States)

    Shimada, Hiroshi; Katori, Shunsuke; Gandrothula, Srinivas; Deguchi, Tomoaki; Mizugaki, Yoshinao

    2016-07-01

    A distinct Bloch nose was demonstrated in the current-voltage characteristics of a one-dimensional array of 20 small Josephson junctions. Arrays of direct-current superconducting quantum interference device (dc-SQUID) structures were used as leads to the array of junctions, and the environmental impedance was tuned with a magnetic field. The observed Bloch nose had a negative differential resistance of its magnitude of as large as 14.3 MΩ, a blockade voltage of 0.36 mV, and a decrease in voltage of 0.21 mV due to the Bloch oscillation, all of which are larger than those obtained in a single junction by more than one order. The observed Bloch oscillation was quantitatively described on the basis of the Bloch oscillation of each single junction in combination with the charge soliton model in a long array. Unexpected constant-current spikes, whose origin lay in the dc-SQUID in the leads, were also observed to be superposed on the current-voltage characteristics when the Coulomb blockade appeared.

  14. Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures

    Energy Technology Data Exchange (ETDEWEB)

    Lazcano, Z.; Arriaga, J., E-mail: arriaga@ifuap.buap.mx [Instituto de Física, Benemérita Universidad Autónoma de Puebla, 18 Sur y San Claudio, Edif. 110-A, Ciudad Universitaria, 72570 Puebla (Mexico); Aliev, G. N. [Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom)

    2014-04-21

    We report the theoretical calculations and the experimental demonstration of acoustic Bloch oscillations and Wannier-Stark ladders in linear tilted multilayer structures based on porous silicon. The considered structures consist of layers with constant porosity alternated by layers with a linear gradient in the parameter η=1/v{sub L}{sup 2} along the growth direction in order to tilt the acoustic band gap. The purpose of this gradient is to mimic the tilted electronic miniband structure of a superlattice semiconductor under an external electric field. In this way, acoustic Wannier-Stark ladders of equidistant modes are formed and they were experimentally confirmed in the transmission spectrum around 1.2 GHz. Their frequency separation defines the period of the acoustic Bloch oscillations. We fabricated three different structures with the same thicknesses but different values in the η parameter to observe the effect on the period of the Bloch oscillations. We measured the acoustic transmission spectra in the frequency domain, and by using the Fourier transform, we obtained the transmission in the time domain. The transmission spectra of the fabricated samples show acoustic Bloch oscillations with periods of 27, 24, and 19 ns. The experimental results are in good agreement with the transfer matrix calculations. The observed phenomenon is the acoustic counterpart of the well known electronic Bloch oscillations.

  15. Probing the intrinsic optical Bloch-mode emission from a 3D photonic crystal.

    Science.gov (United States)

    Hsieh, Mei-Li; Bur, James A; Du, Qingguo; John, Sajeev; Lin, Shawn-Yu

    2016-10-14

    We report experimental observation of intrinsic Bloch-mode emission from a 3D tungsten photonic crystal at low thermal excitation. After the successful removal of conventional metallic emission (normal emission), it is possible to make an accurate comparison of the Bloch-mode and the normal emission. For all biases, we found that the emission intensity of the Bloch-mode is higher than that of the normal emission. The Bloch-mode emission also exhibits a slower dependence on [Formula: see text] than that of the normal emission. The observed higher emission intensity and a different T-dependence is attributed to Bloch-mode assisted emission where emitters have been located into a medium having local density of states different than the isotropic case. Furthermore, our finite-difference time-domain (FDTD) simulation shows the presence of localized spots at metal-air boundaries and corners, having intense electric field. The enhanced plasmonic field and local non-equilibrium could induce a strong thermally stimulated emission and may be the cause of our unusual observation. PMID:27606574

  16. Homogenization of the Schrodinger equation with a time oscillating potential

    OpenAIRE

    Allaire, Grégoire; Vanninathan, M.

    2005-01-01

    International audience We study the homogenization of a Schrodinger equation in a periodic medium with a time dependent potential. This is a model for semiconductors excited by an external electromagnetic wave. We prove that, for a suitable choice of oscillating (both in time and space) potential, one can partially transfer electrons from one Bloch band to another. This justifies the famous "Fermi golden rule" for the transition probability between two such states which is at the basis of ...

  17. Bloch wave deafness and modal conversion at a phononic crystal boundary

    Directory of Open Access Journals (Sweden)

    Vincent Laude

    2011-12-01

    Full Text Available We investigate modal conversion at the boundary between a homogeneous incident medium and a phononic crystal, with consideration of the impact of symmetry on the excitation of Bloch waves. We give a quantitative criterion for the appearance of deaf Bloch waves, which are antisymmetric with respect to a symmetry axis of the phononic crystal, in the frame of generalized Fresnel formulas for reflection and transmission at the phononic crystal boundary. This criterion is used to index Bloch waves in the complex band structure of the phononic crystal, for directions of incidence along a symmetry axis. We argue that within deaf frequency ranges transmission is multi-exponential, as it is within frequency band gaps.

  18. Bloch wave deafness and modal conversion at a phononic crystal boundary

    Science.gov (United States)

    Laude, Vincent; Moiseyenko, Rayisa P.; Benchabane, Sarah; Declercq, Nico F.

    2011-12-01

    We investigate modal conversion at the boundary between a homogeneous incident medium and a phononic crystal, with consideration of the impact of symmetry on the excitation of Bloch waves. We give a quantitative criterion for the appearance of deaf Bloch waves, which are antisymmetric with respect to a symmetry axis of the phononic crystal, in the frame of generalized Fresnel formulas for reflection and transmission at the phononic crystal boundary. This criterion is used to index Bloch waves in the complex band structure of the phononic crystal, for directions of incidence along a symmetry axis. We argue that within deaf frequency ranges transmission is multi-exponential, as it is within frequency band gaps.

  19. Integral type operators from normal weighted Bloch spaces to QT,S spaces

    Directory of Open Access Journals (Sweden)

    Yongyi GU

    2016-08-01

    Full Text Available Operator theory is an important research content of the analytic function space theory. The discussion of simultaneous operator and function space is an effective way to study operator and function space. Assuming that  is an analytic self map on the unit disk Δ, and the normal weighted bloch space μ-B is a Banach space on the unit disk Δ, defining a composition operator C∶C(f=f on μ-B for all f∈μ-B, integral type operator JhC and CJh are generalized by integral operator and composition operator. The boundeness and compactness of the integral type operator JhC acting from normal weighted Bloch spaces to QT,S spaces are discussed, as well as the boundeness of the integral type operators CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.

  20. Observation of fractional Bloch band quantum Hall states in graphene/h-BN superlattices

    Science.gov (United States)

    Wang, Lei; Gao, Yuanda; Wen, Bo; Hone, James; Dean, Cory

    The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. Here we report measurements of high mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observe coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observe signatures of another series of states, which appears at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point towards a distinct type of many-body state.

  1. Bloch mode synthesis: Ultrafast methodology for elastic band-structure calculations

    Science.gov (United States)

    Krattiger, Dimitri; Hussein, Mahmoud I.

    2014-12-01

    We present a methodology for fast band-structure calculations that is generally applicable to problems of elastic wave propagation in periodic media. The methodology, called Bloch mode synthesis, represents an extension of component mode synthesis, a set of substructuring techniques originally developed for structural dynamics analysis. In Bloch mode synthesis, the unit cell is divided into interior and boundary degrees-of-freedom, which are described, respectively, by a set of normal modes and a set of constraint modes. A combination of these mode sets then forms a reduced basis for the band structure eigenvalue problem. The reduction is demonstrated on a phononic-crystal model and a locally resonant elastic-metamaterial model and is shown to accurately predict the frequencies and Bloch mode shapes with a dramatic decrease in computation time in excess of two orders of magnitude.

  2. Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice.

    Science.gov (United States)

    Xu, Ye-Long; Fegadolli, William S; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng

    2016-01-01

    As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform. PMID:27095533

  3. Bloch bound states in the radiation continuum in a periodic array of dielectric rods

    CERN Document Server

    Bulgakov, Evgeny N

    2014-01-01

    We consider an infinite periodic array of dielectric rods in vacuum with the aim to demonstrate three types of a Bloch bound states in the continuum (BSC), symmetry protected with a zero Bloch vector, embedded into one diffraction channel with nonzero Bloch vector, and embedded into two and three diffraction channels. The first and second types of the BSC exist in a wide range of material parameters of the rods, while the third occurs only at a specific value of the radius of the rods. We show that the second type supports the power flux along the array. In order to find BSC we put forward an approach based on the expansion over the Hankel functions. We show how the BSC reveals itself in the scattering function when the singular BSC point is approached along a specific path in the parametric space.

  4. Non-destructive monitoring of Bloch oscillations in an optical cavity

    CERN Document Server

    Keßler, H; Venkatesh, B P; Georges, Ch; Hemmerich, A

    2016-01-01

    Bloch oscillations are a hallmark of coherent wave dynamics in periodic potentials. They occur as the response of quantum mechanical particles in a lattice if a weak force is applied. In optical lattices with their perfect periodic structure they can be readily observed and employed as a quantum mechanical force sensor, for example, for precise measurements of the gravitational acceleration. However, the destructive character of the measurement process in previous experimental implementations poses serious limitations for the precision of such measurements. In this article we show that the use of an optical cavity operating in the regime of strong cooperative coupling allows one to directly monitor Bloch oscillations of a cloud of cold atoms in the light leaking out of the cavity. Hence, with a single atomic sample the Bloch oscillation dynamics can be mapped out, while in previous experiments, each data point required the preparation of a new atom cloud. The use of a cavity-based monitor should greatly impro...

  5. Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice.

    Science.gov (United States)

    Xu, Ye-Long; Fegadolli, William S; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng

    2016-04-20

    As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform.

  6. Observation of Bloch oscillations in complex PT-symmetric photonic lattices

    CERN Document Server

    Wimmer, Martin; Christodoulides, Demetrios; Peschel, Ulf

    2016-01-01

    Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals ...

  7. Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments.

    Science.gov (United States)

    Lermer, M; Gregersen, N; Dunzer, F; Reitzenstein, S; Höfling, S; Mørk, J; Worschech, L; Kamp, M; Forchel, A

    2012-02-01

    We have employed Bloch-wave engineering to realize submicron diameter high quality factor GaAs/AlAs micropillars (MPs). The design features a tapered cavity in which the fundamental Bloch mode is subject to an adiabatic transition to match the Bragg mirror Bloch mode. The resulting reduced scattering loss leads to record-high vacuum Rabi splitting of the strong coupling in MPs with modest oscillator strength quantum dots. A quality factor of 13, 600 and a splitting of 85  μeV with an estimated visibility v of 0.41 are observed for a small mode volume MP with a diameter d{c} of 850 nm.

  8. Visualization of Bloch surface waves and directional propagation effects on one-dimensional photonic crystal substrate.

    Science.gov (United States)

    Hung, Yu-Ju; Lin, I-Sheng

    2016-07-11

    This paper reports a novel approach to the direct observation of Bloch surface waves, wherein a layer of fluorescent material is deposited directly on the surface of a semi-infinite periodic layered cell. A set of surface nano-gratings is used to couple pumping light to Bloch surface waves, while the sample is rotated until the pumping light meets the quasi-phase matching conditions. This study investigated the directional propagation of waves on stripe and circular one-dimensional grating structures by analyzing the dispersion relationship of the first two eigen modes. Our results demonstrate the efficacy of the proposed scheme in visualizing Bloch surface waves, which could be extended to a variety of other devices. PMID:27410869

  9. Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice

    Science.gov (United States)

    Xu, Ye-Long; Fegadolli, William S.; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng

    2016-01-01

    As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform. PMID:27095533

  10. Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice

    Science.gov (United States)

    Xu, Ye-Long; Fegadolli, William S.; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng

    2016-04-01

    As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform.

  11. The Barkas-Effect Correction to Bethe-Bloch Stopping Power

    Science.gov (United States)

    Porter, L. E.

    A brief history of the discovery of the Barkas-effect correction to the Bethe-Bloch stopping power formula is presented, followed by a recounting of the initial theoretical calculations prepared as a quantitative explanation. A current version of the modified Bethe-Bloch formula is described in detail. An overview of the current capability to assess the validity of several existing formalisms for calculating the Barkas-effect correction term is provided, in the course of which discussion of numerous sources of uncertainty ensues. Finally, an opinion on the significance of this departure from Bethe-Bloch theory is offered, along with a presentation of a few recent developments and of some areas for focus in future exploration in the field of the stopping power of matter for charged particles.

  12. Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model.

    Science.gov (United States)

    Ma, Yu-Quan

    2014-10-01

    We study the Riemannian metric and the Euler characteristic number of the Bloch band in a one-dimensional spin model with multisite spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phase transition in zero temperature can be distinguished by the Euler number of the Bloch band.

  13. Atomic Bloch-Zener oscillations and Stückelberg interferometry in optical lattices.

    Science.gov (United States)

    Kling, Sebastian; Salger, Tobias; Grossert, Christopher; Weitz, Martin

    2010-11-19

    We report on experiments investigating quantum transport and band interferometry of an atomic Bose-Einstein condensate in an optical lattice with a two-band miniband structure, realized with a Fourier-synthesized optical lattice potential. Bloch-Zener oscillations, the coherent superposition of Bloch oscillations and Landau-Zener tunneling between the two bands, are observed. When the relative phase between paths in different bands is varied, an interference signal is observed, demonstrating the coherence of the dynamics in the miniband system. Measured fringe patterns of this Stückelberg interferometer allow us to interferometrically map out the band structure of the optical lattice over the full Brillouin zone.

  14. The intensive terahertz electroluminescence induced by Bloch oscillations in SiC natural superlattices.

    Science.gov (United States)

    Sankin, Vladimir; Andrianov, Alexandr; Petrov, Alexey; Zakhar'in, Alexey; Lepneva, Ala; Shkrebiy, Pavel

    2012-10-09

    : We report on efficient terahertz (THz) emission from high-electric-field-biased SiC structures with a natural superlattice at liquid helium temperatures. The emission spectrum demonstrates a single line, the maximum of which shifts linearly with increases in bias field. We attribute this emission to steady-state Bloch oscillations of electrons in the SiC natural superlattice. The properties of the THz emission agree fairly with the parameters of the Bloch oscillator regime, which have been proven by high-field electron transport studies of SiC structures with natural superlattices.

  15. Bloch-Zener oscillations across a merging transition of Dirac points.

    Science.gov (United States)

    Lim, Lih-King; Fuchs, Jean-Noël; Montambaux, Gilles

    2012-04-27

    Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition toward a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling probability is computed from the low-energy universal Hamiltonian describing the vicinity of the merging. The agreement with a recent experiment on cold atoms in an optical lattice is very good.

  16. Schrodinger cat states prepared by Bloch oscillation in a spin-dependent optical lattice

    CERN Document Server

    Wu, B J

    2011-01-01

    We propose to use Bloch oscillation of ultra-cold atoms in a spin-dependent optical lattice to prepare schrodinger cat states. Depending on its internal state, an atom feels different periodic potentials and thus has different energy band structures for its center-of-mass motion. Consequently, under the same gravity force, the wave packets associated with different internal states perform Bloch oscillation of different amplitudes in space and in particular they can be macroscopically displaced with respect to each other. In this way, a cat state can be prepared.

  17. Influence of size, station time and satiation amount on prey handling time in Anabas testudineus (Bloch)

    OpenAIRE

    Sreekumari, T.; Aravindan, C.M.

    1993-01-01

    Satiation amount, satiation time and handling time of Anabas testudineus (Bloch), an air breathing predatory fish was experimentally estimated using guppy (Lebistes reticulatus) as prey. Weight of the fish and satiation time influenced prey handling time. As satiation time is related to the level of hunger, level of hunger was found to influence handling time of prey.

  18. Floquet-Bloch waves and suppression of vibrations in multi-scale fluid-solid systems

    CERN Document Server

    Carta, Giorgio; Movchan, Alexander B

    2016-01-01

    The paper presents a mathematical model for an industry inspired problem of vibration isolation applied to a cluster of elastic fluid-filled containers. We develop a systematic approach employing full fluid-solid interaction and Floquet-Bloch waves in periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and computations in the transient regime.

  19. Proof of an entropy conjecture for Bloch coherent spin states and its generalizations

    DEFF Research Database (Denmark)

    H. Lieb, Elliott; Solovej, Jan Philip

    2014-01-01

    in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum $J$. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from $J$ to $K=J+1/2, J+1, ...$, with $K=\\infty$ corresponding to the Wehrl map to classical...

  20. Dynamic localization and Bloch oscillations in the spectrum of a frequency mode-locked laser.

    Science.gov (United States)

    Longhi, Stefano

    2005-04-01

    It is shown that a frequency mode-locked laser with a sinusoidal sweep of modulation frequency around a mode-locking condition represents an ideal optical system for observing in the spectral domain the phenomena of dynamic localization and Bloch oscillations of electrons in an ideal solid placed in an external ac electric field.

  1. Dynamic Behavior and Quasi-energy Spectrum of Multiband Superlattice Bloch Electrons in Quantum Kicked Potential

    Institute of Scientific and Technical Information of China (English)

    OUYANG BiYao; ZHAO XianGeng; CHEN ShiGang; LIU Jie

    2001-01-01

    In this paper, we study the dynamic behavior and quasi-energy spectrum of multiband superlattice Bloch electrons in quantum kicked potential. We show analytically and numerically the avoided crossing and band suppression about the quasi-energy spectrum, the dynamic nonlocalization, and the electron oscillation behavior between two bands.

  2. Beam splitter and combiner based on Bloch oscillations in spatially modulated waveguide arrays

    CERN Document Server

    Zhang, Yiqi; Zhong, Weiping; Wen, Feng; Guo, Yang; Guo, Yao; Lu, Keqing; Zhang, Yanpeng

    2014-01-01

    We numerically investigate the light beam propagation in periodic waveguide arrays which are elaborately modulated with certain structures. We find that the light beam may split, coalesce, deflect, and be localized during propagation in these spatially modulated waveguide arrays. All the phenomena originate from Bloch oscillations, and supply possible method for fabricating on-chip beam splitters and beam combiners.

  3. Populating the Large-Wavevector Realm: Bloch Volume Plasmon Polaritons in Hyperbolic and Extremely Anisotropic Metamaterials

    DEFF Research Database (Denmark)

    Zhukovsky, Sergei; Babicheva, Viktoriia; Orlov, A. A.;

    2014-01-01

    Optics of hyperbolic metamaterials is revisited in terms of large-wavevector waves, evanescent in isotropic media but propagating in presence of extreme anisotropy. Identifying the physical nature of these waves as Bloch volume plasmon polaritons, we derive their existence conditions and outline...... the strategy for tailoring their properties in multiscale metamaterials....

  4. Floquet-Bloch vs. Nicolson-Ross-Weir Extraction for Magneto-Dielectric Bragg Stacks

    DEFF Research Database (Denmark)

    Clausen, Niels Christian Jerichau; Arslanagic, Samel; Breinbjerg, Olav

    2014-01-01

    We extract and compare the permittivity and permeability from a dielectric and a magnetodielectric Bragg stack with the Floquet-Bloch (FB) method for the infinite stack and the Nicolson-Ross- Weir (NRW) method for the finite stack. While the extracted propagation constants are identical, the wave...

  5. A redescription of grey pomfret Pampus cinereus (Bloch,1795) with the designation of a neotype (Teleostei:Stromateidae)

    Institute of Scientific and Technical Information of China (English)

    LIU Jing; LI Chunsheng; NING Ping

    2013-01-01

    Pampus cinereus (Bloch,1795) (Stromateidae),a species believed to be widely distributed throughout the Indo-Western Pacific region,was redescribed and a neotype was designated.The designation of a neotype was necessary because of ambiguous data in Bloch's original description and the loss of the original type specimen.Morphological data indicated that 10 recently-collected specimens from the coasts of southern China agreed well with Bloch's original description and figure ofP.cinereus.A neotype for this species was selected from among the 10 specimens,and a detailed description is presented in this paper.

  6. Web-based description of the space radiation environment using the Bethe-Bloch model

    Science.gov (United States)

    Cazzola, Emanuele; Calders, Stijn; Lapenta, Giovanni

    2016-01-01

    Space weather is a rapidly growing area of research not only in scientific and engineering applications but also in physics education and in the interest of the public. We focus especially on space radiation and its impact on space exploration. The topic is highly interdisciplinary, bringing together fundamental concepts of nuclear physics with aspects of radiation protection and space science. We give a new approach to presenting the topic by developing a web-based application that combines some of the fundamental concepts from these two fields into a single tool that can be used in the context of advanced secondary or undergraduate university education. We present DREADCode, an outreach or teaching tool to rapidly assess the current conditions of the radiation field in space. DREADCode uses the available data feeds from a number of ongoing space missions (ACE, GOES-13, GOES-15) to produce a first order approximation of the radiation dose an astronaut would receive during a mission of exploration in deep space (i.e. far from the Earth’s shielding magnetic field and from the radiation belts). DREADCode is based on an easy-to-use GUI interface available online from the European Space Weather Portal (www.spaceweather.eu/dreadcode). The core of the radiation transport computation to produce the radiation dose from the observed fluence of radiation observed by the spacecraft fleet considered is based on a relatively simple approximation: the Bethe-Bloch equation. DREADCode also assumes a simplified geometry and material configuration for the shields used to compute the dose. The approach is approximate and sacrifices some important physics on the altar of rapid execution time, which allows a real-time operation scenario. There is no intention here to produce an operational tool for use in space science and engineering. Rather, we present an educational tool at undergraduate level that uses modern web-based and programming methods to learn some of the most important

  7. Cubic Equation

    Institute of Scientific and Technical Information of China (English)

    2004-01-01

    At the beginning of 16th century, mathematicians found it easy to solve equations of the first degree(linear equations, involving x) and of the second degree(quadratic equatiorts, involving x2). Equations of the third degree(cubic equations, involving x3)defeated them.

  8. Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate

    Science.gov (United States)

    Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.

    2016-10-01

    We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin-? system. The spin state of a spin-? quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases and the relative frequencies. We experimentally demonstrate key features of this model with a ?Rb spinor Bose-Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.

  9. A Refresher of the Original Bloch’s Law Paper (Bloch, July 1885)

    Science.gov (United States)

    2015-01-01

    In 1885, Adolphe-Moïse Bloch asked the following simple question “Is there a law describing the relationship between the duration of a light and its perceived intensity?” Based on a series of experiments using a Foucault regulator and a candle, Bloch concluded that “when the lighting duration varies from 0.00173 to 0.0518 seconds (…) the [visible] light is markedly in inverse proportion to its duration”—his famous law. As this law pertains to the more general and hotly debated question of accumulation of sensory information over time, it is timely to offer the public a full translation of Bloch’s original paper (from French) and to present it within the context of contemporary research. PMID:27433317

  10. Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction

    CERN Document Server

    Tallarico, Domenico; Movchan, Alexander B; Colquitt, Daniel J

    2016-01-01

    We consider a vibrating triangular mass-truss lattice whose unit cell contains a resonator of a triangular shape. The resonators are connected to the triangular lattice by trusses. Each resonator is tilted, i.e. it is rotated with respect to the triangular lattice's unit cell through an angle $\\vartheta_0$. This geometrical parameter is responsible for the emergence of a resonant mode in the Bloch spectrum for elastic waves and strongly affects the dispersive properties of the lattice. Additionally, the tilting angle $\\vartheta_0$ triggers the opening of a band gap at a Dirac-like point. We provide a physical interpretation of these phenomena and discuss the dynamical implications on elastic Bloch waves. The dispersion properties are used to design a structured interface containing tilted resonators which exhibit negative refraction and focussing, as in a "flat elastic lens".

  11. Magneto-optical switching of Bloch surface waves in magnetophotonic crystals

    Science.gov (United States)

    Romodina, M. N.; Soboleva, I. V.; Fedyanin, A. A.

    2016-10-01

    Bloch-surface-wave (BSW) excitation controlled by Faraday rotation in one-dimensional magnetophotonic crystals is presented. Dispersion curves of the Bloch surface wave and waveguide modes of magnetophotonic crystals consisting of silicon dioxide and bismuth-substituted yttrium-iron-garnet (Bi:YIG) quarter-wavelength-thick layers are calculated using Berreman's 4×4 transfer matrix method. Enhanced Faraday rotation observed in the magnetophotonic crystals in the spectral vicinity of the BSW resonance enables the magneto-optical switching of BSWs. The excitation of the BSWs at the magnetophotonic crystal surface for p-polarized incident light is induced by magneto-optical activity in the Bi:YIG layers.

  12. Bloch oscillations as generators of polarons in a 1D crystal

    Science.gov (United States)

    Nazareno, H. N.; Brito, P. E. de

    2016-08-01

    The main purpose of this work is to characterize the kind of propagation/localization of carriers in a one-dimensional crystalline structure along the tight-binding model while the electron-phonon interaction is taken into account through a deformation potential and the system is under the action of a dc electric field. The lattice was treated in the classical formalism of harmonic vibrations. A remarkable effect is obtained due to the presence of the electric field. On one side the particle performs Bloch oscillations and at the same time it interacts with the lattice and as a result at each turning point of its trajectory phonons are generated that carry with them a fraction of the electronic wave packet, it is the polaron formation. This way the Bloch oscillations pump polarons into the system. We explain why the polaron is formed at returning points of the oscillations.

  13. Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models

    Directory of Open Access Journals (Sweden)

    Qiang-Hua Wang

    2013-11-01

    Full Text Available We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially under point-group operations, their point-group behavior in the band language can be simplified by choosing a suitable Bloch basis. We first give two analytically accessible examples. Then, we show that, for a large class of models, a natural Bloch basis exists, in which the vertex functions in the band language transform trivially under all point-group operations. As a consequence, the point-group symmetries can be used to reduce the computational effort in perturbative many-particle approaches, such as the functional renormalization group.

  14. Suppression of space broadening of exciton polariton beams by Bloch oscillation effects

    CERN Document Server

    Duan, Xudong; Zhang, Yongyou

    2015-01-01

    We theoretically study the transport of exciton polaritons under different applied photon potentials. The relation between the photon potentials and the thickness of the cavity layer is calculated by the finite element simulation. The theoretical analysis and numerical calculation indicate that the cavity photon potential is proportional to the thickness of the cavity layer with the coefficient being about $1.8$ meV/nm. Further, the periodic and linear photon potentials are considered to control the transport of the exciton polaritons in weak- and strong-field pump situations. In both situations the periodic potential cannot by itself effectively suppress the scatterings of the disorder potentials of the cavity photons and excitons and the nonlinear exciton-exciton interaction. When the linear potential is added to the cavity photons, the polariton transport exhibits the Bloch oscillation behavior. Importantly, the polariton Bloch oscillation can strongly suppress the space broadening due to the disorder pote...

  15. Exciting Molecules Close to the Rotational Quantum Resonance: Anderson Wall and Rotational Bloch Oscillations.

    Science.gov (United States)

    Floß, Johannes; Averbukh, Ilya Sh

    2016-05-19

    We describe a universal behavior of linear molecules excited by a periodic train of short laser pulses under conditions close to the quantum resonance. The quantum resonance effect causes an unlimited ballistic growth of the angular momentum. We show that a disturbance of the quantum resonance, either by the centrifugal distortion of the rotating molecules or a controlled detuning of the pulse train period from the so-called rotational revival time, eventually halts the growth by causing Anderson localization beyond a critical value of the angular momentum, the Anderson wall. Below the wall, the rotational excitation oscillates with the number of pulses due to a mechanism similar to Bloch oscillations in crystalline solids. We suggest optical experiments capable of observing the rotational Anderson wall and Bloch oscillations at near-ambient conditions with the help of existing laser technology.

  16. Phase transition to spatial Bloch-like oscillation in squeezed photonic lattices

    CERN Document Server

    Nezhad, M Khazaei; Golshani, M; Mahdavi, S M; Langari, A

    2013-01-01

    We propose an exactly solvable waveguide lattice incorporating inhomogeneous coupling coefficient. This structure provides a classical analogue to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguides ($ \\alpha $). Our analytical results show that the Bloch-like oscillations appear above a critical value for the linear gradient of propagation constant ($ \\alpha > \\alpha_{c} $). The phase transition (in the propagation properties of the waveguide) is a result of competition between discrete and Bragg diffraction. Moreover, the light intensity decay algebraically along each waveguide at the critical point while it falls off exponentially below the cri...

  17. Delocalization-enhanced Bloch oscillations and driven resonant tunneling in optical lattices for precision force measurements

    CERN Document Server

    Tarallo, M G; Poli, N; Chiofalo, M L; Wang, F -Y; Tino, G M

    2012-01-01

    In this paper we describe and compare different methods used for accurate determination of forces acting on matter-wave packets in optical lattices. The quantum interference nature responsible for the production of both Bloch oscillations and coherent delocalization is investigated in detail. We study conditions for optimal detection of Bloch oscillation for a thermal ensemble of cold atoms with a large velocity spread. We report on the experimental observation of resonant tunneling in an amplitude-modulated (AM) optical lattice up to the sixth harmonic with Fourier-limited linewidth. We then explore the fundamental and technical phenomena which limit both the sensitivity and the final accuracy of the atomic force sensor at 10^{-7} precision level [1], with an analysis of the coherence time of the system and addressing few simple setup changes to go beyond the current accuracy.

  18. Reflectors and resonators for high-k bulk Bloch plasmonic waves in multilayer hyperbolic metamaterials

    DEFF Research Database (Denmark)

    Zhukovsky, Sergei; Lavrinenko, Andrei

    2012-01-01

    We propose proof-of-concept designs of Bragg reflectors and Fabry-Pe´rot resonators for large wave vector waves (Bloch bulk plasmon polaritons) in multilayer metal-dielectric hyperbolic metamaterials. The designs are based on hybrid multilayers having both subwavelength and wavelength-scale struc......We propose proof-of-concept designs of Bragg reflectors and Fabry-Pe´rot resonators for large wave vector waves (Bloch bulk plasmon polaritons) in multilayer metal-dielectric hyperbolic metamaterials. The designs are based on hybrid multilayers having both subwavelength and wavelength......-scale structuring. This multiscale approach is shown to be a promising platform for using bulk plasmonic waves in complex multilayer metamaterials as a new kind of information carriers....

  19. Measuring h /mCs and the Fine Structure Constant with Bragg Diffraction and Bloch Oscillations

    Science.gov (United States)

    Parker, Richard

    2016-05-01

    We have demonstrated a new scheme for atom interferometry based on large-momentum-transfer Bragg beam splitters and Bloch oscillations. In this new scheme, we have achieved a resolution of δα / α =0.25ppb in the fine structure constant measurement, which gives up to 4.4 million radians of phase difference between freely evolving matter waves. We suppress many systematic effects, e.g., Zeeman shifts and effects from Earth's gravity and vibrations, use Bloch oscillations to increase the signal and reduce the diffraction phase, simulate multi-atom Bragg diffraction to understand sub-ppb systematic effects, and implement spatial filtering to further suppress systematic effects. We present our recent progress toward a measurement of the fine structure constant, which will provide a stringent test of the standard model of particle physics.

  20. Dynamics of open quantum spin systems: An assessment of the quantum master equation approach.

    Science.gov (United States)

    Zhao, P; De Raedt, H; Miyashita, S; Jin, F; Michielsen, K

    2016-08-01

    Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation. PMID:27627265

  1. Dynamics of open quantum spin systems: An assessment of the quantum master equation approach

    Science.gov (United States)

    Zhao, P.; De Raedt, H.; Miyashita, S.; Jin, F.; Michielsen, K.

    2016-08-01

    Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.

  2. Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball

    OpenAIRE

    Stević Stevo; Clahane Dana D

    2006-01-01

    For , let and denote, respectively, the -Bloch and holomorphic -Lipschitz spaces of the open unit ball in . It is known that and are equal as sets when . We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator from to .

  3. Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains

    Institute of Scientific and Technical Information of China (English)

    Robert F.Allen

    2014-01-01

    We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient condi-tions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ”computable” estimates on the operator norm.

  4. EXTENDED CES(A)RO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF Cn

    Institute of Scientific and Technical Information of China (English)

    胡璋剑

    2003-01-01

    The paper defines an extended Cesàro operator Tg with holomorphic symbolg in the unit ball B of Cn asWhere g(z)= ∑j=1∑n zj g/ zj is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch spaceB and the little Blochspace B0.

  5. Genetic Diversity Analysis of Lates calcarifer (Bloch 1790) in Captive and Wild Populations Using RAPD Markers

    OpenAIRE

    Muthusamy RAJASEKAR; Muthusamy THANGARAJ; Thathiredypalli R. BARATHKUMAR; Jayachandran SUBBURAJ; Kaliyan MUTHAZHAGAN

    2012-01-01

    Lates calcarifer (Bloch 1790) is one of the major economically important cultivable fish species in India. In this study, three populations of L. calcarifer was selected to assess the genetic diversity. Of which, two wild (Mudaslodai, Muthupettai) and one captive (Mutukadu) population. The genetic diversity of three populations of this species was studied using Random Amplified Polymorphic DNA (RAPD) markers. Ten random primers were used for the assessment of their genetic diversity and const...

  6. Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles

    CERN Document Server

    Longhi, Stefano

    2014-01-01

    We predict that two correlated particles hopping on a one-dimensional Hubbard lattice can show transient self-acceleration and self-induced Bloch oscillations as a result of anti-Newtonian dynamics. Self-propulsion occurs for two particles with opposite effective mass on the lattice and requires long-range particle interaction. A photonic simulator of the two-particle Hubbard model with controllable long-range interaction, where self-propulsion can be observed, is discussed.

  7. Sensitive measurement of forces at the micron scale using Bloch oscillations of ultracold atoms.

    Science.gov (United States)

    Carusotto, I; Pitaevskii, L; Stringari, S; Modugno, G; Inguscio, M

    2005-08-26

    We show that Bloch oscillations of ultracold fermionic atoms in the periodic potential of an optical lattice can be used for a sensitive measurement of forces at the micrometer length scale, e.g., in the vicinity of a dielectric surface. In particular, the proposed approach allows us to perform a local and direct measurement of the Casimir-Polder force which is, for realistic experimental parameters, as large as 10(-4) gravity.

  8. Bloch oscillations and Zener tunneling in two-dimensional photonic lattices.

    Science.gov (United States)

    Trompeter, Henrike; Krolikowski, Wieslaw; Neshev, Dragomir N; Desyatnikov, Anton S; Sukhorukov, Andrey A; Kivshar, Yuri S; Pertsch, Thomas; Peschel, Ulf; Lederer, Falk

    2006-02-10

    We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap spectrum.

  9. The peripheral olfactory organ in the Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801)

    OpenAIRE

    Laura Ghigliotti; Julius Nielsen; Jorgen Schou Christiansen; Eva Pisano

    2015-01-01

    The Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801) is the largest predatory fish in Arctic waters. The socio-economic significance of Greenland shark is demonstrated by its impact on the fishing cultures in Greenland, Scandinavia and Iceland for centuries. The fundamental biology and ecological role of Greenland shark, on the other hand, is virtually unknown. Although knowledge of its life history is limited, increasing evidence indicates that the Greenland shark may unde...

  10. Real-time protein aggregation monitoring with a Bloch surface wave-based approach

    Science.gov (United States)

    Santi, Sara; Barakat, Elsie; Descrovi, Emiliano; Neier, Reinhard; Herzig, Hans Peter

    2014-05-01

    The misfolding and aggregation of amyloid proteins has been associated with incurable diseases such as Alzheimer's or Parkinson's disease. In the specific case of Alzheimer's disease, recent studies have shown that cell toxicity is caused by soluble oligomeric forms of aggregates appearing in the early stages of aggregation, rather than by insoluble fibrils. Research on new strategies of diagnosis is imperative to detect the disease prior to the onset of clinical symptoms. Here, we propose the use of an optical method for protein aggregation dynamic studies using a Bloch surface wave based approach. A one dimension photonic crystal made of a periodic stack of silicon oxide and silicon nitride layers is used to excite a Bloch surface wave, which is sensitive to variation of the refractive index of an aqueous solution. The aim is to detect the early dynamic events of protein aggregation and fibrillogenesis of the amyloid-beta peptide Aβ42, which plays a central role in the onset of the Alzheimer's disease. The detection principle relies on the refractive index changes caused by the depletion of the Aβ42 monomer concentration during oligomerization and fibrillization. We demonstrate the efficacy of the Bloch surface wave approach by monitoring in real-time the first crucial steps of Aβ42 oligomerization.

  11. Observation of Bloch oscillations in complex PT-symmetric photonic lattices

    Science.gov (United States)

    Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf

    2015-12-01

    Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.

  12. Representability of Bloch states on Projector-augmented-wave (PAW) basis sets

    Science.gov (United States)

    Agapito, Luis; Ferretti, Andrea; Curtarolo, Stefano; Buongiorno Nardelli, Marco

    2015-03-01

    Design of small, yet `complete', localized basis sets is necessary for an efficient dual representation of Bloch states on both plane-wave and localized basis. Such simultaneous dual representation permits the development of faster more accurate (beyond DFT) electronic-structure methods for atomistic materials (e.g. the ACBN0 method.) by benefiting from algorithms (real and reciprocal space) and hardware acceleration (e.g. GPUs) used in the quantum-chemistry and solid-state communities. Finding a `complete' atomic-orbital basis (partial waves) is also a requirement in the generation of robust and transferable PAW pseudopotentials. We have employed the atomic-orbital basis from available PAW data sets, which extends through most of the periodic table, and tested the representability of Bloch states on such basis. Our results show that PAW data sets allow systematic and accurate representability of the PAW Bloch states, better than with traditional quantum-chemistry double-zeta- and double-zeta-polarized-quality basis sets.

  13. Dynamic scattering of electron vortex beams – A Bloch wave analysis

    Energy Technology Data Exchange (ETDEWEB)

    Mendis, B.G., E-mail: b.g.mendis@durham.ac.uk

    2015-02-15

    Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum () transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±ħ angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in . This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the pendellösung. - Highlights: • Dynamic scattering of vortex beams is analysed using Bloch waves. • Fundamental origins of pendellösung oscillations are identified. • Effect on magnetic dichroism measurements and nanoparticle manipulation is discussed.

  14. Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach.

    Science.gov (United States)

    Pusch, Andreas; Wuestner, Sebastian; Hamm, Joachim M; Tsakmakidis, Kosmas L; Hess, Ortwin

    2012-03-27

    Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.

  15. Observation of Bloch oscillations in complex PT-symmetric photonic lattices.

    Science.gov (United States)

    Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf

    2015-12-07

    Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.

  16. Dynamic scattering of electron vortex beams – A Bloch wave analysis

    International Nuclear Information System (INIS)

    Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum () transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±ħ angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in . This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the pendellösung. - Highlights: • Dynamic scattering of vortex beams is analysed using Bloch waves. • Fundamental origins of pendellösung oscillations are identified. • Effect on magnetic dichroism measurements and nanoparticle manipulation is discussed

  17. A supercell, Bloch wave method for calculating low-energy electron reflectivity with applications to free-standing graphene and molybdenum disulfide

    Science.gov (United States)

    McClain, John

    This dissertation reports on a novel theoretical and computational framework for calculating low-energy electron reflectivities from crystalline surfaces and its application to two layered systems of two-dimensional materials, graphene and molybdenum disulfide. The framework provides a simple and efficient approach through the matching of a small set of Fourier components of Bloch wave solutions to the Schrodinger Equation in a slab-in-supercell geometry to incoming and outgoing plane waves on both sides of the supercell. The implementation of this method is described in detail for the calculation of reflectivities in the lowest energy range, for which only specular reflection is allowed. This implementation includes the calculation of reflectivities from beams with normal or off-normal incidence. Two different algorithms are described in the case of off-normal incidence which differ in their dependence on the existence of a symmetry with a mirror plane parallel to the crystal surface. Applications to model potentials in one, two, and three dimensions display consistent results when using different supercell sizes and convergent results with the density of Fourier grids. The design of the Bloch wave matching also allows for the accurate modeling of crystalline slabs through the use of realistic potentials determined via density functional theory. The application of the method to low-energy electron scattering from free-standing systems of a few layers of graphene, including the use of these realistic potentials, demonstrates this ability of the method to accurately model real systems. It reproduces the layer-dependent oscillations found in experimental, normal incidence reflectivity curves for a few layers of graphene grown on silicon carbide. The normal incidence reflectivity curves calculated for slabs consisting of few-layer graphene on 10 layers of nickel show some qualitative agreement with experiment. General incidence reflectivity spectra for free

  18. Bethe-ansatz equations for quantum Heisenberg chains with elliptic exchange

    OpenAIRE

    Inozemtsev, V. I.

    1999-01-01

    The eigenvectors of the Hamiltonian ${\\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.

  19. Bloch oscillations of ultracold atoms and measurement of the fine structure constant; Oscillations de Bloch d'atomes ultrafroids et mesure de la constante de structure fine

    Energy Technology Data Exchange (ETDEWEB)

    Clade, P

    2005-10-15

    From a measurement of the recoil velocity of an atom absorbing a photon, it is possible to deduce a determination of the ratio h/m between the Planck constant and the mass of the atoms and then to deduce a value of the fine structure constant alpha. To do this measurement, we use the technique of Bloch oscillations, which allows us to transfer a large number of recoils to atoms. A velocity sensor, based on velocity selective Raman transition, enables us to measure the momentum transferred to the atoms. A measurement with a statistical uncertainty of 4.4 10{sup -9}, in conjunction with a careful study of systematic effects (5 10{sup -9}), has led us to a determination of alpha with an uncertainty of 6.7 10{sup -9}: {alpha}{sup -1}(Rb) = 137.03599878 (91). This uncertainty is similar to the uncertainty of the best determinations of alpha based on atom interferometry. (author)

  20. Bloch walls and the non-ideal bose gas spectrum

    International Nuclear Information System (INIS)

    The quasi-particle spectrum of non-ideal Bose gas with domain walls in the condensate is investigated. The existence of such a system is determined from solutions of Gross-Pitaevskii equation which represent many-soliton systems. The walls which make the condensate non-uniform are responsible for density and velocity fields ρ(x) and υ(x) repectively. In the laboratory, the Bogoliubov spectrum, supposed to be true for an uniform condensate at rest, is changed due to the velocity field to which the quasi-particles are submited. The spectrum in the laboratory frame is obtained by considering the Galileu invariance principle and the interaction energy between the quasi-particle and its medium. The importance in considering the last two facts is illustrated by the analyse of a constant density condensate which moves uniformly in the laboratory. The many-soliton spectrum configuration and structure function are studied by the Monte Carlo method. In an approximation that assumes the quasi-particle to be point like, the condensate can be treated as locally uniform. For each event the position x of a quasi-particle and its momentum in a frame with velocity υ(x) are determined. Thus, by a convenient Galileu transformation the energy spectrum in the laboratory an be obtained. The results show a phonon spectrum which splits in two branches in the high momenta region. In this region the lower energy branch exibiths a point of minimum. Analogies with the He II are explored. (author)

  1. Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation

    Science.gov (United States)

    Lindgren, I.; Salomonson, S.; Hedendahl, D.

    2005-03-01

    The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.

  2. Dynamics of open quantum spin systems: An assessment of the quantum master equation approach

    CERN Document Server

    Zhao, P; Miyashita, S; Jin, F; Michielsen, K

    2016-01-01

    Data of the numerical solution of the time-dependent Schr\\"odinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects in as much the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-like equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this equation yields a rather poor description of the original data.

  3. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  4. Magnon localization and Bloch oscillations in finite Heisenberg spin chains in an inhomogeneous magnetic field.

    Science.gov (United States)

    Kosevich, Yuriy A; Gann, Vladimir V

    2013-06-19

    We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.

  5. Weighted Composition Operators from α-Bloch Spaces to H∞%α-Bloch空间到H∞的加权复合算子

    Institute of Scientific and Technical Information of China (English)

    唐笑敏

    2007-01-01

    The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces(or little α-Bloch spaces) to H∞, but also gives some estimates for the norm of the weighted composition operator.

  6. Determination of the orientation of pieces of zigzag-Bloch walls in bulk FeSi-single crystals by neutron small-angle scattering

    International Nuclear Information System (INIS)

    Small-angle scattering of neutrons allows the determination of the orientation of Bloch walls in the interior of bulk single crystals. The zigzag angle psi=280 of the 900 Bloch wall and its field dependence are measured. We also observe walls or wall pieces with psi=00. With 1800 walls we measure zigzag angles of psi approximately equal to 300. (orig.)

  7. Bloch oscillating transistor as the readout element for hot electron bolometers

    Science.gov (United States)

    Hassel, Juha; Seppä, Heikki; Lindell, Rene; Hakonen, Pertti

    2004-10-01

    In this paper we analyse the properties of the Bloch oscillating transistor as a preamplifier in cryogenic devices. We consider here especially the readout of hot electron bolometers (HEBs) based on Normal-Superconductor-Insulator tunnel junctions, but the results also apply more generally. We show that one can get an equivalent noise voltage below 1 nV/√Hz with a single BOT. By using N BOTs in a parallel array configuration, a further reduction by factor √N may be achieved.

  8. LDRD final report on Bloch Oscillations in two-dimensional nanostructure arrays for high frequency applications.

    Energy Technology Data Exchange (ETDEWEB)

    Lyo, Sungkwun Kenneth; Pan, Wei; Reno, John Louis; Wendt, Joel Robert; Barton, Daniel Lee

    2008-09-01

    We have investigated the physics of Bloch oscillations (BO) of electrons, engineered in high mobility quantum wells patterned into lateral periodic arrays of nanostructures, i.e. two-dimensional (2D) quantum dot superlattices (QDSLs). A BO occurs when an electron moves out of the Brillouin zone (BZ) in response to a DC electric field, passing back into the BZ on the opposite side. This results in quantum oscillations of the electron--i.e., a high frequency AC current in response to a DC voltage. Thus, engineering a BO will yield continuously electrically tunable high-frequency sources (and detectors) for sensor applications, and be a physics tour-de-force. More than a decade ago, Bloch oscillation (BO) was observed in a quantum well superlattice (QWSL) in short-pulse optical experiments. However, its potential as electrically biased high frequency source and detector so far has not been realized. This is partially due to fast damping of BO in QWSLs. In this project, we have investigated the possibility of improving the stability of BO by fabricating lateral superlattices of periodic coupled nanostructures, such as metal grid, quantum (anti)dots arrays, in high quality GaAs/Al{sub x}Ga{sub 1-x}As heterostructures. In these nanostructures, the lateral quantum confinement has been shown theoretically to suppress the optical-phonon scattering, believed to be the main mechanism for fast damping of BO in QWSLs. Over the last three years, we have made great progress toward demonstrating Bloch oscillations in QDSLs. In the first two years of this project, we studied the negative differential conductance and the Bloch radiation induced edge-magnetoplasmon resonance. Recently, in collaboration with Prof. Kono's group at Rice University, we investigated the time-domain THz magneto-spectroscopy measurements in QDSLs and two-dimensional electron systems. A surprising DC electrical field induced THz phase flip was observed. More measurements are planned to investigate this

  9. Experimental reconstruction of the Berry curvature in a topological Bloch band

    Science.gov (United States)

    Weitenberg, Christof; Flaeschner, Nick; Rem, Benno; Tarnowski, Matthias; Vogel, Dominik; Luehmann, Dirk-Soeren; Sengstock, Klaus

    2016-05-01

    Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Employing fermionic ultracold atoms in a hexagonal optical lattice, we engineer the Berry curvature of the Bloch bands using resonant driving and measure it with full momentum resolution. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures.

  10. Experimental reconstruction of the Berry curvature in a Floquet Bloch band

    Science.gov (United States)

    Fläschner, N.; Rem, B. S.; Tarnowski, M.; Vogel, D.; Lühmann, D.-S.; Sengstock, K.; Weitenberg, C.

    2016-05-01

    Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved measurement of the ensuing Berry curvature. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures.

  11. UGROŽENE VRSTE RIBA U SVIJETU: Mystus vittatus (Bloch, 1794) (Siluriformes: Bagridae)

    OpenAIRE

    Hossain, Yeamin

    2014-01-01

    Autohtona vrsta, Mystus vittatus (Bloch, 1794), pripadnik porodice Bagridae, široke je distribucije u azijskim zemljama, uključujući Bangladeš, Indiju, Pakistan, Šri Lanku, Nepal i Mianmar. Međutim, prirodne populacije ozbiljno opadaju zbog visokog ribolovnog pritiska, gubitka staništa, zagađenja, prirodnih katastrofa, sanacije močvara i prekomjernog poplavnog zamuljivanja pa se stoga nalazi se u kategoriji osjetljive vrste. U članku se predlažu mjere za očuvanje ostatka izolirane populacije ...

  12. Influence of Temperature on Equilibrium Separation Between Vertical Bloch Lines in OHBs in Garnet Bubble Films

    Institute of Scientific and Technical Information of China (English)

    SUN Hui-Yuan; HU Yun-Zhi; LIU Li-Hu

    2009-01-01

    The diameters of the ordinary hard bubbles (OHBs) and soft bubbles in epitaxial garnet films are measured under the microscope at various temperatures. It is found that the bubble diameters of OHBs increase with temperature, and it is concluded that the equilibrium separation between two neighbouring vertical Bloch lines (VBLs) Seq is widened with increasing temperature. At the same time, the results can be understood simply as that there are more VBLs in the domain walls of the first dumbbell domains (IDs) than those in walls of OH Bs at the same temperature.

  13. High sensitivity, low-systematics atom interferometers using Bragg diffraction and Bloch oscillations

    CERN Document Server

    Estey, Brian; Müller, Holger; Kuan, Pei-Chen; Lan, Shau-Yu

    2014-01-01

    We describe a new scheme for atom interferometry based on both large-momentum transfer Bragg beam splitters and Bloch oscillations. Combining the advantages of previous approaches to recoil-sensitive interferometers, we increase the signal and suppress a systematic phase shift caused by Bragg diffraction at least 60-fold, matching experiment to theory; the systematic shift can be eliminated from Mach-Zehnder interferometers. We demonstrate high contrast, interference with up to 4.4 million radians of phase difference between freely evolving matter waves, and a resolution of $\\delta \\alpha/\\alpha=0.33\\,$ppb$\\sqrt{\\rm 6h}$ available to measurements of the fine structure constant.

  14. Nontrivial Bloch oscillations in waveguide arrays with second-order coupling.

    Science.gov (United States)

    Wang, Gang; Huang, Ji Ping; Yu, Kin Wah

    2010-06-01

    Under the influence of the next-nearest-neighbor interaction, we theoretically investigate the occurrence of Bloch oscillations in zigzag waveguide arrays. Because of the special topological configuration of the lattice itself, the second-order coupling (SOC) can be enhanced significantly and leads to the band alteration beyond the nearest-neighbor model, i.e., the offset of minimum value from the band edge. Contrary to the behavior in the vanishing SOC, the oscillation patterns exhibit new features, namely, a double turning-back occurs when the beam approaches the band edge. Our results can be applied to some ordered-lattice systems.

  15. Bloch Oscillations of Cold Atoms in a Cavity: Effects of Quantum Noise

    CERN Document Server

    Venkatesh, B Prasanna

    2013-01-01

    In this communication we extend our theory of Bloch oscillations of cold atoms inside an optical cavity [Venkatesh et al., Phys. Rev. A 80, 063834 (2009)] to include the effects of quantum noise. By solving the coupled dynamics of linearized fluctuations about the atomic and optical meanfields, we are able to include the effects of quantum measurement backaction upon the atoms and ultimately examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the cold atom cavity-QED context.

  16. On-chip optical isolation via unidirectional Bloch oscillations in a waveguide array.

    Science.gov (United States)

    Kumar, Pradeep; Levy, Miguel

    2012-09-15

    We propose to use the unidirectionality of the optical Bloch oscillation phenomenon achievable in a magneto-optic asymmetric waveguide array to achieve optical isolation. At the 1.55 μm telecommunication wavelength, our isolator design exhibits an isolation ratio of 36 dB between forward- and backward-propagating waves. The proposed design consists of a waveguide array made in a silicon-on-insulator substrate with a magnetic garnet cover layer. A key role is played by the transverse-magnetic mode nonreciprocal phase shift effect.

  17. Bloch oscillations of quasispin polaritons in a magneto-optically controlled atomic ensemble

    CERN Document Server

    Jiang, Chang; Zhou, Lan

    2012-01-01

    We consider the propagation of a quantized polarized light in a magneto-optically manipulated atomic ensemble with a tripod configuration. Polariton formalism is applied when the medium is subjected to a washboard magnetic field under electromagnetically induced transparency. The dark-state polariton with multiple components is achieved. We analyze quantum dynamics of the dark-state polariton by some experiment data from rubidium D1-line. It is found that one component propagates freely, however the wavepacket trajectory of the other component performs Bloch oscillations.

  18. Stopping and time reversal of light in dynamic photonic structures via Bloch oscillations.

    Science.gov (United States)

    Longhi, Stefano

    2007-02-01

    It is theoretically shown that storage and time reversal of light pulses can be achieved in a coupled-resonator optical waveguide by dynamic tuning of the cavity resonances without maintaining the translational invariance of the system. The control exploits the Bloch oscillation motion of a light pulse in the presence of a refractive index ramp, and it is therefore rather different from the mechanism of adiabatic band compression and reversal proposed by Yanik and Fan in recent works [Phys. Rev. Lett., 92, 083901 (2004); 93, 173903 (2004)].

  19. An Optical Parametric Amplifier in Photonic Crystals of Nondispersive Medium with Perfect Bloch Phase Matching

    Institute of Scientific and Technical Information of China (English)

    CHEN Li-Xue(陈历学); KIM Dalwoo; SONG Ying-Lin(宋瑛琳); DING Wei-Qiang(丁卫强); LI Wen-Hui(李文惠); LIU Shu-Tian(刘树田)

    2004-01-01

    One-dimensional photonic crystal of second-order nonlinearity is studied. Among the three waves of the parametric interaction process of down-conversion with a nondispersive medium, two gap-edge localized modes and one travelling-mode are proposed, and an exact phase matching condition is realized using the periodic condition of the Bloch phase. Numerical simulation is implemented by the slow-envelope finite difference time domain method. In the case of a pulse wave pump of amplitude half-width 5.2 × 10-13 s, an intense optical parametric pulse with half-width about 5 × 10-14 s is observed.

  20. Toxicity studies of butachlor to the freshwater fish Channa punctata (Bloch).

    Science.gov (United States)

    Tilak, K S; Veeraiah, K; Bhaskara Thathaji, P; Butchiram, M S

    2007-04-01

    The toxicity studies were conducted on the fish Channa punctata (Bloch) by employing static and continuous flow through systems, for the toxicant butachlor (technical grade+) and its commercial formulation+ (machete 50% EC). The LC50 values are 297.89 ppb and 247.46 ppb for 24 hr and 48 hr in static for technical and 636.45 and 546.09 for machete. In continuous flow through the values are 270.05, 233.52 to the technical and 567.85 and 481.49 respectively for machete. The tissues show qualitative accumulation and were quantitatively analysed by gas liquid chromatography (GLC).

  1. Extraction of optical Bloch modes in a photonic-crystal waveguide

    CERN Document Server

    Huisman, S R; Stobbe, S; Herek, J L; Lodahl, P; Vos, W L; Pinkse, P W H

    2011-01-01

    We perform phase-sensitive near-field scanning optical microscopy on photonic-crystal waveguides. The observed intricate field patterns are analyzed by spatial Fourier transformations, revealing several guided TE- and TM-like modes. Using the reconstruction algorithm proposed by Ha, et al. (Opt. Lett. 34 (2009)), we decompose the measured two-dimensional field pattern in a superposition of propagating Bloch modes. This opens new possibilities to study specific modes in near-field measurements. We apply the method to study the transverse behavior of a guided TE-like mode, where the mode extends deeper in the surrounding photonic crystal when the band edge is approached.

  2. EMUstack: An open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method

    Science.gov (United States)

    Sturmberg, Björn C. P.; Dossou, Kokou B.; Lawrence, Felix J.; Poulton, Christopher G.; McPhedran, Ross C.; Martijn de Sterke, C.; Botten, Lindsay C.

    2016-05-01

    We describe EMUstack, an open-source implementation of the Scattering Matrix Method (SMM) for solving field problems in layered media. The fields inside nanostructured layers are described in terms of Bloch modes that are found using the Finite Element Method (FEM). Direct access to these modes allows the physical intuition of thin film optics to be extended to complex structures. The combination of the SMM and the FEM makes EMUstack ideally suited for studying lossy, high-index contrast structures, which challenge conventional SMMs.

  3. Riccati equations

    Directory of Open Access Journals (Sweden)

    Lloyd K. Williams

    1987-01-01

    Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.

  4. Surface acoustic BLOCH oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling in a solid.

    Science.gov (United States)

    de Lima, M M; Kosevich, Yu A; Santos, P V; Cantarero, A

    2010-04-23

    We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The use of a planar geometry for the realization of the Bloch oscillations and Landau-Zener tunneling allows a direct access to the elastic field distribution. The vertical surface displacement has been measured by interferometry.

  5. Demonstration of photon Bloch oscillations and Wannier-Stark ladders in dual-periodical multilayer structures based on porous silicon.

    Science.gov (United States)

    Estevez, J Octavio; Arriaga, Jesús; Mendez-Blas, Antonio; Reyes-Ayona, Edgar; Escorcia, José; Agarwal, Vivechana

    2012-07-23

    : Theoretical demonstration and experimental evidence of photon Bloch oscillations and Wannier-Stark ladders (WSLs) in dual-periodical (DP) multilayers, based on porous silicon, are presented. An introduction of the linear gradient in refractive indices in DP structure, which is composed by stacking two different periodic substructures N times, resulted in the appearance of WSLs. Theoretical time-resolved reflection spectrum shows the photon Bloch oscillations with a period of 130 fs. Depending on the values of the structural parameters, one can observe the WSLs in the near infrared or visible region which may allow the generation of terahertz radiation with a potential applications in several fields like imaging.

  6. Combination of BLOCH oscillations with a Ramsey-Bordé interferometer: new determination of the fine structure constant.

    Science.gov (United States)

    Cadoret, Malo; de Mirandes, Estefania; Cladé, Pierre; Guellati-Khélifa, Saïda; Schwob, Catherine; Nez, François; Julien, Lucile; Biraben, François

    2008-12-01

    We report a new experimental scheme which combines atom interferometry with Bloch oscillations to provide a new measurement of the ratio h/mRb. By using Bloch oscillations, we impart to the atoms up to 1600 recoil momenta and thus we improve the accuracy on the recoil velocity measurement. The deduced value of h/mRb leads to a new determination of the fine structure constant alpha(-1) =137.03599945 (62) with a relative uncertainty of 4.6 x 10(-9). The comparison of this result with the value deduced from the measurement of the electron anomaly provides the most stringent test of QED.

  7. Nonperturbative shell correction to the Bethe-Bloch formula for the energy losses of fast charged particles

    Science.gov (United States)

    Matveev, V. I.; Makarov, D. N.

    2011-09-01

    A simple method including nonperturbative shell corrections has been developed for calculating energy losses on complex atoms. The energy losses of fast highly charged ions on neon, argon, krypton, and xenon atoms have been calculated and compared with experimental data. It has been shown that the inclusion of the non-perturbative shell corrections noticeably improves agreement with experimental data as compared to calculations by the Bethe-Bloch formula with the standard corrections. This undoubtedly helps to reduce the number of fitting parameters in various modifications of the Bethe-Bloch formula, which are usually determined semiempirically.

  8. Quantum Diffraction of Wave Function in Time-domain by Bloch Vector Model%波函数时域衍射的布洛赫矢量模型

    Institute of Scientific and Technical Information of China (English)

    刘碧蕊; 伏振兴

    2014-01-01

    To explore the physical mechanism and the essence of the quantum diffraction in time-domain, the wave function diffraction in time-domain of a two-level system under the pulse field with a chirped frequency is investigated by means of the density matrix equation and the Bloch vector model. The modulations of the quantum diffraction by the chirped factors are discussed. The dynamic evolution process of the population transfer and the effect of the quantum diffraction with different chirped factors are analyzed. The interaction mechanism and the physical process can found a clear description in the Bloch vector picture.%为了揭示波函数时域衍射的物理本质,采用密度矩阵的矢量模型方法,研究线性啁啾脉冲光场作用下二能级系统波函数的时域衍射效应;讨论光场啁啾因子对时域衍射效应的调制作用;分析不同啁啾因子作用时,量子系统粒子布居转移和时域衍射效应的动态演化过程。在布洛赫矢量表象下,对时域衍射效应的物理作用机制给出了清晰的描述。

  9. Dynamics of Bloch State Positronium Emission from MOF Targets Studied via Rydberg TOF Spectroscopy

    Science.gov (United States)

    Piñeiro Escalera, Alina; Jones, Adric; Mills, Allen

    2016-05-01

    Recent advances in the efficient production and detection of Rydberg positronium (Ps) have made it possible to perform energy- and angle- resolved time-of-flight (TOF) spectroscopy with Ps. We report here TOF measurements of Ps emission from the metal-oxide framework (MOF) targets, MOF-5 and ZIF-8. MOFs are a recently synthesized class of chemical structures, characterized by high long-range order and large surface area to volume ratios (i.e., they are highly porous and uniform, crystalline materials). Ps is found to be emitted predominantly in a series of monoenergetic peaks, providing clear evidence of Ps Bloch states. Measuring the relative populations of the monoenergetic peaks, as a function of implantation energy and target temperature, provides insight into the target-dependent dynamics of Bloch state Ps. Work supported by the U.S. National Science Foundation Grants No. PHY 1206100 and No. PHY 1040590 and the National Science Foundation Graduate Research Fellowship Progam (NSF-GRFP). DOE BES DE-FG02-13ER46972 (MOF-5 synthesis and characterization).

  10. Wannier-Bloch approach to localization in high harmonics generation in solids

    CERN Document Server

    Osika, Edyta N; Ortmann, Lisa; Suárez, Noslen; Pérez-Hernández, Jose Antonio; Szafran, Bartłomiej; Ciappina, Marcelo F; Sols, Fernando; Landsman, Alexandra S; Lewenstein, Maciej

    2016-01-01

    Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine with any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process, and hence addresses precisely the question of localization of harmonic emission...

  11. Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere.

    Science.gov (United States)

    Oh, Sangchul; Hu, Xuedong; Nori, Franco; Kais, Sabre

    2016-01-01

    Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov-Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs. PMID:26916031

  12. Creating full-Bloch Bose-Einstein condensates with Raman q-plates

    Science.gov (United States)

    Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.

    2016-06-01

    A coherent two-photon optical Raman interaction in a pseudo-spin-1/2 Bose-Einstein condensate (BEC) serves as a q-plate for atoms, converting spin to orbital angular momentum. This Raman q-plate has a singular pattern in its polarization distribution in analogy to the singular birefringent q-plates used in singular optics. The vortex winding direction and magnitude as well as the final spin state of the BEC depend on the initial spin state and the topology of the optical Raman q-plate beams. Drawing on the mathematical and geometric foundations of singular optics, we derive the equivalent Jones matrix for this Raman q-plate and use it to create and characterize atomic spin singularities in the BEC that are analogous to optical C-point singularities in polarization. By tuning the optical Raman parameters, we can generate a coreless vortex spin texture which contains every possible superposition in a two-state system. We identify this spin texture as a full-Bloch BEC since every point on the Bloch sphere is represented at some point in the cross section of the atomic cloud. This spin-orbit interaction and the spin textures it generates may allow for the observation of interesting geometric phases in matter waves and lead to schemes for topological quantum computation with spinor BECs.

  13. Dynamic scattering of electron vortex beams--a Bloch wave analysis.

    Science.gov (United States)

    Mendis, B G

    2015-02-01

    Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum (〈Lz〉) transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the 〈Lz〉 pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±ħ angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in 〈Lz〉. This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the 〈Lz〉 pendellösung.

  14. Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate

    CERN Document Server

    Schultz, Justin T; Murphree, Joseph D; Jayaseelan, Maitreyi; Bigelow, Nicholas P

    2016-01-01

    We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin-1/2 system. The spin state of a spin-1/2 quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases, and the relative frequencies. We experimentally demonstrate key features of this model with a $^{87}$Rb spinor Bose-Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.

  15. Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation

    CERN Document Server

    Dohnal, Tomas; Plum, Michael; Reichel, Wolfgang

    2012-01-01

    We consider the problem of verifying the existence of $H^1$ ground states of the 1D nonlinear Schr\\"odinger equation for an interface of two periodic structures: $$-u" +V(x)u -\\lambda u = \\Gamma(x) |u|^{p-1}u \\ {on} \\R$$ with $V(x) = V_1(x), \\Gamma(x)=\\Gamma_1(x)$ for $x\\geq 0$ and $V(x) = V_2(x), \\Gamma(x)=\\Gamma_2(x)$ for $x1$. The article [T. Dohnal, M. Plum and W. Reichel, "Surface Gap Soliton Ground States for the Nonlinear Schr\\"odinger Equation," \\textit{Comm. Math. Phys.} \\textbf{308}, 511-542 (2011)] provides in the 1D case an existence criterion in the form of an integral inequality involving the linear potentials $V_{1},V_2$ and the Bloch waves of the operators $-\\tfrac{d^2}{dx^2}+V_{1,2}-\\lambda$. We choose here the classes of piecewise constant and piecewise linear potentials $V_{1,2}$ and check this criterion for a set of parameter values. In the piecewise constant case the Bloch waves are calculated explicitly and in the piecewise linear case verified enclosures of the Bloch waves are computed ...

  16. Magnetic Bloch oscillations in the near-Ising antiferromagnet CoCl2#center dot#2D2O

    DEFF Research Database (Denmark)

    Christensen, N.B.; Lefmann, K.; Johannsen, I.;

    2000-01-01

    We have investigated the possible occurrence of magnetic Bloch oscillations in CoCl2 . 2D(2)O. We were unable to observe these oscillations at 20.0 K, just above T-N. In an attempt to explain this result, we studied spin waves in the a*-c* plane in order to estimate the effect of the interchain...

  17. Spontaneous emission of Bloch oscillation radiation under the competing influences of microcavity enhancement and inhomogeneous interface degradation

    Energy Technology Data Exchange (ETDEWEB)

    Sokolov, V. N. [Department of Theoretical Physics, Institute for Semiconductor Physics, NASU, Pr. Nauki 41, Kiev 03028 (Ukraine); Iafrate, G. J. [Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695-8617 (United States)

    2014-02-07

    A theory for the spontaneous emission (SE) of terahertz radiation for a Bloch electron traversing a single energy miniband of a superlattice (SL) in a cavity, while undergoing elastic scattering is presented. The Bloch electron is accelerated under the influence of a superimposed external constant electric field and an internal inhomogeneous electric field, while radiating into a microcavity. The analysis of the SE accounts for both the spectral structure of nonharmonic miniband components and the Bloch oscillation degradation effects arising from elastic scattering due to SL interface roughness. The interface roughness effects are decomposed into contributions arising from independent planar and cross-correlated neighboring planar interfaces; parametric numerical estimates show that the cross-correlated contribution to the SE relaxation rate is relatively small, representing less than roughly 10% of the total relaxation rate. It is shown that the degradation effects from SL interface roughness can be more than compensated for by the enhancements derived from microcavity-based tuning of the emission frequency to the cavity density of states peak. The theoretical approach developed herein has general applicability beyond its use for elastic scattering due to interface roughness. As well, the results obtained in this analysis can be useful in the development of SL-based Bloch-oscillator terahertz devices.

  18. Bloch Brane

    CERN Document Server

    Bazeia, D

    2004-01-01

    We investigate a system described by two real scalar fields coupled with gravity in (4, 1) dimensions in warped spacetime involving one extra dimension. The results show that the parameter which controls the way the two scalar fields interact induces the appearence of thick brane which engenders internal structure, driving the energy density to localize inside the brane in a very specific way.

  19. Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations.

    Science.gov (United States)

    Meinert, F; Mark, M J; Kirilov, E; Lauber, K; Weinmann, P; Gröbner, M; Nägerl, H-C

    2014-05-16

    We study atomic Bloch oscillations in an ensemble of one-dimensional tilted superfluids in the Bose-Hubbard regime. For large values of the tilt, we observe interaction-induced coherent decay and matter-wave quantum phase revivals of the Bloch oscillating ensemble. We analyze the revival period dependence on interactions by means of a Feshbach resonance. When reducing the value of the tilt, we observe the disappearance of the quasiperiodic phase revival signature towards an irreversible decay of Bloch oscillations, indicating the transition from regular to quantum chaotic dynamics.

  20. Beautiful equations

    Science.gov (United States)

    Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

    2014-07-01

    In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

  1. Effects of gamma radiations on certain tissues of heteropneustes fossils bloch

    International Nuclear Information System (INIS)

    In the present investigation effect of gamma radiation on certain tissues (kidney, stomach and gills) of Heteropneustes fossilis Bloch, an Indian Cat fish, were studied. The fish were irradiated with 10 Gy of gamma radiations at the dose rate of 1.60 Gy/minute from a 60Co source. Five fish were autopsied at each post-irradiation time of 1,2,3,7,15 and 30 days. Radiation induced histopathology was observed in all the tissues studied. The radio lesions appeared on day-1 after exposure which became exaggerated on day-2 and 3. Signs of recovery were noticed on day-7 which progressed on day-15 and normal histology was observed on day-30. (author). 18 refs

  2. Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC

    Science.gov (United States)

    Stirling, W. J.; Vryonidou, E.

    2013-04-01

    We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2 → 2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/γ+jet and also the ratio of Z to γ production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak corrections. We also comment on the effect of electroweak corrections and the presence of BN violation for QCD processes, in particular dijet production, and also for purely electroweak processes such as W + H and W + Z associated production.

  3. Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC

    CERN Document Server

    Stirling, W J

    2013-01-01

    We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2-to-2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/photon+jet and also the ratio of Z to photon production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak corrections. We also comment on the effect of electroweak corrections and the presence of BN violation for QCD processes, in particular dijet production, and also for purely electroweak processes such as W + H and W + Z associated production.

  4. Bloch oscillations of ultracold atoms and measurement of the fine structure constant

    International Nuclear Information System (INIS)

    From a measurement of the recoil velocity of an atom absorbing a photon, it is possible to deduce a determination of the ratio h/m between the Planck constant and the mass of the atoms and then to deduce a value of the fine structure constant alpha. To do this measurement, we use the technique of Bloch oscillations, which allows us to transfer a large number of recoils to atoms. A velocity sensor, based on velocity selective Raman transition, enables us to measure the momentum transferred to the atoms. A measurement with a statistical uncertainty of 4.4 10-9, in conjunction with a careful study of systematic effects (5 10-9), has led us to a determination of alpha with an uncertainty of 6.7 10-9: α-1(Rb) = 137.03599878 (91). This uncertainty is similar to the uncertainty of the best determinations of alpha based on atom interferometry. (author)

  5. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations

    CERN Document Server

    Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R

    2016-01-01

    Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...

  6. Chirped dual periodic structures for photonic Bloch oscillations and Zener tunneling.

    Science.gov (United States)

    Estevez, J O; Arriaga, J; Reyes-Ayona, E; Agarwal, V

    2015-06-29

    Experimental evidence of photon Wannier-stark ladders (WSLs) and Zener tunneling (ZT) in one dimensional dual-periodical (DP) optical superlattices based on Porous Silicon (PSi), is presented. An introduction of linear gradient in physical thickness of the layers, composed of five stacks of two different periodic substructures, resulted in the appearance of four WSLs resonances and resonant Zener tunneling of nearest resonances of two consecutive WSLs. Theoretical analysis of time-resolved reflection spectra as a function of gradient reveals the presence of photonic Bloch oscillations (BOs) and an eventual tunneling at a specific value of linear gradient (20%), has been demonstrated through scattering maps. Measured reflection from different DP photonic structures confirm the presence of minibands, WSLs and ZT in the near infrared region.

  7. Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/m Rb.

    Science.gov (United States)

    Battesti, Rémy; Cladé, Pierre; Guellati-Khélifa, Saïda; Schwob, Catherine; Grémaud, Benoît; Nez, François; Julien, Lucile; Biraben, François

    2004-06-25

    We use Bloch oscillations in a horizontal moving standing wave to transfer a large number of photon recoils to atoms with a high efficiency (99.5% per cycle). By measuring the photon recoil of 87Rb, using velocity-selective Raman transitions to select a subrecoil velocity class and to measure the final accelerated velocity class, we have determined h/m(Rb) with a relative precision of 0.4 ppm. To exploit the high momentum transfer efficiency of our method, we are developing a vertical standing wave setup. This will allow us to measure h/m(Rb) better than 10(-8) and hence the fine structure constant alpha with an uncertainty close to the most accurate value coming from the (g-2) determination.

  8. Backaction-driven transport of Bloch oscillating atoms in ring cavities.

    Science.gov (United States)

    Goldwin, J; Venkatesh, B Prasanna; O'Dell, D H J

    2014-08-15

    We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counterpropagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.

  9. Tunable hybridization at midzone and anomalous Bloch-Zener oscillations in optical waveguide ladders.

    Science.gov (United States)

    Zheng, Ming Jie; Wang, Gang; Yu, Kin Wah

    2010-12-01

    We have studied the optical oscillation and tunneling of light waves in optical waveguide ladders (OWLs) formed by two coupled planar optical waveguide arrays. For the band structure, a midzone gap is formed owing to band hybridization, and its wavenumber position can be tuned throughout the whole Brillouin zone, which is different from the Bragg gap. By imposing a gradient in the propagation constant in each array, Bloch-Zener oscillation (BZO) is realized with Zener tunneling between the bands occurring at the midzone, which is contrary to the common BZO with tunneling at the center or edge of the Brillouin zone. The occurrence of BZO is demonstrated by using the field-evolution analysis. The tunable hybridization at the midzone enhances the tunability of BZO in the OWLs. This Letter may offer new insights into the coherent phenomena in optical lattices.

  10. Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices.

    Science.gov (United States)

    Xiao, Fajun; Zhu, Weiren; Shang, Wuyun; Wang, Meirong; Zhang, Peng; Liu, Sheng; Premaratne, Malin; Zhao, Jianlin

    2016-08-01

    We report on the existence of optical Bloch oscillations (OBOs) and Zener tunneling (ZT) of Airy beams in ionic-type photonic lattices with a refractive index ramp. Different from their counterparts in uniform lattices, Airy beams undergoing OBOs show an alternatively switched concave and convex trajectory as well as a periodical revival of input beam profiles. Moreover, the ionic-type photonic lattice established in photorefractive crystal exhibits a reconfigurable lattice structure, which provides a flexible way to tune the amplitude and period of the OBOs. Remarkably, it is demonstrated that the band gap of the lattice can be readily controlled by rotating the lattice inducing beam, which forces the ZT rate to follow two significant different decay curves amidst decreasing index gradient. Our results open up new possibilities for all-optical switching, routing and manipulation of Airy beams.

  11. Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

    CERN Document Server

    Graefe, E M; Rush, A

    2016-01-01

    Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.

  12. Coexisting localized and extended optical Bloch states in a periodic deep wire array microcavity

    Science.gov (United States)

    Löchner, Franz J. F.; Mischok, Andreas; Brückner, Robert; Lyssenko, Vadim G.; Zakhidov, Alexander A.; Fröb, Hartmut; Leo, K.

    2015-09-01

    We embed periodic SiO2 wires in an organic microcavity, producing a rectangular potential by the different optical thicknesses of the active layer due to the additional SiO2 layer. By μ -photoluminescence spectroscopy, we observe the energy dispersion of the photons and obtain discrete localized below and extended Bloch states above the potential barrier, respectively, showing that electro-magnetic waves can behave like massive particles, such as electrons, in crystal lattices. We investigate the dependencies on wire width and period and use the Kronig-Penney model to describe the photon energy dispersion, including an "effective mass" of a photon propagating through a microcavity implying polarization splitting. We obtain excellent agreement between experiment, simulation and analytical calculation.

  13. Measuring the fine structure constant with Bragg diffraction and Bloch oscillations

    Science.gov (United States)

    Yu, Chenghui; Estey, Brian; Parker, Richard; Dudley, Jordan; Müller, Holger

    2016-05-01

    We have demonstrated a new scheme for atom interferometry based on large-momentum-transfer Bragg beam splitters and Bloch oscillations. In this new scheme, we have achieved a resolution of δα / α =0.25ppb in the fine structure constant measurement, which gives up to 4.4 million radians of phase difference between freely evolving matter waves. We have suppressed many systematic effects known in most atom interferometers with Raman beam splitters such as light shift, Zeeman effect shift as well as vibration. We have also simulated multi-atom Bragg diffraction to understand sub-ppb systematic effects, and implemented spatial filtering to further suppress systematic effects. We present our recent progress toward a measurement of the fine structure constant, which will provide a stringent test of the standard model of particle physics.

  14. Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory

    CERN Document Server

    Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis

    2003-01-01

    The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).

  15. Dynamics of cold bosons in optical lattices: effects of higher Bloch bands

    Science.gov (United States)

    Łącki, Mateusz; Delande, Dominique; Zakrzewski, Jakub

    2013-01-01

    The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.

  16. THE ACTION OF CORAGEN INSECTICIDE ON CERTAIN PHYSIOLOGICAL BIOMARKERS ON CARASSIUS AURATUS GIBELIO BLOCH L. 1758

    Directory of Open Access Journals (Sweden)

    Claudiu Alexandru Baciu

    2015-12-01

    Full Text Available In our researches we have determined the variation of certain physiological indexes, such as the oxygen consume, the breathing rhythm, the glycaemia and the number of red blood cells under the action of Coragen insecticide on Carassius auratus gibelio Bloch. Under the action of Coragen, we have registered significant changes in the oxygen consume, the breathing rhythm, the number of red blood cells and glycemia at the Carassius auratus gibelio Bloch items, considered as answers to the stress provoked by emissions. The highest variations of the physiological indexes, from the perspective of the percentage, were noticed at the glycemia, which at the mark was 28 mg/dl, and in the treated sample, with 0.1 ml/l Coragen is 42 mg/dl, representing a 50% growth and at the breathing rhythm in 24 hours, where values significantly decreased with 41.18% at the concentration of 0.07 ml/l and with 39.33% at the concentrations of 0.05 and 0.1 ml/l Coragen. The slightest variations of the physiological indexes, from the perspective of percentage, were noticed at the oxygen consumption, which, at the mark is of 55.302 ml oxygen/kg/hour, and for the treated sample, with 0.1 ml/l Coragen is 34.81 ml oxygen/kg/hour, representing a decrease of 37.06% in 24 hours and the number of red blood cells, where the values have significantly decrease with 9.58%, 13.48%, respectively 18.44% for the concentrations of 0.05, 0.07 and 0.1 ml/l Coragen.

  17. Dieta do tucunaré-amarelo Cichla monoculus (Bloch & Schneider) (Osteichthyes, Cichlidae), no Reservatório de Lajes, Rio de Janeiro, Brasil Diet of Cichla monoculus (Bloch & Schneider) (Osteichthyes, Cichlidae) in Lajes' Reservoir, Rio de Janeiro, Brazil

    OpenAIRE

    Luciano Neves dos Santos; Alejandra Filippo Gonzalez; Francisco Gerson de Araújo

    2001-01-01

    The diet of Cichla monoculus (Bloch & Schneider, 1801) in Lajes's Reservoir, a major impoundment in Rio de Janeiro State, Brazil, was assessed, from fishes collected in 1994,1996 and 1999/2000. Gut contents in individuals was analyzed by the index of relative importance (IRI) which deals with numerical, gravimetrical and frequency of occurrence. Cichla monoculus showed a strong piscivorous habits feeding on Cichlidae, Characidae and Pimelodidae, in decreasing order of importance, with a remar...

  18. An Optomechanical Elevator: Transport of a Bloch Oscillating Bose–Einstein Condensate up and down an Optical Lattice by Cavity Sideband Amplification and Cooling

    Directory of Open Access Journals (Sweden)

    B. Prasanna Venkatesh

    2015-12-01

    Full Text Available In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose–Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force, such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a high-finesse optical cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice depth at the Bloch frequency which can in turn transport the atoms up or down the lattice. In the optomechanical picture, the transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the Bloch oscillator. Depending on the sign of the pump-cavity detuning, atoms are transported either with or against the bias force accompanied by an up- or down-conversion of the frequency of the pump laser light. We also evaluate the prospects for using the optomechanical Bloch oscillator to make continuous measurements of forces by reading out the Bloch frequency. In this context, we establish the significant result that the optical spring effect is absent and the Bloch frequency is not modified by the backaction.

  19. Rogue-wave interaction of the generalized variable-coefficient Hirota–Maxwell–Bloch system in fiber optics

    International Nuclear Information System (INIS)

    In this paper, a generalized variable-coefficient Hirota–Maxwell–Bloch system is investigated, which can describe the propagation of optical solitons in an erbium-doped optical fiber. Higher-step generalized Darboux transformation and rogue-wave solutions are obtained. Rogue-wave interaction is analyzed as follows: (1) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the first-step rogue waves for the modulus of the normalized slowly varying amplitude of the complex pulse envelope, modulus of the measure of the polarization of the resonant medium and extant population inversion; (2) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the second-step rogue-wave interaction. Those phenomena can not be attained through the existing Hirota–Maxwell–Bloch system

  20. Bloch oscillation and Landau-Zener tunnelling in a modulated optical lattice in a photovoltaic photorefractive crystal

    Institute of Scientific and Technical Information of China (English)

    Zhang Bing-Zhi; Cui Hu; Li Xiang-Heng; She Wei-Long

    2009-01-01

    We theoretically study the beam dynamical hehaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau-Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau-Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau-Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.

  1. On the zero-field orbital magnetic susceptibility of Bloch electrons in graphene-like solids: Some rigorous results

    CERN Document Server

    Savoie, Baptiste

    2012-01-01

    Starting with a nearest-neighbors tight-binding model, we rigorously investigate the bulk zero-field orbital susceptibility of a non-interacting Bloch electrons gas in graphene-like solids at fixed temperature and density of particles. In the zero-temperature limit and in the semiconducting situation, we derive a complete expression which holds for an arbitrary number of bands with possible degeneracies. In the particular case of a two-bands gapped model, all involved quantities are exactly written down. Besides the formula we obtain have the special feature to be suitable for numerical computations since it only involves the eigenvalues and associated eigenfunctions of the Bloch Hamiltonian, together with the derivatives (up to the second order) w.r.t. the quasi-momentum of the matrix-elements of the Bloch Hamiltonian. Finally we give a simple application for the two-bands gapped model by considering the case of a dispersion law which is linear w.r.t. the quasi-momentum in the gapless limit. Through this ins...

  2. Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\\"odinger equation

    OpenAIRE

    Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.

    2014-01-01

    Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in gene...

  3. The analysis of cytochrome b nucleotidic sequence for Carassius gibelio (Bloch, 1782

    Directory of Open Access Journals (Sweden)

    Lucian D. Gorgan

    2009-01-01

    Full Text Available The paper is part of a larger scale study for some genes` (Cytb, ND4L and D-loop nucleotidic structure identification by sequencing, to distinguish the structural differences and their exact length inase pairs. Research was carried out on individuals of Carassius gibelio (Bloch, 1782 (Actinopterygii,Cypriniformes from two different populations, Iezăreni and Movileni (Iaşi, from which dorsal musculartissue was sampled. Mitochondrial DNA (mtDNA isolation and purification was carried out automaticallyusing Promega’s Maxwell 16 (SEV module. Cytochrome b (cytb was multiplied by a two stage>polymerase chain reaction (PCR, using two sets of complementary primers (1 set for each fragment.Direct sequencing of PCR products revealed that the cytochrome b has one sequence of 1140bp. Theobtained sequences were subsequently compared with sequences of the same gene from otherindividuals within this species, towards identifying possible differences in the nucleotidic structure.Key Words: Carassius, cytocrhome b, mtDNA.

  4. Establishment of a cell line from kidney of seabass, Lates calcarifer (Bloch

    Directory of Open Access Journals (Sweden)

    Phromkunthong, W.

    2003-01-01

    Full Text Available Primary cell culture from caudal fin and kidney of seabass (Lates calcarifer Bloch using tissue explant method were cultured in three different medias with various salt concentrations. Only seabass kidney (SK cells grew well in Leibovitze's-15 medium containing 8 g/l of NaCl supplemented with 10 % fetal bovine serum at an optimum temperature of 25 oC. Over a period of 24 months, SK cells were subcultured over than 75 passages and exhibited epithelial-like cells. The chromosome number of SK cells was 42. The cells were found to be free from bacterial, fungal and mycoplasma contamination. Seabass cells can be kept at -80 oC and/or in liquid nitrogen (-196 oC for at least 24 months with a survival rate of 83.20 and 74.50 %, respectively. Nine fish viruses were tested for their infectivity and this SK cells were susceptible to sand goby virus (SGV, chub reovirus (CRV, snake-head rhabdovirus (SHRV, red seabream iridovirus (RSIV, seabass iridovirus (SIV and grouper iridovirus-2 (GIV-2.

  5. Cadmium induced histopathology in the olfactory epithelium of a snakehead fish, Channa punctatus (Bloch

    Directory of Open Access Journals (Sweden)

    Debraj Roy

    2013-10-01

    Full Text Available Histopathology on the olfactory organ of a snakehead fish, Channa punctatus (Bloch, 1793 were assessed after exposing the fish to 2.5 mg/L and 5mg/L of CdCl2 for 15 days, 30 days and 45 days. Cellular organization of the epithelium was affected severely with degeneration of sensory and supporting cells and hyperplasia of basal cells and mucous cells. Mucous cell proliferation indicates the upregulation of mucous secretion to protect the epithelium from toxic effect of cadmium. The olfactory epithelium was endowed with the multipotent basal cells which differentiate into sensory cells, supporting cells and other cell types of the epithelium during normal cells turn over and in the event of cell death.  However, due to cadmium exposure proliferating basal cells failed to differentiate into normal cells and the undifferentiated proliferated cell formed lump and intraepithelial lesion altering the composition of the entire epithelium. Present study indicates that in prolonged exposure to cadmium chloride olfactory functions of the fish might be impaired due to loss of all sensory cells.

  6. Genetic Diversity Analysis of Lates calcarifer (Bloch 1790 in Captive and Wild Populations Using RAPD Markers

    Directory of Open Access Journals (Sweden)

    Muthusamy RAJASEKAR

    2012-08-01

    Full Text Available Lates calcarifer (Bloch 1790 is one of the major economically important cultivable fish species in India. In this study, three populations of L. calcarifer was selected to assess the genetic diversity. Of which, two wild (Mudaslodai, Muthupettai and one captive (Mutukadu population. The genetic diversity of three populations of this species was studied using Random Amplified Polymorphic DNA (RAPD markers. Ten random primers were used for the assessment of their genetic diversity and construction of the dendrogram. A total of 589 scorable bands were obtained, 93.12% of them were polymorphic. The Nei�s gene diversity (H of two wild populations were more (0.0504 � 0.0670 and 0.0519 � 0.0953 than the captive population (0.0489 � 0.0850. The clustering pattern obtained by UPGMA method emphasized the wild populations were clustered in one clade and captive population was deviated into another clade. This study proved that RAPD analysis has the ability to discriminate L. calcarifer populations. Further molecular studies, comprising a higher number of molecular tools are still required to precisely evaluate the genetic structure of all seabass populations along the Indian coast.

  7. Grating-Coupling-Based Excitation of Bloch Surface Waves for Lab-on-Fiber Nanoprobes

    CERN Document Server

    Scaravilli, Michele; Cusano, Andrea; Galdi, Vincenzo

    2016-01-01

    In this paper, we investigate for the first time the possibility to excite Bloch surface waves (BSWs) on the tip of single-mode optical fibers. Within this framework, we first demonstrate the possibility to exploit a grating-coupling mechanism for on-tip excitation of BSWs, and highlight the flexibility of the proposed design as well as its intrinsic robustness to unavoidable fabrication tolerances. Subsequently, with a view towards label-free chemical and biological sensing, we present an optimized design to maximize the sensitivity (in terms of wavelength shift) of the arising resonances with respect to changes in the refractive properties of the surrounding environment. Numerical results indicate that the attained sensitivities are in line with those exhibited by state-of-the-art plasmonic nanoprobes, with the key advantage of exhibiting much narrower spectral resonances. This prototype study paves the way for a new class of miniaturized high-performance surface-wave fiber-optic devices for high-resolution...

  8. Differential geometric invariants for time-reversal symmetric Bloch-bundles: The "Real" case

    Science.gov (United States)

    De Nittis, Giuseppe; Gomi, Kiyonori

    2016-05-01

    Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related "Real" (resp. "Quaternionic") Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303-338 (2014)] for the "Real" case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1-55 (2015)] for the "Quaternionic" case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. De Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the "Real" case we generalize the Chern-Weil theory and we show that the assignment of a "Real" connection, along with the related differential Chern class and its holonomy, suffices for the classification of "Real" vector bundles in low dimensions.

  9. The peripheral olfactory organ in the Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801

    Directory of Open Access Journals (Sweden)

    Laura Ghigliotti

    2015-11-01

    Full Text Available The Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801 is the largest predatory fish in Arctic waters. The socio-economic significance of Greenland shark is demonstrated by its impact on the fishing cultures in Greenland, Scandinavia and Iceland for centuries. The fundamental biology and ecological role of Greenland shark, on the other hand, is virtually unknown. Although knowledge of its life history is limited, increasing evidence indicates that the Greenland shark may undertake long-distance migrations and perform vertical movements from the surface to the deep sea. It is an omnivorous species feeding on carrion and a wide variety of pelagic and bottom-dwelling organisms ranging from invertebrates to mammals, and including active species such as fishes and seals. Accordingly, Greenland shark should be recognized as a top predator, with a strong potential to influence the trophic dynamics of the Arctic marine ecosystem. The sensory biology of Greenland shark is scarcely studied, and considering the importance of olfaction in chemoreception, feeding and other behavioral traits, we examined the architecture of the peripheral olfactory organ where olfactory cues are received from the environment – the olfactory rosette. The structural organization of the olfactory rosette, in terms of histological features of the sensory epithelium, number of primary lamellae and total sensory surface area, provides a first proxy of the olfactory capability of Greenland shark. Based on own results and published studies, the overall morphology of the olfactory rosette is viewed in context of the functional and trophic ecology among other elasmobranch species.

  10. Photonic lattices in organic microcavities: Bloch states and control of lasing

    Science.gov (United States)

    Mischok, Andreas; Brückner, Robert; Fröb, Hartmut; Lyssenko, Vadim G.; Leo, Karl

    2015-09-01

    Organic microcavities comprising the host:guest emitter system Alq3:DCM offer an interesting playground to experimentally study the dispersion characteristics of laterally patterned microlasers due to the broad emission spectrum and large oscillator strength of the organic dye. By structuring of metallic or dielectric sublayers directly on top of the bottom mirror, we precisely manipulate the mode structure and influence the coherent emission properties of the device. Embedding silver layers into a microcavity leads to an interaction of the optical cavity-state in the organic layer and the neighboring metal which red-shifts the cavity resonance, creating a Tamm-plasmon-polariton state. A patterning of the metal can in turn be exploited to fabricate deep photonic wells of micron-size, efficiently confining light in lateral direction. In periodic arrays of silver wires, we create a Kronig-Penney-like optical potential in the cavity and in turn observe optical Bloch states spanning over several photonic wires. We modify the Kronig-Penney theory to analytically describe the full far-field emission dispersion of our cavities and show the emergence of either zero- , π-, or 2π- phase-locking in the system. By investigating periodic SiO2 patterns, we experimentally observe stimulated emission from the ground and different excited discrete states at room temperature and are able to directly control the laser emission from both extended and confined modes of the photonic wires at room-temperature.

  11. Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane

    Science.gov (United States)

    Longhi, Stefano

    2015-10-01

    Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.

  12. Effects of the projectile electronic structure on Bethe-Bloch stopping parameters for Ag

    Science.gov (United States)

    Moussa, D.; Damache, S.; Ouichaoui, S.

    2010-06-01

    Energy losses of protons and alpha particles in silver have been accurately measured under the same experimental conditions over the velocity range E=(0.192-2.595) MeV/amu using the transmission method. Deduced S(E) stopping powers are compared to most accurate ones from the literature, to values generated by the SRIM-2008 computer code and to ICRU-49 compilation. They were analyzed in the framework of modified Bethe-Bloch theory for extracting Ag target mean excitation and ionization potential, I, and Barkas effect parameter, b. Values of ( 466±5) eV and 1.20±0.01 for these two parameters were inferred from the proton S(E) data while the alpha particle data yielded values of (438±4) eV and 1.38±0.01, respectively. The ( I, b) stopping parameters thus exhibit opposite variations as the projectile charge increases, similarly as we have found previously for nickel [6]. This can be ascribed only to an effect of the projectile electronic structure at low velocities. The obtained results are discussed in comparison to previous ones reported in the literature.

  13. Mass Spectrum of Fermion on Bloch Branes with New Scalar-fermion Coupling

    CERN Document Server

    Xie, Qun-Ying; Zhao, Zhen-Hua; Du, Yun-Zhi; Zhang, Yu-Peng

    2015-01-01

    In order to localize a left- or right-handed fermion zero mode on a thick brane, one usually introduces the Yukawa coupling $\\eta \\bar{\\Psi} F(\\chi) \\Psi$ between a bulk fermion and the background scalar field $\\chi$. However, the Yukawa coupling will do not work if the background scalar is an even function of the extra dimension. Recently, Ref. [Phy. Rev. \\textbf{D} 89 (2014) 086001] has presented a new scalar-fermion coupling form $\\lambda \\bar \\Psi \\Gamma^M \\partial_M F(\\chi) \\gamma^5 \\Psi$ in order to deal with this problem. In this paper, we investigate the localization and mass spectrum of fermion on the Bloch brane by using the new scalar-fermion coupling with $F(\\chi)=\\chi^n$. It is found that the effective potentials have rich structure and may be volcano-like, finite square well-like, and infinite potentials, which depend on the parameter $n$. As a result, there may appear some resonant KK fermions, finite or infinite numbers of bound KK fermions.

  14. Respiration gating and Bloch fitting improve pH measurements with acidoCEST MRI in an ovarian orthotopic tumor model

    Science.gov (United States)

    Jones, Kyle M.; Randtke, Edward A.; Howison, Christine M.; Pagel, Mark D.

    2016-03-01

    We have developed a MRI method that can measure extracellular pH in tumor tissues, known as acidoCEST MRI. This method relies on the detection of Chemical Exchange Saturation Transfer (CEST) of iopamidol, an FDA-approved CT contrast agent that has two CEST signals. A log10 ratio of the two CEST signals is linearly correlated with pH, but independent of agent concentration, endogenous T1 relaxation time, and B1 inhomogeneity. Therefore, detecting both CEST effects of iopamidol during in vivo studies can be used to accurately measure the extracellular pH in tumor tissues. Past in vivo studies using acidoCEST MRI have suffered from respiration artifacts in orthotopic and lung tumor models that have corrupted pH measurements. In addition, the non-linear fitting method used to analyze results is unreliable as it is subject to over-fitting especially with noisy CEST spectra. To improve the technique, we have recently developed a respiration gated CEST MRI pulse sequence that has greatly reduced motion artifacts, and we have included both a prescan and post scan to remove endogenous CEST effects. In addition, we fit the results by parameterizing the contrast of the exogenous agent with respect to pH via the Bloch equations modified for chemical exchange, which is less subject to over-fitting than the non-linear method. These advances in the acidoCEST MRI technique and analysis methods have made pH measurements more reliable, especially in areas of the body subject to respiratory motion.

  15. An optomechanical elevator: Transport of a Bloch oscillating Bose-Einstein condensate up and down an optical lattice by cavity sideband amplification and cooling

    CERN Document Server

    Venkatesh, B Prasanna; Goldwin, J

    2015-01-01

    We analyze the optomechanics of an atomic Bose-Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a uniform bias force such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice at the Bloch frequency. When the Bloch frequency is on the order of the cavity damping rate we find transport of the atoms either up or down the lattice. The transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the optomechanical Bloch oscillator. Depending on the sign of the pump-cavity detuning, atoms are transported either with or against the bias force accompanied by an up- or down-conversion of the frequency of the pump laser light. We also evaluate the prospects for using the optomechanical Bloch oscillator to make continuous measurements of forces by reading...

  16. Nutritional evaluation of the moonfish Mene maculata (Bloch & Schneider, 1801) from Parangipettai, southeast coast of India

    Institute of Scientific and Technical Information of China (English)

    Palanivel Bharadhirajan; Natarajan Periyasamy; Sambantham Murugan

    2014-01-01

    Objective: To assess the nutritions in Mene maculata (Bloch & Schneider, 1801) (M. maculata). Methods: Fishes (14-16 cm) were obtained from the landings at Parangipettai for the evaluation of biochemical composition. The present study deals with biochemical composition such as protein, carbohydrate, lipid, amino acids fatty acids, vitamins and minerals which were evaluated in the moonfish.Results:protein was high in the tissue (23.16%), followed by the carbohydrate (1.3%) and lipid (2.62%). Totally 20 essential and nonessential amino acids were present at the rate of 46.72% and 43.91%. In the analysis, the fatty acid profile by gas chromatography revealed the presence of higher amount of saturated fatty acid (palmitic acid 22.17%) than monounsaturated fatty acid (oleic acid 14.51%) and polyunsaturated fatty acid (alpha linolenic acid 16.07%). Vitamins were detected in M. maculata. Among them, vitamin A was found in higher levels (124.5 mg/g), whereas vitamin B6 was noticed as lower levels (0.34 mg/g). In the present study, totally 5 macro minerals and 2 trace minerals were reported. The macro mineral calcium (156.7 mg/g) was found at the highest level and other minerals such as sodium (31.98 mg/g), potassium (21.33 mg/g), copper (1.43 mg/g) and magnesium (0.341 mg/g) were also detected in the moonfish.Conclusions:The results of proximate composition in M. maculata showed that the percentage of The result showed that the moonfish M. maculata tissue is a valuable food recipe for human consumption, due to its high quality protein and well-balanced amino acids.

  17. Nutritional evaluation of the moonfish Mene maculata (Bloch & Schneider, 1801 from Parangipettai, southeast coast of India

    Directory of Open Access Journals (Sweden)

    Palanivel Bharadhirajan

    2014-01-01

    Full Text Available Objective: To assess the nutritions in Mene maculata (Bloch & Schneider, 1801 (M. maculata. Methods: Fishes (14-16 cm were obtained from the landings at Parangipettai for the evaluation of biochemical composition. The present study deals with biochemical composition such as protein, carbohydrate, lipid, amino acids fatty acids, vitamins and minerals which were evaluated in the moonfish. Results: The results of proximate composition in M. maculata showed that the percentage of protein was high in the tissue (23.16%, followed by the carbohydrate (1.3% and lipid (2.62%. Totally 20 essential and nonessential amino acids were present at the rate of 46.72% and 43.91%. In the analysis, the fatty acid profile by gas chromatography revealed the presence of higher amount of saturated fatty acid (palmitic acid 22.17% than monounsaturated fatty acid (oleic acid 14.51% and polyunsaturated fatty acid (alpha linolenic acid 16.07%. Vitamins were detected in M. maculata. Among them, vitamin A was found in higher levels (124.5 mg/g, whereas vitamin B6 was noticed as lower levels (0.34 mg/g. In the present study, totally 5 macro minerals and 2 trace minerals were reported. The macro mineral calcium (156.7 mg/g was found at the highest level and other minerals such as sodium (31.98 mg/g, potassium (21.33 mg/g, copper (1.43 mg/g and magnesium (0.341 mg/g were also detected in the moonfish. Conclusions: The result showed that the moonfish M. maculata tissue is a valuable food recipe for human consumption, due to its high quality protein and well-balanced amino acids.

  18. Antes, desde y para el exilio. Herencia de esta época (1935/1962 de Ernst Bloch

    Directory of Open Access Journals (Sweden)

    Salmerón Infante, Miguel

    2009-10-01

    Full Text Available The first edition of Erbschaft dieser Zeit was published in Zurich in 1935, during Ernst Bloch’s five-year period of emigration from Nazi-Germany in various European capitals before his final emigration to America for ten years in 1938. In this book Bloch made a courageous stand in defence of the artistic avant-garde against the dogmatic advocates of socialist realism. His particularly adversary was Georg Lukács. But of course one of the most fascinating aspects of the book is that is also reads as a contemporary observation of the rise of the Nazis. Erbschaft is undoubtedly the major work of Weimar Germany Exile.La primera edición de Erbschaft dieser Zeit fue publicada en 1935 en Zurich, durante la emigración de Ernst Bloch de la Alemania nazi por un período de cinco años en el que residió en varias capitales europeas antes de su marcha definitiva a América en 1938, donde vivió diez años. En este libro Bloch hace una encorajinada defensa de la vanguardia artística contra los abogados del realismo socialista. Su adversario específico era Georg Lukács. Pero sin duda alguna uno de los aspectos más fascinantes de este libro es que puede leerse como una observación contemporánea de la ascensión al poder de los nazis. Erbschaft es indudablemente la obra clave del exilio de la Alemania de Weimar.

  19. Complex solitary waves and soliton trains in KdV and mKdV equations

    Science.gov (United States)

    Modak, Subhrajit; Singh, Akhil Pratap; Panigrahi, Prasanta Kumar

    2016-06-01

    We demonstrate the existence of complex solitary wave and periodic solutions of the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity (𝓟) and time-reversal (𝓣) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The 𝓟𝓣-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental sech2 solution through supersymmetry. Physically, these complex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow water waves and hence may also find physical verification.

  20. Numerical investigation of the flat band Bloch modes in a 2D photonic crystal with Dirac cones.

    Science.gov (United States)

    Zhang, Peng; Fietz, Chris; Tassin, Philippe; Koschny, Thomas; Soukoulis, Costas M

    2015-04-20

    A numerical method combining complex-k band calculations and absorbing boundary conditions for Bloch waves is presented. We use this method to study photonic crystals with Dirac cones. We demonstrate that the photonic crystal behaves as a zero-index medium when excited at normal incidence, but that the zero-index behavior is lost at oblique incidence due to excitation of modes on the flat band. We also investigate the formation of monomodal and multimodal cavity resonances inside the photonic crystals, and the physical origins of their different line-shape features.

  1. Bloch k-selective resonant inelastic scattering of hard X-rays from valence electrons of 3d-metals

    OpenAIRE

    Enkisch, Hartmut

    2002-01-01

    Die Form von resonant angeregen Valenz-Fluoreszenzspektren hängt sowohl vonder Energie der einfallenden Strahlung, als auch von Größe und Richtung desImpulsübertrags q ab, falls harte Röntgenstrahlen benutzt werden. DieserEffekt ist auf die elektronische Bandstruktur der Valenz- undLeitungselektronen der Probe, in Kombination mit der Energie- undImpulserhaltung des Streuprozesses zurückzuführen, woraus dieBloch-k-Impulserhaltung des resonant inelastischen Streuprozesses folgt.In dieser Arbeit...

  2. A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals

    CERN Document Server

    Lawrence, Felix J; Dossou, Kokou B; McPhedran, R C; de Sterke, C Martijn

    2011-01-01

    We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous work which relied on specialized multipole and FEM techniques underpinning transfer matrix methods. We describe the numerical technique for mode extraction, and apply it to calculate a complex band structure and to design two photonic crystal antireflection coatings. We do this for frequencies at which other methods fail, but which nevertheless are of significant practical interest.

  3. Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices.

    Science.gov (United States)

    Morsch, O; Müller, J H; Cristiani, M; Ciampini, D; Arimondo, E

    2001-10-01

    We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.

  4. Long-lived BLOCH oscillations with bosonic sr atoms and application to gravity measurement at the micrometer scale.

    Science.gov (United States)

    Ferrari, G; Poli, N; Sorrentino, F; Tino, G M

    2006-08-11

    We report on the observation of Bloch oscillations on the unprecedented time scale of several seconds. The experiment is carried out with ultracold bosonic 88Sr atoms loaded into a vertical optical standing wave. The negligible atom-atom elastic cross section and zero angular momentum in the ground state makes 88Sr an almost ideal Bose gas, insensitive to typical mechanisms of decoherence due to thermalization and external stray fields. The small size of the system enables precision measurements of forces at micrometer scale. This is a challenge in physics for studies of surfaces, Casimir effects, and searches for deviations from Newtonian gravity predicted by theories beyond the standard model.

  5. Determination of the fine structure constant based on BLOCH oscillations of ultracold atoms in a vertical optical lattice.

    Science.gov (United States)

    Cladé, Pierre; de Mirandes, Estefania; Cadoret, Malo; Guellati-Khélifa, Saïda; Schwob, Catherine; Nez, François; Julien, Lucile; Biraben, François

    2006-01-27

    We report an accurate measurement of the recoil velocity of 87Rb atoms based on Bloch oscillations in a vertical accelerated optical lattice. We transfer about 900 recoil momenta with an efficiency of 99.97% per recoil. A set of 72 measurements of the recoil velocity, each one with a relative uncertainty of about 33 ppb in 20 min integration time, leads to a determination of the fine structure constant with a statistical relative uncertainty of 4.4 ppb. The detailed analysis of the different systematic errors yields to a relative uncertainty of 6.7 ppb. The deduced value of alpha-1 is 137.035 998 78(91).

  6. FORTRAN source listing for simulating three-dimensional convergent beam patterns with absorption by the Bloch wave method.

    Science.gov (United States)

    Zuo, J M; Gjonnes, K; Spence, J C

    1989-05-01

    The FORTRAN source code is given for a computer program that calculates the two-dimensional intensity distribution in convergent-beam transmission electron microdiffraction (CBED) patterns from perfect crystals. The program uses the eigenvalue or Bloch-wave method. It allows three-dimensional dynamical diffraction, and so includes all higher-order Laue zone effects without approximation. No symmetry reduction is included. The program accepts noncentrosymmetric or centrosymmetric crystal structures and allows absorption corrections to be included. It uses the "EISPACK" subroutines for the diagonalisation of a general complex matrix. Up to 100 CBED disks may be included. The code is also available via "Bitnet."

  7. Porous silicon Bloch surface and sub-surface wave structure for simultaneous detection of small and large molecules

    Science.gov (United States)

    Rodriguez, Gilberto A.; Lonai, John D.; Mernaugh, Raymond L.; Weiss, Sharon M.

    2014-08-01

    A porous silicon (PSi) Bloch surface wave (BSW) and Bloch sub-surface wave (BSSW) composite biosensor is designed and used for the size-selective detection of both small and large molecules. The BSW/BSSW structure consists of a periodic stack of high and low refractive index PSi layers and a reduced optical thickness surface layer that gives rise to a BSW with an evanescent tail that extends above the surface to enable the detection of large surface-bound molecules. Small molecules were detected in the sensor by the BSSW, which is a large electric field intensity spatially localized to a desired region of the Bragg mirror and is generated by the implementation of a step or gradient refractive index profile within the Bragg mirror. The step and gradient BSW/BSSW sensors are designed to maximize both resonance reflectance intensity and sensitivity to large molecules. Size-selective detection of large molecules including latex nanospheres and the M13KO7 bacteriophage as well as small chemical linker molecules is reported.

  8. The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem

    Energy Technology Data Exchange (ETDEWEB)

    Aerts, Diederik, E-mail: diraerts@vub.ac.be [Center Leo Apostel for Interdisciplinary Studies and Department of Mathematics, Brussels Free University, Brussels (Belgium); Sassoli de Bianchi, Massimiliano, E-mail: autoricerca@gmail.com [Laboratorio di Autoricerca di Base, 6914 Lugano (Switzerland)

    2014-12-15

    A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement. - Highlights: • An extended Bloch representation of quantum measurements is given. • Quantum measurements are explained in terms of hidden-measurement interactions. • Quantum measurements are explained as tripartite processes. • The Born rule results from a universal average, over all possible measurement processes.

  9. Plasmonic Photonic-Crystal Slabs: Visualization of the Bloch Surface Wave Resonance for an Ultrasensitive, Robust and Reusable Optical Biosensor

    Directory of Open Access Journals (Sweden)

    Alexander V. Baryshev

    2014-12-01

    Full Text Available A one-dimensional photonic crystal (PhC with termination by a metal film—a plasmonic photonic-crystal slab—has been theoretically analyzed for its optical response at a variation of the dielectric permittivity of an analyte and at a condition simulating the molecular binding event. Visualization of the Bloch surface wave resonance (SWR was done with the aid of plasmon absorption in a dielectric/metal/dielectric sandwich terminating a PhC. An SWR peak in spectra of such a plasmonic photonic crystal (PPhC slab comprising a noble or base metal layer was shown to be sensitive to a negligible variation of refractive index of a medium adjoining to the slab. As a consequence, the considered PPhC-based optical sensors exhibited an enhanced sensitivity and a good robustness in comparison with the conventional surface-plasmon and Bloch surface wave sensors. The PPhC biosensors can be of practical importance because the metal layer is protected by a capping dielectric layer from contact with analytes and, consequently, from deterioration.

  10. Integrable motion of curves in self-consistent potentials: Relation to spin systems and soliton equations

    Energy Technology Data Exchange (ETDEWEB)

    Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)

    2014-06-13

    Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.

  11. Comparative histological and histochemical studies on the pancreas of Labeo rohita (Hamilton, 1822), Mystus vittatus (Bloch, 1790) and Notopterus notopterus (Pallas, 1769)

    OpenAIRE

    Padmanabha Chakrabarti; Saroj Kumar Ghosh

    2015-01-01

    The histological analysis, disposition and histochemical localization of tryptophan were investigated in the pancreas to compare the cellular organization and histochemical characterization in the pancreas of Labeo rohita (Hamilton, 1822), Mystus vittatus (Bloch, 1790) and Notopterus notopterus (Pallas, 1769) having different feeding habits. Histological analysis demonstrated that the exocrine pancreatic tissues were dispersed within the hepatic parenchyma and spleen in L. rohita. Thin septa ...

  12. Difference equations by differential equation methods

    CERN Document Server

    Hydon, Peter E

    2014-01-01

    Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

  13. Dieta do tucunaré-amarelo Cichla monoculus (Bloch & Schneider (Osteichthyes, Cichlidae, no Reservatório de Lajes, Rio de Janeiro, Brasil Diet of Cichla monoculus (Bloch & Schneider (Osteichthyes, Cichlidae in Lajes' Reservoir, Rio de Janeiro, Brazil

    Directory of Open Access Journals (Sweden)

    Luciano Neves dos Santos

    2001-07-01

    Full Text Available The diet of Cichla monoculus (Bloch & Schneider, 1801 in Lajes's Reservoir, a major impoundment in Rio de Janeiro State, Brazil, was assessed, from fishes collected in 1994,1996 and 1999/2000. Gut contents in individuals was analyzed by the index of relative importance (IRI which deals with numerical, gravimetrical and frequency of occurrence. Cichla monoculus showed a strong piscivorous habits feeding on Cichlidae, Characidae and Pimelodidae, in decreasing order of importance, with a remarkable cannibalism on young-of-the-year. Others minor items in the diet were Macrobrachium sp. and Odonata. Changes in feeding composition varied with reservoir's zones and seasons, with higher diversity in Autumn and peaks of cannibalism in lower zone during Spring/Summer. Overall, only one third of fish species composition in the reservoir are predated by C. monoculus. Condition factor (k and fullness index varied closely with higher values in lower zone, and lower records in Winter.

  14. Random diophantine equations, I

    OpenAIRE

    Brüdern, Jörg; Dietmann, Rainer

    2012-01-01

    We consider additive diophantine equations of degree $k$ in $s$ variables and establish that whenever $s\\ge 3k+2$ then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.

  15. Kinetic energy equations for the average-passage equation system

    Science.gov (United States)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  16. Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient.

    Science.gov (United States)

    Xiao, Fajun; Li, Baoran; Wang, Meirong; Zhu, Weiren; Zhang, Peng; Liu, Sheng; Premaratne, Malin; Zhao, Jianlin

    2014-09-22

    We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.

  17. Comparative characteristics of quantum key distribution protocols with alphabets corresponding to the regular polyhedrons on the Bloch sphere

    Science.gov (United States)

    Sych, Denis V.; Grishanin, Boris A.; Zadkov, Victor N.

    2005-06-01

    Possibilities of improving characteristics of quantum key distribution (QKD) protocols via variation of character set in quantum alphabets are investigated. QKD protocols with discrete alphabets letters of which form regular polyhedrons on the Bloch sphere (tetrahedron octahedron cube icosahedron and dodecahedron which have 4, 6, 8, 12, and 20 vertexes) and QKD protocol with continuous alphabet which corresponds to the limiting case of a polyhedron with infinitive number of vertexes are considered. Stability of such QKD protocols to the interceptresend and optimal eavesdropping strategies at the individual attacks is studied in detail. It is shown that in case of optimal eavesdropping strategy after safety bases reconciliation critical error rate of the QKD protocol with continuous alphabet surpasses all other protocols. Without basis reconciliation the highest critical error rate have the protocol with tetrahedron-type alphabet.

  18. Mean excitation energies extracted from stopping power measurements of protons in polymers by using the modified Bethe Bloch formula

    Science.gov (United States)

    Ammi, H.; Zemih, R.; Mammeri, S.; Allab, M.

    2005-04-01

    Recent stopping power measurements in thin polymeric films have been performed for protons of 0.4-3.5 MeV energies using the indirect transmission technique [H. Ammi, S. Mammeri, M. Chekirine, B. Bouzid, M. Allab, Nucl. Instr. and Meth. B 198 (2002) 5]. Experimental stopping data have been analyzed with the modified Bethe-Bloch formula and the mean excitation energies I have been then extracted from the data. Resulting values for each thin film are 76 ± 1 eV in Mylar, 70.8 ± 1 eV in Makrofol, 82.2 ± 1.2 eV in LR-115 and 55.4 ± 1 eV in Polypropylene. The I-extracted values are compared to those IB calculated by using the Bragg's rule.

  19. A força da tradição: a persistência do antigo regime historiográfico na obra de Marc Bloch The power of tradition: the persistence of historic old regime in Marc Bloch's Oeuvre

    Directory of Open Access Journals (Sweden)

    Tiago de Melo Gomes

    2006-12-01

    Full Text Available Este artigo se foca na obra de Marc Bloch, em especial em seu livro tido como mais importante, A Sociedade Feudal (1939, argumentando que mesmo no trabalho de um dos mais importantes do século XX ainda é possível encontrar elementos associados a uma historiografia mais tradicional.This article is focused on Marc Bloch's oeuvre, especially in his so-called masterpiece, Feudal Society (1939, arguing that even in the work of one of the most important historians of the century, we can find important elements of the traditional historiography.

  20. Bloch Oscillations, Zener Tunneling, and Wannier-Stark Ladders in the Time Domain

    DEFF Research Database (Denmark)

    Rotvig, Jon; Jauho, Antti-Pekka; Smith, Henrik

    1995-01-01

    We present a time-domain analysis of carrier dynamics in a semiconductor superlattice with two minibands. Integration of the density-matrix equations of motion reveals a number of new features: (i) for certain values of the applied static electric field strong interminiband transitions occur; (ii...

  1. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    EvangelosChaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.

  2. A generalized harmonic map equation for micromagnetics (abstract)

    Science.gov (United States)

    Kotiuga, P. R.

    1991-04-01

    Static micromagnetic configurations are determined by minimizing the sum of anisotropy, demagnetization, exchange, and external interaction energies subject to the constraint that the magnitude of the magnetization vector is constant throughout a sample. If this constraint is not explicitly imposed in a numerical or analytical investigation, a Lagrange multiplier type of term must be appended to the energy functional. In a region R, two candidates are λ∫R(1 - ‖m(r)‖2)2 dV and ∫Rλ(r)(1 - ‖m(r)‖2)dV. The first expression is a Higgs or penalty term in the terminology of physicists and numerical analysts. The penalty parameter λ is given a physical meaning through the Ginsburg-Landau theory.1 The second expression is avoided by physicists and numerical analysts since the scalar Lagrange multiplier λ(r) represents an unwelcomed proliferation of variables. Following the theory of harmonic maps, the scalar Lagrange multiplier field is eliminated in this paper and a generalized harmonic map equation for micromagnetics is obtained. This equation has no extraneous phenomenological constants and enables one to ignore the original constraint in numerical solutions. It also provides a means for tying together results concerning singularities of harmonic maps2 with Block point phenomena believed to exist in VBL memories. This, in turn, enables one to make general inferences about the energetics of Bloch points which are not possible through purely topological investigations or simulations involving specific geometries.

  3. Spectral validation of the Whitham equations for periodic waves of lattice dynamical systems

    Science.gov (United States)

    Kabil, Buğra; Rodrigues, L. Miguel

    2016-02-01

    In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the time evolution of slowly modulated wavetrains. Then, for waves whose period is commensurable to the lattice, we prove that the formally-derived first-order averaged system must be at least weakly hyperbolic if the background waves are to be spectrally stable, and, when weak hyperbolicity is met, the characteristic velocities of the modulation system provide group velocities of the original system. Historically, for dynamical evolutions obeying partial differential equations, this has been proved, according to increasing level of algebraic complexity, first for systems of reaction-diffusion type, then for generic systems of balance laws, at last for Hamiltonian systems. Here, for their semi-discrete counterparts, we give at once simultaneous proofs for all these cases. Our main analytical tool is the discrete Bloch transform, a discrete analogue to the continuous Bloch transform. Nevertheless, we needed to overcome the absence of genuine space-translation invariance, a key ingredient of continuous analyses.

  4. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    George F R Ellis

    2007-07-01

    The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.

  5. Bloch Electron in a Magnetic Field Diagonalization of Tight-Binding Models

    CERN Document Server

    Moroz, A V

    1992-01-01

    A connection of a variety of tight-binding models of noninteracting electrons on a rectangular lattice in a magnetic field with theta functions is established. A new spectrum generating symmetry is discovered which essentialy reduces the problem of diagonalization of these models. Provided that one knows one eigenvector at one point in the parameter space of the corresponding Harper equation one knows an eigenfunction of the corresponding model in the whole range of momentum singlet out by the Landau gauge.

  6. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  7. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  8. Reducible functional differential equations

    Directory of Open Access Journals (Sweden)

    S. M. Shah

    1985-01-01

    Full Text Available This is the first part of a survey on analytic solutions of functional differential equations (FDE. Some classes of FDE that can be reduced to ordinary differential equations are considered since they often provide an insight into the structure of analytic solutions to equations with more general argument deviations. Reducible FDE also find important applications in the study of stability of differential-difference equations and arise in a number of biological models.

  9. New unified evolution equation

    OpenAIRE

    Lim, Jyh-Liong; Li, Hsiang-nan

    1998-01-01

    We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables $x$, which is an improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this new equation the cancellation of soft divergences between virtual and real gluon emissions is explicit without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically. It is shown that the new equation reduc...

  10. Diophantine equations and identities

    Directory of Open Access Journals (Sweden)

    Malvina Baica

    1985-01-01

    Full Text Available The general diophantine equations of the second and third degree are far from being totally solved. The equations considered in this paper are    i  x2−my2=±1 ii  x3+my3+m2z3−3mxyz=1iii  Some fifth degree diopantine equations

  11. The invariant polarisation-tensor field for deuterons in storage rings and the Bloch equation for the polarisation-tensor density

    Energy Technology Data Exchange (ETDEWEB)

    Barber, D.P.

    2015-10-15

    I extend and update earlier work, summarised in an earlier paper (D.P. Barber, M. Voigt, AIP Conference Proceedings 1149 (28)), whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.

  12. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    Evangelos Chaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.

  13. Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Jianping Zhao

    2012-01-01

    Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.

  14. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  15. Metazoan parasites of Mystus vittatus (Bloch) of River Godavari with description of a new species of Acanthocephala, Raosentis godavarensis sp. nov.

    OpenAIRE

    Vankara, Anu Prasanna; Vijayalakshmi, C.

    2009-01-01

    A total of 9 metazoan parasitic species were identified from Mystus vittatus (Bloch) in river Godavari during 2005–2007 including 2 monogeneans, 2 digeneans, 3 acanthocephalans and 2 copepods. Two species of monogeneans (Bifurcohaptor indicus and Thaparocleidus tengra), digeneans (Haplorchoides macrones and metacercariae of Isoparorchis hypselobagri), an acanthocephalan (Raosentis podderi) found during the present study are of common occurrence in this fish. M. vittatus constitutes a new host...

  16. Gastroprotective Effect of Freeze Dried Stripped Snakehead Fish (Channa striata Bloch.) Aqueous Extract against Aspirin Induced Ulcerogenesis in Pylorus Ligated Rats

    OpenAIRE

    Mohammed Safwan Ali Khan; Abdul Manan Mat Jais; Javeed Hussain; Faiza Siddiqua; Gopala Reddy, A.; P. Shivakumar; Madhuri, D.

    2014-01-01

    Channa striata (Bloch.) is a fresh water fish belonging to the family Channidae. The stripped snakehead fish possesses wide range of medicinal properties. In view of traditional use of C. striata for wound healing, the present study was undertaken to investigate the beneficial effects of orally administered freeze dried aqueous extract of Channa striata (AECS) in experimentally induced gastric ulcers in Wistar rats. Aspirin induced ulcerogenesis in pyloric ligation model was used for the asse...

  17. Lanczos's equation to replace Dirac's equation ?

    CERN Document Server

    Gsponer, A; Gsponer, Andre; Hurni, Jean-Pierre

    1994-01-01

    Lanczos's quaternionic interpretation of Dirac's equation provides a unified description for all elementary particles of spin 0, 1/2, 1, and 3/2. The Lagrangian formulation given by Einstein and Mayer in 1933 predicts two main classes of solutions. (1) Point like partons which come in two families, quarks and leptons. The correct fractional or integral electric and baryonic charges, and zero mass for the neutrino and the u-quark, are set by eigenvalue equations. The electro-weak interaction of the partons is the same as with the Standard model, with the same two free parameters: e and sin^2 theta. There is no need for a Higgs symmetry breaking mechanism. (2) Extended hadrons for which there is no simple eigenvalue equation for the mass. The strong interaction is essentially non-local. The pion mass and pion-nucleon coupling constant determine to first order the nucleon size, mass and anomalous magnetic moment.

  18. Bloch-state-based interpolation: An efficient generalization of the Shirley approach to interpolating electronic structure

    Science.gov (United States)

    Prendergast, David; Louie, Steven G.

    2009-12-01

    We present an efficient generalization of the k -space interpolation scheme for electronic structure presented by Shirley [Phys. Rev. B 54, 16464 (1996)]. The method permits the construction of a compact k -dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of effective single-particle electronic-structure calculations (based on density-functional theory in this work). We provide some generalizations of the initial approach which reduce the number of required initial electronic-structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone center only for large systems. We also generalize the representation of nonlocal Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. Furthermore, accurate eigenfunctions—expressed in the optimal basis—provide easy access to useful matrix elements for simulating spectroscopy and we provide details for computing optical transition amplitudes. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.

  19. Bloch-state-based interpolation -- an efficient generalization of the Shirley approach to interpolating electronic structure

    Science.gov (United States)

    Prendergast, David; Louie, Steven G.

    2010-03-01

    We present an efficient generalization of the k-space interpolation scheme for electronic structure presented by E. L. Shirley, Phys. Rev. B 54, 16464 (1996), which permits the construction of a compact k-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of density functional theory calculations. We provide some generalizations of the initial approach which reduce the number of required initial electronic structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone-center only for large systems. We also generalize the representation of non-local Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.

  20. On separable Pauli equations

    International Nuclear Information System (INIS)

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A0(t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  1. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  2. Elliptic partial differential equations

    CERN Document Server

    Volpert, Vitaly

    If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...

  3. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  4. Fractional Chemotaxis Diffusion Equations

    CERN Document Server

    Langlands, T A M

    2010-01-01

    We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.

  5. 自适应Bloch球面的量子遗传算法%Adaptive quantum genetic algorithm based on Bloch sphere

    Institute of Scientific and Technical Information of China (English)

    易正俊; 侯坤; 何荣花

    2012-01-01

    在基于量子位Bloch坐标的量子遗传算法的基础上,提出一种自适应Bloch球面的量子遗传算法.该算法按两种方式自适应地选取Bloch球面的一部分进行搜索:沿经线方向选取和沿纬线方向选取,并在理论上证明了这两种选取方式都能够包含所求连续优化问题的所有可行解.在对选取的Bloch球面进行搜索时,提出了近似等面积搜索的方法,进而推导出两个相位转角大小之间的反比例关系,染色体的变异操作也作了相应的修改以适应选取区域的限制.实验表明该算法在搜索能力方面与基于量子位Bloch坐标的量子遗传算法基本相当,但优化效率方面有明显提高.%An adaptive quantum genetic algorithm based on Bloch sphere is proposed based on the quantum genetic algorithm which is based on Bloch coordinates of qubits. The algorithm uses two ways to select a part of the Bloch sphere for searching: along the warp direction and weft direction. The paper proves that the two methods are able to contain all the solutions of the continuous optimization problem in theory, and proposes a method of approximately equal-area to search the selected Bloch sphere, and derives the inverse relationship between the two-phase. The chromosomes mutation is modified to meet the restrictions of selected region. The simulation results show that the approach is equal to quantum genetic algorithm based on Bloch coordinates of qubits in search capability, but the optimization efficiency is significantly improved.

  6. Drift-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    K. Banoo

    1998-01-01

    equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

  7. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  8. Fundamental Equation of Economics

    OpenAIRE

    Wayne, James J.

    2013-01-01

    Recent experience of the great recession of 2008 has renewed one of the oldest debates in economics: whether economics could ever become a scientific discipline like physics. This paper proves that economics is truly a branch of physics by establishing for the first time a fundamental equation of economics (FEOE), which is similar to many fundamental equations governing other subfields of physics, for example, Maxwell’s Equations for electromagnetism. From recently established physics laws of...

  9. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  10. On separable Pauli equations

    OpenAIRE

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-1/2 particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the eleven classes of vector-potentials of the electro-magnetic field A(t,x) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is...

  11. A new evolution equation

    International Nuclear Information System (INIS)

    A new evolution equation is proposed for the gluon density relevant (GLR) for the region of small xB. It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multi gluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed αs. It is found that the effects of multi gluon correlations on the deep-inelastic structure function are small. (author) 15 refs, 5 figs, 2 tabs

  12. A Bloch-McConnell simulator with pharmacokinetic modeling to explore accuracy and reproducibility in the measurement of hyperpolarized pyruvate

    Science.gov (United States)

    Walker, Christopher M.; Bankson, James A.

    2015-03-01

    Magnetic resonance imaging (MRI) of hyperpolarized (HP) agents has the potential to probe in-vivo metabolism with sensitivity and specificity that was not previously possible. Biological conversion of HP agents specifically for cancer has been shown to correlate to presence of disease, stage and response to therapy. For such metabolic biomarkers derived from MRI of hyperpolarized agents to be clinically impactful, they need to be validated and well characterized. However, imaging of HP substrates is distinct from conventional MRI, due to the non-renewable nature of transient HP magnetization. Moreover, due to current practical limitations in generation and evolution of hyperpolarized agents, it is not feasible to fully experimentally characterize measurement and processing strategies. In this work we use a custom Bloch-McConnell simulator with pharmacokinetic modeling to characterize the performance of specific magnetic resonance spectroscopy sequences over a range of biological conditions. We performed numerical simulations to evaluate the effect of sequence parameters over a range of chemical conversion rates. Each simulation was analyzed repeatedly with the addition of noise in order to determine the accuracy and reproducibility of measurements. Results indicate that under both closed and perfused conditions, acquisition parameters can affect measurements in a tissue dependent manner, suggesting that great care needs to be taken when designing studies involving hyperpolarized agents. More modeling studies will be needed to determine what effect sequence parameters have on more advanced acquisitions and processing methods.

  13. Infection and pathology in Queensland grouper, Epinephelus lanceolatus, (Bloch), caused by exposure to Streptococcus agalactiae via different routes.

    Science.gov (United States)

    Delamare-Deboutteville, J; Bowater, R; Condon, K; Reynolds, A; Fisk, A; Aviles, F; Barnes, A C

    2015-12-01

    Since 2007, 96 wild Queensland groupers, Epinephelus lanceolatus, (Bloch), have been found dead in NE Australia. In some cases, Streptococcus agalactiae (Group B Streptococcus, GBS) was isolated. At present, a GBS isolate from a wild grouper case was employed in experimental challenge trials in hatchery-reared Queensland grouper by different routes of exposure. Injection resulted in rapid development of clinical signs including bilateral exophthalmia, hyperaemic skin or fins and abnormal swimming. Death occurred in, and GBS was re-isolated from, 98% fish injected and was detected by PCR in brain, head kidney and spleen from all fish, regardless of challenge dose. Challenge by immersion resulted in lower morbidity with a clear dose response. Whilst infection was established via oral challenge by admixture with feed, no mortality occurred. Histology showed pathology consistent with GBS infection in organs examined from all injected fish, from fish challenged with medium and high doses by immersion, and from high-dose oral challenge. These experimental challenges demonstrated that GBS isolated from wild Queensland grouper reproduced disease in experimentally challenged fish and resulted in pathology that was consistent with that seen in wild Queensland grouper infected with S. agalactiae. PMID:25117665

  14. STUDIES REGARDING THE INFLUENCE OF TOPSIN M 70 PU FUNGICIDE ON CARASSIUS AURATUS GIBELIO BLOCH L. 1758

    Directory of Open Access Journals (Sweden)

    Bogdan Mihai Udroiu

    2015-12-01

    Full Text Available The main objective of this study is to see how the metylthiophanate fungicide influences the energetic metabolism and the breathing rhythm at Carassius auratus gibelio Bloch L. 1758. Experimental samples were subjected to under-lethal concentrations of 3.75mg/l, 7.5mg/l, 15mg/l and 30mg/l methyl-thiophanate fungicide from 24 to 336 hours. The physiologic parameter with the highest growth rate was the oxygen consumption, which, at the concentration of 7.5mg/l grew by 40.3% in 6 hours, compared to the witness values, registering the value of 179.52 mg oxygen/l/h compared to 127.95 mg oxygen/l/h. Also, the breathing rhythm grew at the concentration of 7.5 mg/l by 24.76% in 6 hours, compared to the witness values. At the concentration of 30mg/l, both physiologic parameters decreased. So, after 6 hours, the oxygen consumption decrease up to 31.38% from the witness values, registering the value of 51.503mg oxygen/l/h compared to 164.09mg oxygen/l/h, and the breathing rhythm decreased to 84.3% compared to the witness martor.

  15. Higher Order Radial Derivatives of Bloch Type Functions%Bloch型函数的高阶径向导数

    Institute of Scientific and Technical Information of China (English)

    卓文新

    2002-01-01

    讨论了复超球上全纯函数的高阶导数的增长速度,证明了f∈Bα的充分必要条件是supa∈B(1-|z|2)m+α-1|Rmf(z)|<∞,或supa∈B∫B(1-|z|2)(m+α-1)|Rmf(z)|pJRφα(z)dv(z)<∞,或(1-|z|2)p(m+α-1)|Rmf(z)|pdv(z)是Bergman-Carleson测度.%In this paper, higher order radial derivatives of Bloch type functions in the unit ball of Cn is discussed and it is proved that for f∈H(B), f∈Bα if and only if supα∈B(1-|z|2)m+α-1|Rmf(z)|<∞, if and only if supa∈B∫B(1-|z|2)P(m+α-1)|Rmf(z)|PJRφα(z)dv(z)<∞, if and only if (1-|z|2)P(m+α-1)|Rmf(z)|Pdv(z) is a Bergman-Carleson measure.

  16. Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

    Science.gov (United States)

    Frazier, Michael J.; Hussein, Mahmoud I.

    2016-05-01

    It is common for dispersion curves of damped periodic materials to be based on real frequencies as a function of complex wavenumbers or, conversely, real wavenumbers as a function of complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained. xml:lang="fr"

  17. Gauge invariant flow equation

    CERN Document Server

    Wetterich, C

    2016-01-01

    We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the flow equation simple.

  18. On the Diophantine equation

    Science.gov (United States)

    Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.

    2013-04-01

    This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.

  19. Some classical Diophantine equations

    Directory of Open Access Journals (Sweden)

    Nikita Bokarev

    2014-09-01

    Full Text Available An attempt to find common solutions complete some Diophantine equations of the second degree with three variables, traced some patterns, suggest a common approach, which being elementary, however, lead to a solution of such equations. Using arithmetic functions allowed to write down the solutions in a single formula with no restrictions on the parameters used.

  20. Braneworld flow equations

    OpenAIRE

    Ramirez, Erandy; Liddle, Andrew

    2004-01-01

    We generalize the flow equations approach to inflationary model building to the Randall–Sundrum Type II braneworld scenario. As the flow equations are quite insensitive to the expansion dynamics, we find results similar to, though not identical to, those found in the standard cosmology.

  1. The Wouthuysen equation

    NARCIS (Netherlands)

    Hazewinkel, M.

    1995-01-01

    Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-

  2. Linear Equations: Equivalence = Success

    Science.gov (United States)

    Baratta, Wendy

    2011-01-01

    The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

  3. Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Hannelore Breckner

    2000-01-01

    Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.

  4. The relativistic Pauli equation

    CERN Document Server

    Delphenich, David

    2012-01-01

    After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charged spinning particle in an external electromagnetic field then implies a second order equation in the matrix-valued wave functions that is of Klein-Gordon type and represents the relativistic analogue of the Pauli equation. We conclude by presenting the Lagrangian form for the relativistic Pauli equation.

  5. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  6. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  7. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  8. Stochastic Gauss equations

    Science.gov (United States)

    Pierret, Frédéric

    2016-02-01

    We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.

  9. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  10. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  11. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  12. Modern introduction to differential equations

    CERN Document Server

    Ricardo, Henry J

    2009-01-01

    A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equat

  13. A Comparison of IRT Equating and Beta 4 Equating.

    Science.gov (United States)

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…

  14. Kinetic equations: computation

    CERN Document Server

    Pareschi, Lorenzo

    2013-01-01

    Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.

  15. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  16. Diophantine Equations and Computation

    Science.gov (United States)

    Davis, Martin

    Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{ mid exists x_1,ldots,x_m [F(a_1,ldots,x_1,ldots)=0] \\} Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes: a set is called Diophantine if it has such a definition in which F is a polynomial with integer coefficients. We write \\cal D for the class of Diophantine sets.

  17. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  18. Stochastic Gauss Equations

    CERN Document Server

    Frédéric, Pierret

    2014-01-01

    The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.

  19. Nonlinear differential equations

    International Nuclear Information System (INIS)

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  20. Exciton laser rate equations

    OpenAIRE

    Garkavenko A. S.

    2011-01-01

    The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.

  1. Complex Maxwell's equations

    Institute of Scientific and Technical Information of China (English)

    A.I.Arbab

    2013-01-01

    A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.

  2. On Dust Charging Equation

    OpenAIRE

    Tsintsadze, Nodar L.; Tsintsadze, Levan N.

    2008-01-01

    A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.

  3. Relativistic Guiding Center Equations

    Energy Technology Data Exchange (ETDEWEB)

    White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association

    2014-10-01

    In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

  4. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    Science.gov (United States)

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  5. Hedin Equations for Superconductors

    OpenAIRE

    Linscheid, A.; Essenberger, F.

    2015-01-01

    We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of s...

  6. Quantum Particle Swarm Optimization Algorithm Based on Bloch Spherical Search%基于Bloch球面搜索的量子粒子群优化算法

    Institute of Scientific and Technical Information of China (English)

    李盼池; 王琪超; 施光尧

    2013-01-01

    通过分析量子势阱粒子群优化算法的设计过程,提出一种基于Bloch球面搜索的量子粒子群优化算法.首先用基于Bloch球面描述的量子位描述粒子,用泡利矩阵建立旋转轴,用Delta势阱模型计算旋转角度,用量子位在Bloch球面上的绕轴旋转实现搜索.然后用Hadamard门实现粒子变异,以避免早熟收敛.这种旋转可使当前量子位沿着Bloch球面上的大圆逼近目标量子位,从而可加速优化进程.仿真结果表明,该算法的优化能力优于原算法.%To enhance optimization ability of quantum potential well-based particle swarm optimization algorithm,a quantum particle swarm optimization algorithm based on Bloch spherical search is proposed by analyzing the design of quantum potential well-based particle swarm optimization algorithms.Firstly,particles are expressed with qubits,axis of rotation is established with Pauli matrix,the angle of rotation is obtained with a model of Delta potential well,and search is realized with rotation of qubits in Bloch sphere.Then,to avoid premature convergence,mutation of particles is achieved with Hadamard gates.Such rotation makes current qubit approximates target qubit along with the biggest circle on Bloch sphere,which accelerates optimization process.It shows that the proposed algorithm is superior to the original one in optimization ability.

  7. 基于Bloch球面搜索的量子蚁群优化算法%Quantum ant colony optimization based on Bloch spherical search

    Institute of Scientific and Technical Information of China (English)

    李盼池; 王海英

    2013-01-01

    To enhance the optimization efficiency of ant colony algorithms,a quantum ant colony optimization algorithm based on Bloch spherical search is proposed.When this algorithm works,ants' locations are encoded by the qubits described on the Bloch sphere,the ants' target locations are determined according to the selected probability constructed by the pheromone and the heuristic information,and the ants' movement is realized with the rotation of the qubits on the Bloch sphere.To avoid premature convergence,the mutation is performed with the Hadamard gates.The pheromone and the heuristic information are updated in the new location of ants.The simulation results show that the proposed algorithm is superior to other quantum intelligent optimization algorithms in both the search capability and the optimization efficiency.%为提高蚁群算法的优化效率,提出一种基于Bloch球面搜索的量子蚁群优化算法.该算法用Bloch球面描述的量子比特对蚂蚁位置编码,用信息素强度和启发式信息构造的选择概率选择蚂蚁的移动目标,用量子比特在Bloch球面上的绕轴旋转实现蚂蚁移动,用Hadamard门实现变异以避免早熟收敛,在移动后的新位置完成信息素和启发式信息的更新.仿真结果表明该方法的搜索能力和优化效率优于其他量子智能优化算法.

  8. BIOLOGIA REPRODUTIVA DO PEIXE MUÇUM, Synbranchus marmoratus BLOCH, 1975 NO AÇUDE MARECHAL DUTRA, RIO GRANDE DO NORTE, BRASIL.

    OpenAIRE

    Nirlei Hirachy Costa Barros; Wallace Silva Nascimento; Andréa Soares Araújo; Arrilton Araujo Souza; Sathyabama Chellappa

    2013-01-01

    A biologia reprodutiva do peixe hermafrodita mussum, Synbranchus marmoratus (Bloch, 1795) (Osteichthyes: Synbranchidae) foi investigada no açude Marechal Dutra, Acari, Rio Grande do Norte, utilizando os exemplares capturados mensalmente no período de julho de 2010 á janeiro de 2011. Os peixes capturados foram numerados, pesados, medidos, dissecados as e gônadas foram retiradas, pesadas e identificadas quanto ao sexo. A relação peso-comprimento foi determinada para sexos agrupados. O índice go...

  9. Metazoan parasites of Mystus vittatus (Bloch) of River Godavari with description of a new species of Acanthocephala, Raosentis godavarensis sp. nov.

    Science.gov (United States)

    Vankara, Anu Prasanna; Vijayalakshmi, C

    2009-12-01

    A total of 9 metazoan parasitic species were identified from Mystus vittatus (Bloch) in river Godavari during 2005-2007 including 2 monogeneans, 2 digeneans, 3 acanthocephalans and 2 copepods. Two species of monogeneans (Bifurcohaptor indicus and Thaparocleidus tengra), digeneans (Haplorchoides macrones and metacercariae of Isoparorchis hypselobagri), an acanthocephalan (Raosentis podderi) found during the present study are of common occurrence in this fish. M. vittatus constitutes a new host record for an acanthocephalan, Raosentis thapari and 2 copepods, Argulus striatus and Lamproglena hospetensis. The occurrence of A. striatus represents unusual for M. vittatus. A new species of acanthocephala, Raosentis godavarensis sp. nov is reported, described and illustrated. PMID:23129893

  10. La conciencia de la libertad (La filosofía moral como filosofía de la historia en Ernst Bloch)

    OpenAIRE

    Gimbernat, José Antonio

    1991-01-01

    Not available.

    A partir del concepto hegeliano de «progreso en la conciencia de la libertad », se puede hacer una lectura de la filosofía moral de Bloch como filosofía de la historia. Ello conduce a una reino reinterpretación libre y materialista de Hegel y a una recuperación de la moral en el marxismo. En diálogo con Kant se hace posible descubrir el potencial utópico del énfasis subjetivo de la moral. El objetivo del reino de la libertad marxiano es la clave de una histor...

  11. Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local ${\\cal PT}$-Symmetry

    CERN Document Server

    Bender, N; Ellis, F M; Kottos, T

    2015-01-01

    We propose a family of {\\it local} $\\cal{PT}$-symmetric photonic lattices with transverse index gradient $\\omega$, where the emergence of {\\it stable} Bloch-Zener oscillations are controlled by the degree of non-Hermiticity $\\gamma$ of the lattice. In the exact $\\cal{PT}$-symmetric phase we identify a condition between $\\omega$ and $\\gamma$ for which a wavepacket self -imaging together with a cascade of splittings and giant recombinations occurs at various propagation distances. The giant wavepacket recombination is further enhanced by introducing local impurities.

  12. 方波电场驱动下的Rabi振荡%Rabi Oscillations Between Bloch Bands in a Square-wave Electric Field

    Institute of Scientific and Technical Information of China (English)

    宫建平; 邵建立; 段素青; 赵宪庚

    2006-01-01

    We investigate double Bloch bands driven by a square-wave electric field with a tight-binding model. Using Fourier analysis, we analytically obtain resonance conditions of Rabi oscillation and Rabi frequency in the weak-coupling limit. The results are verified by numerical evolution of electrons.%研究了方波电场驱动下的双Bloch带的紧束缚模型.借助Fourier分析,得到了在弱耦合极限下Rabi振荡及Rabi频率的解析解;这些结果均由电子的数值演化所证实.

  13. Functional Equations and Fourier Analysis

    OpenAIRE

    Yang, Dilian

    2010-01-01

    By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.

  14. Integral equations and computation problems

    International Nuclear Information System (INIS)

    Volterra's Integral Equations and Fredholm's Integral Equations of the second kind are discussed. Computational problems are found in the derivations and the computations. The theorem of the solution of the Fredholm's Integral Equation is discussed in detail. (author)

  15. Scaling Equation for Invariant Measure

    Institute of Scientific and Technical Information of China (English)

    LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui

    2003-01-01

    An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

  16. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  17. Unified derivation of evolution equations

    OpenAIRE

    Li, Hsiang-nan

    1998-01-01

    We derive the evolution equations of parton distribution functions appropriate in different kinematic regions in a unified and simple way using the resummation technique. They include the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for large momentum transfer $Q$, the Balitskii-Fadin-Kuraev-Lipatov equation for a small Bjorken variable $x$, and the Ciafaloni-Catani-Fiorani-Marchesini equation which embodies the above two equations. The relation among these equations is explored, and p...

  18. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  19. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  20. Stochastic porous media equations

    CERN Document Server

    Barbu, Viorel; Röckner, Michael

    2016-01-01

    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  1. Generalization of Hopf Functional Equation

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    This paper generalizes the Hopf functional equation in order to apply it to a wider class of not necessarily incompressible fluid flows. We start by defining characteristic functionals of the velocity field, the density field and the temperature field of a compressible field. Using the continuity equation, the Navier-Stokes equations and the equation of energy we derive a functional equation governing the motion of an ideal gas flow and a van der Waals gas flow, and then give some general methods of deriving a functional equation governing the motion of any compressible fluid flow. These functional equations can be considered as the generalization of the Hopf functional equation.

  2. Symplectic Dirac Equation

    CERN Document Server

    Amorim, R G G; Silva, Edilberto O

    2015-01-01

    Symplectic unitary representations for the Poincar\\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.

  3. Gas Dynamics Equations: Computation

    CERN Document Server

    Chen, Gui-Qiang G

    2012-01-01

    Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.

  4. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2002-01-01

    Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

  5. The relativistic Pauli equation

    OpenAIRE

    Delphenich, David

    2012-01-01

    After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charge...

  6. Systematic Equation Formulation

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2007-01-01

    A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

  7. ON A FUNCTIONAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    Ding Yi

    2009-01-01

    In this article, the author derives a functional equation η(s)=[(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.

  8. Solving Diophantine Equations

    OpenAIRE

    Cira, Octavian; Smarandache, Florentin

    2016-01-01

    In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation {\\eta}({\\pi}(x)) = {\\pi}({\\eta}(x)), where {\\eta} is the Smarandache function and {\\pi} is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and th...

  9. Theory of differential equations

    CERN Document Server

    Gel'fand, I M

    1967-01-01

    Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations.This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cau

  10. Kepler Equation solver

    Science.gov (United States)

    Markley, F. Landis

    1995-01-01

    Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

  11. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  12. Application of Bloch oscillations and atomic interferometry for the measurement of the h/m ratio and the determination of the fine structure constant

    International Nuclear Information System (INIS)

    It is possible to determine the h/mRb ratio between the Planck constant and the mass of the atoms, and then to deduce a value of the fine structure constant alpha, from the accurate measurement of the recoil velocity of an atom absorbing a photon. To perform this measurement we combine the high efficiency of Bloch oscillations with the high sensitivity of a Ramsey-Borde interferometer. The Bloch oscillations technic allows us to transfer a large number of recoils to the atoms (up to 1600 recoil momenta). An interferometric Ramsey-Borde velocity sensor, based on velocity selective Raman transitions, allows us to measure the momentum transferred to the atoms. A measurement with a statistical uncertainty of 3 ppb (3*10-9), in conjunction with a careful study of systematic effects (3.4 ppb), lead us to a determination of alpha with a relative uncertainty of 4.8 ppb. The value of α-1 is 137.03599887(65). It is the best determination of alpha, independent from quantum electrodynamics

  13. RELACIONES TALLA-PESO DEL BARBUL (Pimelodus clarias f.c. Bloch, 1785 EN LA CUENCA DEL RIO SINU,

    Directory of Open Access Journals (Sweden)

    Iliana Santos-Sanes,

    2006-12-01

    Full Text Available Objetivo. Establecer las relaciones de talla y peso del barbul (Pimelodus clarias en la cuenca del río Sinú. Materiales y Métodos. Se estimaron las relaciones talla-peso de 4324 individuos de Barbul (Pimelodus clarias f.c. Bloch, 1785 colectados entre enero 2000 y diciembre 2002. Resultados. La longitud total (LT osciló entre 13.0-30.0 cm, promedio de 19.5 (±1.6 cm y el peso total (WT entre 20.0 y 248.1 g, promedio de 65.8 (±23.2 g. Las relaciones lineales estimadas fueron: LT = 1.92 (�� 0.16 + 1.20 (± 0.01 LS, r = 0.96; LT = 1.21 (± 0.16 + 1.15 (± 0.01 LH; r = 0.97 y LH = 0.91 (± 0.10 + 1.02 (± 0.01 LS, r = 0.97; con diferencias significativas entre las pendientes de la relación longitud estándar (LS-longitud horquilla (LH. La relación longitud-peso fue: WT = 0.005 (± 0.09 LT 3.16 (± 0.07, n = 4324, r = 0.81, con diferencias estadísticas significativas entre los diferentes coeficientes de crecimiento y factores de condición. Se encontró correlación entre el factor de condición, los niveles del Río Sinú y la época de desove del Barbul, la cual se extiende de marzo a octubre. Conclusión. Los resultados alcanzados en este estudio sugieren que las nuevas condiciones del río no han afectado la dinámica poblacional de la especie en lo que al crecimiento en talla y peso se refiere, y que el Barbul se ha adaptado a estas nuevas condiciones.

  14. On difference Riccati equations and second order linear difference equations

    OpenAIRE

    Ishizaki, Katsuya

    2011-01-01

    In this paper, we treat difference Riccati equations and second order linear difference equations in the complex plane. We give surveys of basic properties of these equations which are analogues in the differential case. We are concerned with the growth and value distributions of transcendental meromorphic solutions of these equations. Some examples are given.

  15. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  16. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation

    Institute of Scientific and Technical Information of China (English)

    LIU Yan-hong; ZHANG Hui-ming

    2007-01-01

    Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.

  17. Dunkl Hyperbolic Equations

    Directory of Open Access Journals (Sweden)

    Hatem Mejjaoli

    2008-12-01

    Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.

  18. Modelling by Differential Equations

    Science.gov (United States)

    Chaachoua, Hamid; Saglam, Ayse

    2006-01-01

    This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

  19. Do Differential Equations Swing?

    Science.gov (United States)

    Maruszewski, Richard F., Jr.

    2006-01-01

    One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

  20. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2013-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

  1. On the Breit Equation

    OpenAIRE

    Kasari, Hikoya; Yamaguchi, Yoshio

    2001-01-01

    Contrary to the conventional belief, it was shown that the Breit equation has the eigenvalues for bound states of two oppositely charged Dirac particles interacting through the (static) Coulomb potential. All eigenvalues reduced to those of the Sch\\"odinger case in the non-relativistic limit.

  2. The Equation of Causality

    OpenAIRE

    Chi, Do Minh

    1999-01-01

    We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence, our theoretical point suggests ideas to build other laws including the law of the Universe's evolution.

  3. Exciton laser rate equations

    Directory of Open Access Journals (Sweden)

    Garkavenko A. S.

    2011-08-01

    Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.

  4. Nonlocal electrical diffusion equation

    Science.gov (United States)

    Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

    2016-07-01

    In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0solar panels, electrochemical phenomena and the description of anomalous complex processes.

  5. Calculus & ordinary differential equations

    CERN Document Server

    Pearson, David

    1995-01-01

    Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

  6. Equational binary decision diagrams

    NARCIS (Netherlands)

    Groote, J.F.; Pol, J.C. van de

    2000-01-01

    We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checkin

  7. Lie Symmetries of Ishimori Equation

    Institute of Scientific and Technical Information of China (English)

    SONG Xu-Xia

    2013-01-01

    The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.

  8. Anticipated backward stochastic differential equations

    OpenAIRE

    Peng, Shige; Yang, Zhe

    2009-01-01

    In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.

  9. Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\\"odinger equation

    CERN Document Server

    Steyerl, A; Müller, G; Malik, S S; Desai, A M; Golub, R

    2014-01-01

    Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.

  10. Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schrödinger equation

    Science.gov (United States)

    Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.

    2014-05-01

    Pendlebury etal . [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schrödinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.

  11. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian N

    2006-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  12. Differential Equations with Linear Algebra

    CERN Document Server

    Boelkins, Matthew R; Potter, Merle C

    2009-01-01

    Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, t

  13. Stochastic differential equations and applications

    CERN Document Server

    Friedman, Avner

    2006-01-01

    This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es

  14. Classical Diophantine equations

    CERN Document Server

    1993-01-01

    The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...

  15. Differential equations with Mathematica

    CERN Document Server

    Abell, Martha L

    2004-01-01

    The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica

  16. The open boundary equation

    Directory of Open Access Journals (Sweden)

    D. Diederen

    2015-06-01

    Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.

  17. Information Equation of State

    Directory of Open Access Journals (Sweden)

    M. Paul Gough

    2008-07-01

    Full Text Available Landauer’s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the ‘Why now?’ question we wonder ‘What next?’ as we expect the information equation of state to tend towards w = 0 in the future.c

  18. 基于Bloch球面搜索的混沌量子免疫算法%Chaos quantum immune algorithm based on Bloch sphere

    Institute of Scientific and Technical Information of China (English)

    李盼池; 林晶晶

    2012-01-01

    In the existing quantum intelligent optimization algorithms, almost all of the individuals are encoded by qubits described on plane unit circle. Since there is only one adjustable parameter, quantum properties have not been fully embodied, which limits the improvement of the optimization ability further. To address this issue, a chaos quantum immune algorithm based on Bloch sphere is proposed. In the proposed algorithm, the antibodies are encoded by qubits described on Bloch sphere, the axis of rotation is designed by using Pauli matrix, the clone of the excellent antibodies is performed by rotating qubits on Bloch sphere, and the local searching is achieved by employing the chaos variables in the rotation angles. The global searching is achieved by the mutations of the inferior individuals based on the Hadamard gates. The simulation results show that the proposed algorithm is superior to other quantum intelligent optimization algorithms in both search capability and optimization efficiency.%目前大多数量子智能优化算法的个体均采用基于平面单位圆描述的量子比特编码,由于量子比特只有一个可调参数,量子特性没有得到充分体现,从而限制了优化能力的进一步提高.针对这一问题提出一种基于Bloch球面搜索的混沌量子免疫算法.该方法采用Bloch球面描述的量子比特对抗体进行编码,用泡利矩阵建立旋转轴,用量子比特在Bloch球面上的绕轴旋转实现优良抗体的克隆,通过在旋转角度中引入混沌变量动态改变转角大小实现局部搜索;用Hadamard门实现较差抗体的变异,实现全局搜索.仿真结果表明,提出的方法在搜索能力和优化效率两方面均比其他量子智能优化算法有所提高.

  19. 基于Bloch球面坐标的量子粒子群算法%Quantum particle swarm optimization based on Bloch coordinates of qubits

    Institute of Scientific and Technical Information of China (English)

    陈义雄; 梁昔明; 黄亚飞

    2013-01-01

    To improve the efficiency of Particle Swarm Optimization ( PSO), a quantum particle swarm optimization algorithm combined with quantum theory on the basis of Bloch sphere was proposed. In Bloch spherical coordinates, the particle automatically updated rotation angle and particle position, without setting the rotation angle in the form of look-up table (or setting fixed value of the interval), making up for the deficiency of quantum evolutionary algorithm and quantum genetic algorithm on the basis of Bloch sphere, and the algorithm is more generalizable. Using quantum Hadamard gate to realize the variation of particle enhanced the diversity of population, and prompted particle jump out of local extreme value. The simulation results of the typical function optimization problem show that the algorithm is stable with high precision and fast convergence rate, and it is practical.%为了提高粒子群优化(PSO)算法的优化效率,结合量子理论提出一种基于Bloch球面坐标的量子粒子群优化算法.在Bloch球面坐标下,粒子自动更新旋转角大小和粒子位置,不需将旋转角以查询表的形式设定(或设定为区间上的固定值),弥补了Bloch球面坐标下量子进化算法和量子遗传算法的不足,算法更具有普遍性;用量子Hadamard门实现粒子的变异,增强了种群的多样性,促使粒子跳出局部极值点.对典型函数优化问题的仿真结果表明,提出的算法稳定性强,精度高,收敛速度快,具有一定的实用价值.

  20. New application to Riccati equation

    Science.gov (United States)

    Taogetusang; Sirendaoerji; Li, Shu-Min

    2010-08-01

    To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.

  1. Telegrapher's equation for light derived from the transport equation

    OpenAIRE

    Hoenders, Bernhard J.; Graaff, R.

    2005-01-01

    Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapher's equations in the well known P-1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapher's equations were de...

  2. Non-Bloch nature of alloy states in a conventional semiconductor alloy - GaxIn1-xP as an example

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Lin-Wang; Zhang, Yong; Mascarenhas, Angelo; Wang, Lin-Wang

    2008-07-11

    Contrary to the conventional wisdom, electronic states in a 'well behaved' semiconductor alloy such as Ga{sub x}In{sub 1-x}P may drastically deviate from a Bloch state, which can be true even for band edge states if they are derived from degenerate critical points. For Ga{sub x}In{sub 1-x}P in the entire composition range, k-space spectral analyses are performed for the important critical points, revealing the significance of the (near) resonant inter-and intra-valley scatterings of the fluctuation potential in the alloy. The non-trivial implications of such scatterings on the transport and strain effect are discussed.

  3. Histopathological alterations of the gills, liver and kidneys in Anabas Testudineus (Bloch) fish living in an unused lignite mine, Li District, Lamphun Povince, Thailand

    Energy Technology Data Exchange (ETDEWEB)

    Saenphet, S.; Thaworn, W.; Saenphet, K. [Chiang Mai University, Chiang Mai (Thailand). Faculty of Science

    2009-09-15

    The acidity of mine water generally makes it toxic to most organisms. The gills, kidneys and livers of Anabas testudineus Bloch fish inhabiting the acidic water (pH 2-4) of an unused lignite mine in Li District, Lamphun Province, Thailand were examined and compared to those of farmed fish. Tissue abnormalities were found in all investigated organs. Deterioration and telangiectasia of gill filaments were found. Liver tissue revealed hemorrhages, blood congestion and necrotic cells with mononuclear cell infiltration. In addition, hypertrophy of the epithelial cells of the renal tubules with reduced lumens, aneurisms of the renal tubules, and contractions of the glomeruli in the Bowman's capsule were observed. These histopathological findings suggest the acidic water in this habitat causes severe damage to the internal organs of fish and consequently alter their physiological status. Since the water in this pond is utilized by local people, these findings highlight the need for adequate water treatment.

  4. Converting fractional differential equations into partial differential equations

    OpenAIRE

    He Ji-Huan; Li Zheng-Biao

    2012-01-01

    A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.

  5. The compressible adjoint equations in geodynamics: equations and numerical assessment

    Science.gov (United States)

    Ghelichkhan, Siavash; Bunge, Hans-Peter

    2016-04-01

    The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.

  6. Ordinary differential equations

    CERN Document Server

    Cox, William

    1995-01-01

    Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further

  7. Differential Equations as Actions

    DEFF Research Database (Denmark)

    Ronkko, Mauno; Ravn, Anders P.

    1997-01-01

    We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....

  8. Dimensional Equations of Entropy

    CERN Document Server

    Sparavigna, Amelia Carolina

    2015-01-01

    Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.

  9. Partial differential equations

    CERN Document Server

    Sloan, D; Süli, E

    2001-01-01

    /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in

  10. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2013-01-01

    Generalized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicat

  11. Matlab differential equations

    CERN Document Server

    Lopez, Cesar

    2014-01-01

    MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential Equations introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduct

  12. Conservational PDF Equations of Turbulence

    Science.gov (United States)

    Shih, Tsan-Hsing; Liu, Nan-Suey

    2010-01-01

    Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

  13. On Certain Dual Integral Equations

    Directory of Open Access Journals (Sweden)

    R. S. Pathak

    1974-01-01

    Full Text Available Dual integral equations involving H-Functions have been solved by using the theory of Mellin transforms. The proof is analogous to that of Busbridge on solutions of dual integral equations involving Bessel functions.

  14. Program Transformation by Solving Equations

    Institute of Scientific and Technical Information of China (English)

    朱鸿

    1991-01-01

    Based on the theory of orthogonal program expansion[8-10],the paper proposes a method to transform programs by solving program equations.By the method,transformation goals are expressed in program equations,and achieved by solving these equations.Although such equations are usually too complicated to be solved directly,the orthogonal expansion of programs makes it possible to reduce such equations into systems of equations only containing simple constructors of programs.Then,the solutions of such equations can be derived by a system of solving and simplifying rules,and algebraic laws of programs.The paper discusses the methods to simplify and solve equations and gives some examples.

  15. Kepler's Differential Equations

    CERN Document Server

    Holder, Martin

    2011-01-01

    Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that Kepler demonstrated the elliptic orbit to be composed of intelligeable differential pieces, in modern language, to result from a differential equation. Kepler was first to attribute planetary orbits to a force from the sun, rather than giving them a predetermined geometric shape. Even though neither the force was known nor its relation to motion, he could determine the differential equations of motion from observation. This is one of the most important achievements in the history of physics. In contrast to Newton's Principia and Galilei's Dialogo Kepler's text is not easy to read, for various reasons. Therefore, in the present article, his results -- most of them well known -- are first presented in modern language. Then, in order to justify the claim, the full text of some rele...

  16. The Dirac equation

    International Nuclear Information System (INIS)

    This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics

  17. Growth Equation with Conservation Law

    OpenAIRE

    Lauritsen, Kent Baekgaard

    1995-01-01

    A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows for a unified investigation of growth equations. From a dynamic renormalization-group analysis critical exponents and universality classes are determined for growth models with a conservation law.

  18. ``Riemann equations'' in bidifferential calculus

    Science.gov (United States)

    Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.

    2015-10-01

    We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.

  19. Hyperbolic Methods for Einstein's Equations

    OpenAIRE

    Reula Oscar

    1998-01-01

    I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.

  20. Successfully Transitioning to Linear Equations

    Science.gov (United States)

    Colton, Connie; Smith, Wendy M.

    2014-01-01

    The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…