Generalized Bloch-Wangsness-Redfield Kinetic Equations
Fatkullin, Nail
2011-01-01
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short correlation times and large heat capacity of the lattice are sufficient to derive the kinetic equations without the use of perturbation theory for the spin-lattice interaction operator. The perturbation theory is only applied for calculation of the kinetic coeff...
On unorthodox solutions of the Bloch equations
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...
Fundamentals and applications of the Landau–Lifshitz–Bloch equation
Atxitia, U.; Hinzke, D.; Nowak, U.
2017-01-01
The influence of thermal excitations on magnetic materials is a topic of increasing relevance in the theory of magnetism. The Landau–Lifshitz–Bloch equation describes magnetisation dynamics at finite temperatures. It can be considered as an extension of already established micromagnetic methods with a comparable numerical effort. This review is a brief summary of this new field of research, with a focus on the fundamentals of the Landau–Lifshitz–Bloch equation, its connection with the stochastic Landau–Lifshitz equation, and its applications in modern magnetism.
Weak solutions of the Landau-Lifshitz-Bloch equation
Le, Kim Ngan
2016-12-01
The Landau-Lifshitz-Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB equation in case the temperature raised higher than the Curie temperature. The existence of weak solution is showed and its regularity properties are also discussed. In this way, we lay foundations for the rigorous theory of LLB equation that is currently not available.
Continuity, the Bloch-Torrey equation, and Diffusion MRI
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...
Bloch-Redfield equations for modeling light-harvesting complexes
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...
Bloch-Redfield equations for modeling light-harvesting complexes.
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.
Landau-Lifhsitz-Bloch equation for exchange coupled grains
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.
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.
Wieser, R
2016-10-05
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.
Circularly polarized few-cycle optical rogue waves: rotating reduced Maxwell-Bloch equations.
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.
Derivation of the Landau-Lifshitz-Bloch equation from continuum thermodynamics
Berti, Alessia; Giorgi, Claudio
2016-11-01
Within the continuum thermodynamic framework, we derive the evolution equation for the magnetization vector in a ferromagnetic body. This procedure leads to an evolution equation that generalizes the well-known Landau-Lifshitz model for magnetically saturated bodies and looks very similar to the Landau-Lifshitz-Bloch equation which was obtained by Garanin in 1997 from statistical mechanics. As a byproduct, we also obtain a generalization of the Gilbert equation when the magnetic field is far from saturation. By virtue of a suitable choice of the Gibbs free energy, this phenomenological model is able to describe the phase transition occurring from the paramagnetic to the ferromagnetic regime in anisotropic ferromagnets.
Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron
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...
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...
Maxwell-Bloch Equations Modeling of Ultrashort Optical Pulse Propagation in Semiconductor Materials
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.
Comment on "On the analytical solution of the optical Bloch equations"
Noh, Heung-Ryoul; Jhe, Wonho
2012-02-01
In a recent paper [P.J. Colmenares and J.L. Paz, Opt. Commun. 284 (2011) 5171], analytical solutions of the optical Bloch equations are presented. This paper follows the same procedures as presented in the paper by the authors [H.R. Noh and W. Jhe, Opt. Commun. 283 (2010) 2353] but concludes that their results are substantially different from the results of the authors. We find that the discrepancy results from the wrong initial conditions employed by those authors for one of the Bloch vector components ( w), whose initial value must be 1 not 0. We also find that if proper initial conditions are used, there are no discrepancies between the two results.
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.
High tip angle approximation based on a modified Bloch-Riccati equation.
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.
Energy Technology Data Exchange (ETDEWEB)
Friedberg, Richard [Department of Physics, Columbia University, New York, NY 10027 (United States); Manassah, Jamal T. [HMS Consultants, Inc., PO Box 592, New York, NY 10028 (United States)], E-mail: jmanassah@gmail.com
2008-07-28
The superradiance from a slab of inverted two-level atoms is theoretically analyzed in the linear regime from both the perspective of the expansion in eigenfunctions of the integral equation with the Lienard-Wiechert potential as kernel, and that of linearizing the Maxwell-Bloch equations. We show the equivalence of both approaches. We show that the so-called Reduced Maxwell-Bloch equations do not yield even approximately the correct solution when applied in the obvious way, but that they can be made to give the correct solution by adding a fictitious input field.
Tscherbul, Timur V; Brumer, Paul
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.
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)
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
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.
Tseitlin, Mark; Eaton, Gareth R; Eaton, Sandra S
2013-12-01
Rapid-scan EPR has been shown to improve the signal-to-noise ratio relative to conventional continuous wave spectroscopy. Equations are derived for the steady-state solution to the Bloch equations as a Fourier expansion in the harmonics of the scan frequency. This simulation method is about two orders of magnitude faster than time-domain numerical integration.
Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.
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.
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.
Surdutovich, G. I.; Ghiner, A. V.
2000-08-01
A famous model of a two-level atom interacting with the classical electromagnetic field is used to illustrate the fundamental problem of the relationship between the dynamical and relaxation processes under the interaction of radiation with a quantum-mechanical system and, as a result, to derive nonlinear Bloch-like equations. The presented considerations are based on the analysis of the balance of the fluxes of energy between atomic and field subsystems. It is shown that the generally accepted model of the exponential relaxation deduced for an isolated excited atom and inserted customarily into optical Bloch equations (OBE) describing atom in an external field always leads to a very strange result: spontaneous emission of an atom should be accompanied by the radiation of the coherent field into the external field's mode. Making use of only the energetic considerations, we found the relaxation mechanism (in the form of additional terms in the OBE) which, on the one hand, guarantees the fulfillment of the energetic balance and, on the other hand, allows to introduce arbitrary additional collision-like relaxation mechanism without violation of this balance. Note that these additional terms introduced into OBE from the energetic considerations in a remarkable manner exactly correspond to the renormalization of the external field with the allowance of the classical radiation damping (RD) effect. The revisited OBE may be used as the starting point for considering the dynamics of an atom by making allowance for the quantum properties of an external field.
Optical Bloch Equations Modified with Phonon-Induced Intensity-Dependent Dephasing
Institute of Scientific and Technical Information of China (English)
无
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.
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.
Resummations in the Bloch-Nordsieck model
Jakovac, A
2011-01-01
We studied different levels of resummations of the exactly solvable Bloch-Nordsieck model in order to be able to compare the approximations with an exact result. We studied one-loop perturbation theory, 2PI resummation and Schwinger-Dyson equations truncated in a way to maintain Ward-identities. At all levels we carefully performed renormalization. We found that although the 2PI resummation does not exhibit infrared sensitivity at the mass shell (the one-loop perturbation theory does), but it is still far from the exact solution. The method of truncated Schwinger-Dyson equations, however, is exact in this model, so it provides a new way of solving the Bloch-Nordsieck model. This method can also be generalized to other, more complicated theories.
Polychromatic optical Bloch oscillations.
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.
Entangled Bloch Spheres: Bloch Matrix And Two Qubit State Space
Gamel, Omar
2016-01-01
We represent a two qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parameterize and visualize the two qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch spheres with superimposed correlation axes. It is shown that unitary transformations, local or nonlocal, have simple interpretations as axis rotations or mixing of certain degrees of freedom. The nonlocal unitary invariants of the state are then derived in terms of local unitary invariants. The positive partial transpose criterion for entanglement is generalized, and interpreted as a reflection, or a change of a single ...
A theory of generalized Bloch oscillations.
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.
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 cal...... oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics.......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...
Observation of anharmonic Bloch oscillations.
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.
Bloch oscillations in carbon nanotubes.
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.
Bloch oscillations in carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Jodar, Esther; Perez-Garrido, Antonio [Departamento Fisica Aplicada, Antiguo Hospital de Marina Campus Muralla del Mar, UPCT, Cartagena 30202 Murcia (Spain); Rojas, Fernando [Centro de Nanociencias y Nanotecnologia-UNAM, Apartado Postal 356, Ensenada, Baja California 22800 (Mexico)], E-mail: ejodar@upct.es
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. (fast track communication)
Hybrid Bloch-Anderson localization of light
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.
Optical analogue of electronic Bloch oscillations.
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.
Hybrid Bloch-Anderson localization of light.
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.
Hybrid Bloch-Anderson localization of light
Stutzer, Simon; Yaroslav V. Kartashov; 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 int...
Bloch oscillations in atom interferometry
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.
Electric dipoles on the Bloch sphere
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.
Bloch-Zener oscillations in binary superlattices.
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.
``Bloch wave'' modification of stimulated Raman by stimulated Brillouin scattering
Dodd, E. S.; Vu, H. X.; DuBois, D. F.; Bezzerides, B.
2013-03-01
Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at kLW˜kIAW/2˜k0 (kLW, kIAW, and k0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are
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
Magnetic Bloch oscillations in nanowire superlattice rings.
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.
Wave impedance retrieving via Bloch modes analysis
DEFF Research Database (Denmark)
Andryieuski, Andrei; Ha, S.; Sukhorukov, A.;
2011-01-01
of the Bloch mode, respectively. Case studies prove that our ap-proach can determine material and wave effective parameters of lossy and lossless metamaterials. In some examples when the passivity is violated we made further analysis and showed that this is due to the failure of concept of impedance retrieving......-ciples violation, like antiresonance behaviour with Im(ε) mode analysis of periodic metamaterials to extract the dominating (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......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...
Bloch oscillations in optical dissipative lattices.
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.
Experimental observation of spectral Bloch oscillations.
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.
Resonant delocalization and Bloch oscillations in modulated lattices.
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.
Fractional Bloch oscillations in photonic lattices.
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.
Fractional Bloch oscillations in photonic lattices
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.
Observation of Bloch oscillations in molecular rotation
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...
Bloch oscillations in complex crystals with PT symmetry.
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.
Terahertz Bloch oscillator with a modulated bias.
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.
Observation of Bloch Oscillations in Molecular Rotation.
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.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
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.
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.
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.
Bloch oscillations in plasmonic waveguide arrays.
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.
Symmetric States on the Octonionic Bloch Ball
Graydon, Matthew
2012-02-01
Finite-dimensional homogeneous self-dual cones arise as natural candidates for convex sets of states and effects in a variety of approaches towards understanding the foundations of quantum theory in terms of information-theoretic concepts. The positive cone of the ten-dimensional Jordan-algebraic spin factor is one particular instantiation of such a convex set in generalized frameworks for quantum theory. We consider a projection of the regular 9-simplex onto the octonionic projective line to form a highly symmetric structure of ten octonionic quantum states on the surface of the octonionic Bloch ball. A uniform subnormalization of these ten symmetric states yields a symmetric informationally complete octonionic quantum measurement. We discuss a Quantum Bayesian reformulation of octonionic quantum formalism for the description of two-dimensional physical systems. We also describe a canonical embedding of the octonionic Bloch ball into an ambient space for states in usual complex quantum theory.
Bloch oscillations of path-entangled photons.
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.
Photonic Bloch oscillations of correlated particles.
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.
Quantum state transfer via Bloch oscillations.
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.
Compact composition operators on the Bloch space in polydiscs
Institute of Scientific and Technical Information of China (English)
ZHOU; Zehua
2001-01-01
［1］Timoney, R., Bloch function in several complex variables, I, Bull. London Math. Soc., 1980, 12(37): 241.［2］Shi, J. H., Luo, L., Composition operators on the Bloch space of several complex variables, Acta Math. Sinica, 2000, 16(1): 85.［3］Madigan, K., Matheson, A., Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., 1995, 347(7): 2679.
Bloch oscillations in the presence of plasmons and phonons
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)].
An approximation formula for the Bloch-Siegert shift of the Rabi model
Rapedius, K
2015-01-01
So far the Bloch-Siegert shift of the Rabi model has only been calculated numerically or by means of perturbation theory valid in either the weak or strong driving regime only. Recently Yan, L\\"u, and Zheng [Phys.~Rev.~A {\\bf 91}, 053834 (2015)] showed how to reduce the problem to solving a system of three nonlinear equations. Here, we pursue an alternative approach based on a perturbation expansion extrapolation technique. We are thus able to derive an explicit analytical approximation formula for the Bloch-Siegert shift of the Rabi model which is valid for all parameter regimes from weak to strong driving. Comparison with numerically exact results reveals an excellent agreement over the entire driving-strength range.
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.
Entangled Bloch spheres: Bloch matrix and two-qubit state space
Gamel, Omar
2016-06-01
We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parametrize and visualize the two-qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch spheres with superimposed correlation axes. It is shown that unitary transformations, local or nonlocal, have simple interpretations as axis rotations or mixing of certain degrees of freedom. The nonlocal unitary invariants of the state are then derived in terms of local unitary invariants. The positive partial transpose criterion for entanglement is generalized, and interpreted as a reflection, or a change of a single sign. The formalism is used to characterize maximally entangled states, and generalize two qubit isotropic and Werner states.
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.
Semiconductor Laser Theory: The Maxwell--Bloch Equations
Gehrig, Edeltraud; Hess, Ortwin
Because of its central importance for fundamental physics as well as for technological applications, the electronic structure of layered semiconductor structures has attracted much interest over the last two decades. In theoretical studies, methods based on the envelope function approximation are predominant, the reason being that the EFA allows a comprehensive description of electron- and hole-like states. It can cope with periodic or aperiodic geometries of quantum structures, as well as perturbations such as a magnetic field, strain, or a built-in or external potential. Details of the underlying crystal potential are included in terms of bulk band structure parameters.
Synchronization of Bloch oscillations by a ring cavity.
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.
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...
Experimental observation of N00N state Bloch oscillations.
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.
Bloch oscillations in chirped layered structures with metamaterials.
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.
Bloch oscillations of THz acoustic phonons in coupled nanocavity structures.
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.
Bloch oscillations in a one-dimensional spinor gas.
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.
Bloch inductance in small-capacitance Josephson junctions.
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.
A Bloch-Wigner complex for SL_2
Hutchinson, Kevin
2011-01-01
We introduce a refinement of the Bloch-Wigner complex of a field F. This is a complex of modules over the multiplicative group of the field. Instead of computing K_2 and indecomposable K_3 - as the classical Bloch-Wigner complex does - it calculates the second and third integral homology of SL_2 of the field. On passing to coinvariants for the action of the multiplicative group we recover the classical Bloch-Wigner complex. The case of finite fields is included throughout the article.
Spin wave vortex from the scattering on Bloch point solitons
Energy Technology Data Exchange (ETDEWEB)
Carvalho-Santos, V.L., E-mail: vagson.carvalho@usach.cl [Instituto Federal de Educação, Ciência e Tecnologia Baiano - Campus Senhor do Bonfim, Km 04 Estrada da Igara, 48970-000 Senhor do Bonfim, Bahia (Brazil); Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Elías, R.G., E-mail: gabriel.elias@usach.cl [Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Nunez, A.S., E-mail: alnunez@dfi.uchile.cl [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago (Chile)
2015-12-15
The interaction of a spin wave with a stationary Bloch point is studied. The topological non-trivial structure of the Bloch point manifests in the propagation of spin waves endowing them with a gauge potential that resembles the one associated with the interaction of a magnetic monopole and an electron. By pursuing this analogy, we are led to the conclusion that the scattering of spin waves and Bloch points is accompanied by the creation of a magnon vortex. Interference between such a vortex and a plane wave leads to dislocations in the interference pattern that can be measurable by means of magnon holography.
Bloch state tomography using Wilson lines
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.
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.
Large momentum beam splitter using Bloch oscillations.
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.
Reexamination of Bloch-Messiah reduction
Cariolaro, Gianfranco; Pierobon, Gianfranco
2016-06-01
The Bloch-Messiah (BM) reduction allows the decomposition of an arbitrarily complicated Gaussian unitary into a very simple scheme in which linear optical components are separated from nonlinear ones. It is based on the combined application of the eigendecomposition (EID) and singular value decomposition (SVD) of the two matrices associated to the Bogoliubov transformation of the given Gaussian unitary, with the constraint that the unitary matrices appearing in the SVDs must verify a stringent condition, called in the paper "rotation condition". Thus, for a correct evaluation of the BM reduction, one has to choose, among the possible SVD pairs, the pair that meets this condition. The paper develops an approach to this problem, which is based on the introduction of a balancing matrix in the SVDs to fulfill the rotation condition. The theory is illustrated with a few application examples.
Long-living BLOCH oscillations of matter waves in periodic potentials.
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.
Coupled bloch-phonon oscillations in semiconductor superlattices
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)].
Estimates on Bloch constants for planar harmonic mappings
Institute of Scientific and Technical Information of China (English)
无
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.
Composition Operators on Dirichlet Spaces and Bloch Space
Institute of Scientific and Technical Information of China (English)
Yuan CHENG; Sanjay KUMAR; Ze Hua ZHOU
2014-01-01
In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.
Calculation of the relativistic Bloch correction to stopping power
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.
Bloch-mode analysis for retrieving effective parameters of metamaterials
DEFF Research Database (Denmark)
Andryieuski, Andrei; Ha, Sangwoo; Sukhorukov, Andrey A.;
2012-01-01
by our method with a high accuracy. We employ both surface and volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes to determine the Bloch and wave impedances, respectively. We discuss how this method works for several characteristic examples, and demonstrate...... that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials....
Supercurrent enhancement in Bloch domain walls.
Robinson, J W A; Chiodi, F; Egilmez, M; Halász, Gábor B; Blamire, M G
2012-01-01
Conventional spin-singlet Cooper pairs convert into spin-triplet pairs in ferromagnetic Josephson junctions in which the superconductor/ferromagnet interfaces (S/F) are magnetically inhomogeneous. Although much of the theoretical work describing this triplet proximity effect has considered ideal junctions with magnetic domain walls (DW) at the interfaces, in practice it is not easily possible to isolate a DW and propagate a supercurrent through it. The rare-earth magnet Gd can form a field-tuneable in-plane Bloch DW if grown between non-co-linearly aligned ferromagnets. Here we report supercurrents through magnetic Ni-Gd-Ni nanopillars: by field annealing at room temperature, we are able to modify the low temperature DW-state in Gd and this result has a striking effect on the junction supercurrent at 4.2 K. We argue that this result can only be explained in terms of the interconversion of triplet and singlet pairs, the efficiency of which depends on the magnetic helicity of the structure.
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.
Landau-Zener Bloch Oscillations with Perturbed Flat Bands.
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.
Bloch Oscillations of Einstein-Podolsky-Rosen States
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...
Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces
Directory of Open Access Journals (Sweden)
Flavia Colonna
2012-01-01
Full Text Available The logarithmic Bloch space Blog is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=supz∈𝔻(1-|z|2log (2/(1-|z|2|f'(z|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy space Hp (with 1≤p≤∞ into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mapping Hp into the little logarithmic Bloch space defined as the subspace of Blog consisting of the functions f such that lim|z|→1(1-|z|2log (2/(1-|z|2|f'(z|=0.
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 ...
Lassoued, R.; Lecheheb, M.; Bonnet, G.
2012-08-01
This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.
Polarization controlled directional propagation of Bloch surface wave.
Kovalevich, Tatiana; Boyer, Philippe; Suarez, Miguel; Salut, Roland; Kim, Myun-Sik; Herzig, Hans Peter; Bernal, Maria-Pilar; Grosjean, Thierry
2017-03-06
Bloch surface waves (BSWs) are recently developing alternative to surface plasmon polaritons (SPPs). Due to dramatically enhanced propagation distance and strong field confinement these surface states can be successfully used in on-chip all-optical integrated devices of increased complexity. In this work we propose a highly miniaturized grating based BSW coupler which is gathering launching and directional switching functionalities in a single element. This device allows to control with polarization the propagation direction of Bloch surface waves at subwavelength scale, thus impacting a large panel of domains such as optical circuitry, function design, quantum optics, etc.
Surface optical Bloch oscillations in semi-infinite waveguide arrays.
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.
Control of interaction-induced dephasing of Bloch oscillations.
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.
Optical BLOCH oscillations and Zener tunneling with nonclassical light.
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.
Unidirectional optical Bloch oscillations in asymmetric waveguide arrays.
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.
Superfluidity versus Bloch oscillations in confined atomic gases.
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.
Generation of 1D interference patterns of Bloch surface waves
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.
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).
The Bloch wave operator: generalizations and applications: Part I. The time-independent case
Energy Technology Data Exchange (ETDEWEB)
Killingbeck, John P [Mathematics Department, University of Hull, Hull HU6 7RX (United Kingdom); Jolicard, Georges [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France)
2003-05-23
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 of test matrices taken from the previous literature on wave operator methods. The main emphasis throughout is on the use of numerical methods which use iterative or perturbation algorithms, with simple Pade approximant methods being found sufficient to deal with most of the cases of divergence which are encountered. The use of damping factors and relaxation parameters is found to be effective in stabilizing calculations which use the energy-dependent effective Hamiltonian of Loewdin. In general the computations suggest that the numerical applications of the nonlinear equation for the reduced wave operator are best carried out with the equation split into a pair of equations in which the Bloch effective Hamiltonian appears as a separate entity. The presentation of the theoretical and computational details throughout is accompanied by references to and discussion of many works which have used wave operator methods in physics, chemistry and engineering. Some of
Topological optical Bloch oscillations in a deformed slab waveguide.
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.
Interaction-induced decoherence of atomic BLOCH oscillations.
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.
The Bloch-Kato Conjecture and Galois Theory
Karagueuzian, Dikran; Miná\\vc, Ján
2010-01-01
We investigate the relations in Galois groups of maximal p-extensions of fields, the structure of their natural filtrations, and their relationship with the Bloch-Kato conjecture proved by Rost and Voevodsky with Weibel's patch. Our main focus is on the third degree, but we provide examples for all degrees.
Compact composition operators on the Bloch space in polydiscs
Institute of Scientific and Technical Information of China (English)
无
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.
Lines crossing a tetrahedron and the Bloch group
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.
The Bloch wave operator: generalizations and applications: II. The time-dependent case
Energy Technology Data Exchange (ETDEWEB)
Jolicard, Georges [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France); Killingbeck, John P [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France); Mathematics Department, University of Hull, Hull HU6 7RX (United Kingdom)
2003-10-10
Part II of the review shows how the stationary Bloch wave operator of part I can be suitably modified to give a time-dependent wave operator. This operator makes it possible to use a relatively small active space in order to describe the dynamical processes which occur in quantum mechanical systems which have a time-dependent Hamiltonian. A close study is made of the links between the time-dependent and time-independent wave operators at the adiabatic limit; the analysis clarifies the way in which the wave operator formalism allows the time evolution of a system or a wave packet to be described in terms of a fast evolution inside the active space together with weak transitions out of this space which can be treated by perturbation methods. Two alternative wave operator equations of motion are derived and analysed. The first one is a non-linear differential equation in the usual Hilbert space; the second one is a differential equation in an extended Hilbert space with an extra time variable added and becomes equivalent to the usual Bloch equation when the Floquet Hamiltonian is taken in place of the ordinary Hamiltonian. A study is made of the close relationships between the time-dependent wave operator formalism, the Floquet theory and the (t, t') theory. Some original methods of solution of the two forms of wave operator equation are proposed and lead to new techniques of integration for the time-dependent Schroedinger equation (e.g., the generalized Green equation procedure). Mixed procedures involving both the time-independent and time-dependent wave operators are shown to be applicable to the internal eigenstate problem for large complex matrices. A detailed account is given of the description of inelastic and photoreactive processes by means of the time-dependent wave operator formalism, with particular attention to laser-molecule interactions. The emphasis is on projection operator techniques, with special attention being given to the method of selection
On the relationship between Bloch modes and phase-related refractive index of photonic crystals.
Sun, Guilin; Kirk, Andrew G
2007-10-01
It has previously been shown that the phase-related refractive index is positive in photonic crystals that display negative refraction at higher bands. We hypothesize that the phase velocity is governed by a wave that can be related to the dominant Bloch mode. This dominant wave can be identified from an approximate solution of Maxwell Equations using a homogeneously averaged dielectric constant and the dominant wavevector is related to the fundamental wavevector and the reciprocal lattice vectors. We validate this hypothesis by numerical Fourier decomposition of the field in the entire simulation domain. It confirms that for negative refraction at higher bands, the phase-related refractive index is indeed positive and differs significantly from the negative value of effective refractive index calculated from the band structure.
Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software.
Kuprov, Ilya; Wagner-Rundell, Nicola; Hore, P J
2007-02-01
We describe a general method for the automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations for liquid-phase spin dynamics in the algebraically challenging case of rotationally modulated interactions. The processing typically takes no more than a few seconds (on a contemporary single-processor workstation) and yields relaxation rate expressions that are completely general with respect to the spectral density functions, relative orientations, and magnitudes of the interaction tensors, with all cross-correlations accounted for. The algorithm easily deals with fully rhombic interaction tensors, and is able, with little if any modification, to treat a large variety of the relaxation mechanisms encountered in NMR, EPR, and spin dynamics in general.
Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers
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...
Huang, Zhongyi; Markowich, Peter; Sparber, Christof
2012-01-01
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by non-periodic potentials describing external electric fields. Our approach is based on the classical Bloch decomposition method which allows to diagonalize the periodic part of the Hamiltonian operator. Hence, the dominant effects from dispersion and periodic lattice potential are computed together, while the non-periodic potential acts only as a perturbation. Because the split-step communicator error between the periodic and non-periodic parts is relatively small, the step size can be chosen substantially larger than for the traditional splitting of the dispersion and potential operators. Indeed it is shown by the given examples, that our method is unconditionally stable and more efficient than the traditional split-step pseudo spectral schemes. To this end a particular fo...
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.
Anderson wall and Bloch oscillations in molecular rotation
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.
Anderson wall and BLOCH oscillations in molecular rotation.
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.
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 surf...... on the nature of microfields returned by Maxwell's solvers, showing that ignoring of difference between magnetic strength and induction lead to incorrect determination of the Poynting vector....
Nonreciprocal Bloch oscillations in magneto-optic waveguide arrays.
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.
Acoustic Bloch oscillations in a two-dimensional phononic crystal.
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.
Super Bloch Oscillation in a PT symmetric system
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.
Bloch oscillations of Bose-Einstein condensates: breakdown and revival.
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.
Damping of Bloch oscillations in the Hubbard model.
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.
Directory of Open Access Journals (Sweden)
Bernhard Streck
2012-10-01
Full Text Available The essay wants to deconstruct the genre of utopias so popular in the 20th century political writings. Human history shows manifold respect to stories about non-existent worlds which mix reality and non-reality, but outside the area of Abrahamitic beliefs there was rarely hope for a future. The secular version of such eschatological teachings begins with Karl Marx in the 19th century and culminates in the prophetic as well as revolutionary writings of Ernst Bloch around the terrible wars of the 20th century. This philosopher succeeded in both parts of post-war Germany and is still venerated inside and outside the academias. Compared with the so-called dystopias of Max Weber, Aldous Huxley or George Orwell the political visions of Bloch lack any sense of reality and seem to be quite useless to the understanding of present tendencies in world politics.
A refined Bloch group and the third homology of SL_2 of a field
Hutchinson, Kevin
2011-01-01
We introduce a variation of the Bloch group of a field F, which we call the refined Bloch group of F, and which bears essentially the same relationship to the third integral homology of SL_2 of the field as the classical Bloch group has to the indecomposable K_3 of the field. We use the properties of the refined Bloch group to prove that H_3 of SL_2 of a global field is never finitely generated, and to calculate - up to some 2- and 3-torsion - H_3 of SL_2 of local fields with finite residue field of odd characteristic.
Traffic restrictions on Routes Bloch, Maxwell and Bohr
TS 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
Tunable photonic Bloch oscillations in electrically modulated photonic crystals.
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.
Localization without recurrence and pseudo-Bloch oscillations in optics.
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.
Plasmonic Bloch oscillations in cylindrical metal-dielectric waveguide arrays.
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.
Localization without recurrence and pseudo-Bloch oscillations in optics
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.
Quasi-BLOCH oscillations in curved coupled optical waveguides.
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.
Photon BLOCH oscillations in porous silicon optical superlattices.
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.
Plasmonic Bloch oscillations in monolayer graphene sheet arrays.
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.
Tunable photonic Bloch oscillations in electrically modulated photonic crystals
Wang, Gang; Yu, Kin Wah
2008-01-01
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 electromagnetic spectrum.
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...
Local gravity measurement with the combination of atom interferometry and Bloch oscillations
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.
Bloch constant of holomorphic mappings on the unit polydisk of C~n
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we give a definition of Bloch mappings defined in the unit polydisk Dn, which generalizes the concept of Bloch functions defined in the unit disk D.It is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex variables.We shall establish the corresponding distortion theorems for subfamiliesβ（K）andβloc（K） of Bloch mappings defined in the polydisk Dn,which extend the distortion theorems of Liu and Minda to higher dimensions.As an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in Dn.In particular,our results reduce to the classical results of Ahlfors and Landau when n=1.
Staying positive: going beyond Lindblad with perturbative master equations
Energy Technology Data Exchange (ETDEWEB)
Whitney, Robert S [Institut Laue-Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble (France)
2008-05-02
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-Schoen 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.
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.
On the origin of the Bloch correction in stopping
Khodyrev, V. A.
2000-11-01
The energy loss in the collision of a moving charged projectile with a free electron is described in a rigorous approach. The collision is treated as stationary scattering of an electron in the projectile Coulomb field. In the laboratory frame, the picture can be represented as a spatial distribution of energy losses to the electron. It has been shown that the local rate of the energy gain can be presented as a product of the induced electron current and the projectile electric field. The analytical results and numerical calculations reveal a principal disagreement with the generally recognized condition for the classical description, η = Z1e2/ℎv≳1 (Z1e and v are, respectively, the charge and velocity of the projectile): for any value of η, the quantum effects appear to be significant in the close vicinity of the projectile trajectory (small impact parameters) restricted by the distance ~λ = ℎ/mv. Essentially, the problem has been cleared in the qualitative analysis of collisions with electron wavepackets. The main results of the Bloch theory are reproduced in a simpler way. The clearer basis permits us to eliminate the ambiguity in the interpretation of the origin of the Bloch correction, which reflects in fact the evolution of the classical features in the quantum mechanical picture.
Nonequilibrium Spin Magnetization Quantum Transport Equations
Buot, F A; Otadoy, R E S; Villarin, D L
2011-01-01
The classical Bloch equations of spin magnetization transport is extended to fully time-dependent and highly-nonlinear nonequilibrium quantum distribution function (QDF) transport equations. The leading terms consist of the Boltzmann kinetic equation with spin-orbit coupling in a magnetic field together with spin-dependent scattering terms which do not have any classical analogue, but should incorporate the spatio-temporal-dependent phase-space dynamics of Elliot-Yafet and D'yakonov-Perel scatterings. The resulting magnetization QDF transport equation serves as a foundation for computational spintronic and nanomagnetic device applications, in performing simulation of ultrafast-switching-speed/low-power performance and reliability analyses.
Tunneling through molecules and quantum dots: master-equation approaches
Timm, Carsten
2008-01-01
An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss various formalisms for deriving a master equation and their interrelations. It is shown that the master equations derived by Wangsness, Bloch, and Redfield and by Koenig et al. are equivalent. The roles of the large-reservoir and Markov approximations are clarified. The Markov approximation is traced back to nonzero bias voltage and tempera...
Bloch-wave engineering of quantum dot-micropillars for cavity quantum electrodynamics experiments
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.
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.
Inducing transport in a dissipation-free lattice with super Bloch oscillations.
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.
Coulomb blockade and BLOCH oscillations in superconducting Ti nanowires.
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.
Bloch-Messiah reduction of Gaussian unitaries by Takagi factorization
Cariolaro, Gianfranco; Pierobon, Gianfranco
2016-12-01
The Bloch-Messiah (BM) reduction allows the decomposition of an arbitrarily complicated Gaussian unitary into a very simple scheme in which linear optical components are separated from nonlinear ones. The nonlinear part is due to the squeezing possibly present in the Gaussian unitary. The reduction is usually obtained by exploiting the singular value decomposition (SVD) of the matrices appearing in the Bogoliubov transformation of the given Gaussian unitary. This paper discusses a different approach, where the BM reduction is obtained in a straightforward way. It is based on the Takagi factorization of the (complex and symmetric) squeeze matrix and has the advantage of avoiding several matrix operations of the previous approach (polar decomposition, eigendecomposition, SVD, and Takagi factorization). The theory is illustrated with an application example in which the previous and present approaches are compared.
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.
Bloch-Nordsieck Estimates of High-Temperature QED
Fried, H M; Sheu, Y -M
2008-01-01
In anticipation of a subsequent application to QCD, we consider the case of QED at high temperature. We introduce a Fradkin representation into the exact, Schwingerian, functional expression of a fermion propagator, as well as a new and relevant version of the Bloch-Nordsieck (BN) model, which extracts the soft contributions of every perturbative graph, in contradistinction to the assumed separation of energy scales of previous semi-perturbative treatments. Our results are applicable to the absorption of a fast particle which enters a heat bath, as well as to the propagation of a symmetric pulse within the thermal medium due to the appearance of an instantaneous, shock-wave-like source acting in the medium. An exponentially-decreasing time dependence of the incident particle's initial momentum combines with a stronger decrease in the particle's energy, estimated by a sum over all Matsubara frequencies, to model an initial "fireball", which subsequently decays in a Gaussian fashion. When extended to QCD, quali...
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.
Stable BLOCH oscillations of cold atoms with time-dependent interaction.
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.
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.
Imaging of Bloch oscillations in erbium-doped curved waveguide arrays.
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.
Photonic Bloch oscillations and Wannier-Stark ladders in exponentially chirped Bragg gratings.
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.
Band structure and Bloch states in birefringent 1D magnetophotonic crystals: An analytical approach
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.
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.
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.
2014-01-01
In this article we propose to discuss the concept of hope and daydream from the writings of Ernst Bloch and Paulo Freire. Based on the production of Ernst Bloch explored the philosophy of hope, as an expression of affection expectant positive, from the imperative to understand how the act related to a political commitment by the constitution from seeking concrete utopias. The problematization of the term from Paulo Freire, in turn, enters the discussion about the importance of Pedagogy of Hop...
Philippe Bloch: Reducing distance between experiments and CERN
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...
Geometry of the generalized Bloch sphere for qutrit
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 ...
Bloch wave approach to the optics of crystals.
Ponti, S; Oldano, C; Becchi, M
2001-08-01
The Bloch wave method is used to find the effective permittivity tensor epsilon of periodic liquid crystals and artificial structures whose period p is short with respect to the light wavelength lambda and whose optical properties are defined by a permittivity field epsilon(r). The main role of the multiple scattering within the periodic medium is evidenced, and very general expressions of epsilon, based on expansions in ascending powers of the ratio p/lambda and of the light wave vector k, are found. Such expansions allow to discuss the general properties of epsilon, to clarify the role of the spatial dispersions, i.e., to separate the part of epsilon explicitly depending on k from its k-independent part, and to find some interesting properties of crystals that are (i) periodic in only one direction, or (ii) locally isotropic. Finally, the limits of validity of the macroscopic model are discussed. Within these limits only a few terms of the power expansions are required, and their expressions are explicitly given. The obtained results are also useful to better understand the macroscopic optical properties of solid crystals.
Polarization controlled directional excitation of Bloch surface waves (Conference Presentation)
Kovalevich, Tatiana; Boyer, Philippe; Bernal, Maria-Pilar; Kim, Myun-Sik; Herzig, Hans Peter; Grosjean, Thierry
2016-09-01
Bloch surface waves (BSWs) are electromagnetic surface waves which can be excited at the interface between periodic dielectric multilayer and a surrounding medium. In comparison with surface plasmon polaritons these surface states perform high quality factor due to low loss characteristics of dielectric materials and can be exited both by TE and TM polarized light. A platform consisting of periodic stacks of alternative SiO2 and Si3N4 layers is designed and fabricated to work at the wavelength of 1.55 µm. The platform has an application in sensing and in integrated optics domain. A standard way of BSW excitation is coupling via Kretschmann configuration, but in this work we investigate a grating coupling of BSWs. Grating parameters are analytically and numerically optimized by RCWA and FDTD methods in order to obtain the best coupling conditions. The light is launched orthogonally to the surface of the photonic crystal and the grating. Due to a special grating configuration we demonstrate directionality of the BSW propagation depending on polarization of the incident light. The structure was experimentally realized on the surface of the photonic crystal by FIB milling. Experimental results are in a good agreement with a theory. The investigated configuration can be successfully used as a BSW launcher in on-chip all-optical integrated systems and work as a surface wave switch or modulator.
Geometry of the generalized Bloch sphere for qutrits
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 .
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.
Bloch Oscillation in a One-Dimensional Array of Small Josephson Junctions
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.
Non-destructive monitoring of Bloch oscillations in an optical cavity
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...
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
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 ...
Bloch bound states in the radiation continuum in a periodic array of dielectric rods
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.
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.
Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments.
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.
Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice.
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.
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 CJh 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 CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.
Bloch wave deafness and modal conversion at a phononic crystal boundary
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.
Observation of fractional Bloch band quantum Hall states in graphene/h-BN superlattices
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.
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......We propose hitherto unexplored and fully analytical insights into laminate elastic materials in a true condensed-matter-physics spirit. Pure mechanical surface waves that decay as evanescent waves from the interface are discussed, and we demonstrate how these designer Scholte waves are controlled......, and we demonstrate this numerically for structures with millimeter and centimeter dimensions in the kilohertz to megahertz range. Analytical predictions agree entirely with full wave simulations showing how elastodynamics can mimic quantum-mechanical condensed-matter phenomena....
Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice
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.
Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model.
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.
The Bloch-vector space for N-level systems -- the spherical-coordinate point of view --
Kimura, G
2003-01-01
The Bloch-vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view. We find that the maximum radius in each direction, which is due to the construction of the Bloch-vector space, is determined by the minimum eigenvalue of the corresponding observable (generator of SU(N)). As one of the applications of this, we reveal the dual properties of the structure of the Bloch-vector space; if one of the direction of the Bloch vector reaches the large ball (pure state), the opposite direction can only reach the small ball, and vice versa. This also leads us to the new representation of quantum states which generalize the Bloch vector.
Atomic Bloch-Zener oscillations and Stückelberg interferometry in optical lattices.
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.
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.
Bloch-Zener oscillations across a merging transition of Dirac points.
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.
Schrodinger cat states prepared by Bloch oscillation in a spin-dependent optical lattice
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.
Nearly three orders of magnitude enhancement of Goos-Hanchen shift by exciting Bloch surface wave.
Wan, Yuhang; Zheng, Zheng; Kong, Weijing; Zhao, Xin; Liu, Ya; Bian, Yusheng; Liu, Jiansheng
2012-04-09
Goos-Hanchen effect is experimentally studied when the Bloch surface wave is excited in the forbidden band of a one-dimensional photonic band-gap structure. By tuning the refractive index of the cladding covering the truncated photonic crystal structure, either a guided or a surface mode can be excited. In the latter case, strong enhancement of the Goos-Hanchen shift induced by the Bloch-surface-wave results in sub-millimeter shifts of the reflected beam position. Such giant Goos-Hanchen shift, ~750 times of the wavelength, could enable many intriguing applications that had been less than feasible to implement before.
Generation of Entangled Bloch States for Two Atomic Samples Trapped in Separated Cavities
Institute of Scientific and Technical Information of China (English)
ZHENG Shi-Biao
2007-01-01
A scheme is presented for the generation of entangled states for two atomic ensembles trapped in two distant cavities.In the scheme,each atomic sample is initially in a Bloch state and the cavity mode is initially in a coherent state with a small amplitude.The dispersive atom-cavity interaction leads to a photon-number dependent phase shift on the atomic system.The detection of a photon leaking from the cavities makes the two atomic samples collapse to an entangled Bloch state.
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...
Floquet-Bloch waves and suppression of vibrations in multi-scale fluid-solid systems
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.
Dynamic localization and Bloch oscillations in the spectrum of a frequency mode-locked laser.
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.
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.
Beam splitter and combiner based on Bloch oscillations in spatially modulated waveguide arrays
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.
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 ...
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...
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...
Generation of Superpositions of Two Bloch States in an Ion Trap
Institute of Scientific and Technical Information of China (English)
ZHENG Shi-Biao
2003-01-01
We propose a scheme for the generation of superpositions of two Bloch states for a collection of ions. Inthe scheme the ions are trapped in a linear potential and interact with laser beams. Our scheme does not put anyrequirement on the Lamb-Dicke parameters.
DEFF Research Database (Denmark)
Bozhevolnyi, Sergey I.; Volkov, V.S.; Søndergaard, Thomas;
2002-01-01
the interference between a quasihomogeneous background field and Bloch harmonics of the PCW mode, we account for spatial frequency spectra of the intensity variations and determine the propagation constant of the PCW mode at 1520 nm. The possibilities and limitations of SNOM imaging for the characterization...
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.
Web-based description of the space radiation environment using the Bethe-Bloch model
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
Acoustic Bloch Wave Propagation in a Periodic Waveguide
1991-07-24
Distribution of Spherical Cavities," J. Acoust. Soc. Am. 81, 595-598. Arfken , G. (1985). Mathematical Methods for Physicists (Academic Press, Inc., New... mathematical -ystem of governing equations and boundary conditions describing lossy, linear acoustic waves in a periodic wave- guide is, under the...Translational Invariance The aim of this section is to present the mathematical system to be solved and show that it exhibits invariance under a certain
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
Ferialdi, L.
2017-02-01
We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.
Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction
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".
Suppression of space broadening of exciton polariton beams by Bloch oscillation effects
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...
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.
Phase transition to spatial Bloch-like oscillation in squeezed photonic lattices
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...
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.
Magneto-optical switching of Bloch surface waves in magnetophotonic crystals
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.
A Refresher of the Original Bloch’s Law Paper (Bloch, July 1885)
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
A Refresher of the Original Bloch’s Law Paper (Bloch, July 1885
Directory of Open Access Journals (Sweden)
Andrei Gorea
2015-08-01
Full Text Available 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.
Nanoscale switch for vortex polarization mediated by Bloch core formation in magnetic hybrid systems
Wohlhüter, Phillip; Bryan, Matthew Thomas; Warnicke, Peter; Gliga, Sebastian; Stevenson, Stephanie Elizabeth; Heldt, Georg; Saharan, Lalita; Suszka, Anna Kinga; Moutafis, Christoforos; Chopdekar, Rajesh Vilas; Raabe, Jörg; Thomson, Thomas; Hrkac, Gino; Heyderman, Laura Jane
2015-08-01
Vortices are fundamental magnetic topological structures characterized by a curling magnetization around a highly stable nanometric core. The control of the polarization of this core and its gyration is key to the utilization of vortices in technological applications. So far polarization control has been achieved in single-material structures using magnetic fields, spin-polarized currents or spin waves. Here we demonstrate local control of the vortex core orientation in hybrid structures where the vortex in an in-plane Permalloy film coexists with out-of-plane maze domains in a Co/Pd multilayer. The vortex core reverses its polarization on crossing a maze domain boundary. This reversal is mediated by a pair of magnetic singularities, known as Bloch points, and leads to the transient formation of a three-dimensional magnetization structure: a Bloch core. The interaction between vortex and domain wall thus acts as a nanoscale switch for the vortex core polarization.
Bloch oscillations as generators of polarons in a 1D crystal
Energy Technology Data Exchange (ETDEWEB)
Nazareno, H.N. [International Center for Condensed Matter Physics, Universidade de Brasília, P.O. Box 04513, 70910-900 Brasília, DF (Brazil); Brito, P.E. de, E-mail: pedebrito@unb.br [Universidade de Brasília, PPG-CIMA, Campus Planaltina, 73345-010 Brasília, DF (Brazil)
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.
Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate
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.
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.
The generalized Hodge and Bloch conjectures are equivalent for general complete intersections
Voisin, Claire
2011-01-01
Let $X$ be a smooth complex projective variety with trivial Chow groups. (By trivial, we mean that the cycle class is injective.) We show (assuming the Lefschetz standard conjecture) that if the vanishing cohomology of a general complete intersection $Y$ of ample hypersurfaces in $X$ has geometric coniveau $\\geq c$, then the Chow groups of cycles of dimension $\\leq c-1$ of $Y$ are trivial. The generalized Bloch conjecture for $Y$ is this statement with "geometric coniveau" replaced by "Hodge coniveau".
Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles
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.
Sensitive measurement of forces at the micron scale using Bloch oscillations of ultracold atoms.
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.
Bloch oscillations and Zener tunneling in two-dimensional photonic lattices.
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.
San agustín y la utopía según ernst bloch
2011-01-01
Nuestro propósito en este breve trabajo es presentar la lectura que Emst Bloch hace del pensamiento de San Agustín sobre la utopía de la Ciudad de Dios en su libro Principio Esperanza y hacer un análisis esquemático de dicha lectura con algunos comentarios críticos a varías de sus afirmaciones.
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 (
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.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices.
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.
Adele Bloch-Bauer (1881-1925): Possible diagnoses for Gustav Klimt's Lady in Gold.
da Mota, Licia Maria H; Neubarth, Fernando; de Carvalho, Jozélio F; Diniz, Leonardo R; Aires, Rodrigo B; Dos Santos-Neto, Leopoldo L
2016-08-01
One of the most famous works by the Austrian symbolist painter Gustav Klimt and one of the most widely reproduced works of art worldwide, Adele Bloch-Bauer I which portrays the beautiful wife of Austrian magnate Ferdinand Bloch-Bauer. Adele was the only woman painted by Klimt on more than one occasion. Apart from the beauty and value of the painting, the daring sea of gold that surrounds Adele and the gentle intimacy with which her fragile figure is portrayed have shrouded the history of this painting in mystery. Beyond speculation as to a special bond between artist and model, observation of the painting with a keener, clinical gaze yields evidence of potential illness in the model: facial erythema which, if not produced artificially by makeup, could represent a malar rash; pallor or cyanosis of the hands; and her draped fingers, which seemingly attempt to hide a deformity. This paper seeks to provide a biographical review both of the painter, Gustav Klimt, and of the subject, Adele Bloch-Bauer; to analyse Klimt's two portrayals of her in a search for evidence of a potential intimate relationship between artist and muse and, finally, to compile clinical evidence of possible diagnoses for the Lady in Gold.
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
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)
Dynamics of open quantum spin systems: An assessment of the quantum master equation approach.
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.
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.
DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rn
Institute of Scientific and Technical Information of China (English)
Tang Xiaomin; Hu Zhangjian; Lu Xiaofen
2011-01-01
Let H(B) be the set of all harmonic functions f on the unit ball B of Rn.For 0 ＜ p,q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q,φ(B) consists of all functions f in H(B) for which the mixed norm ||·||p,q,φ ＜ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q,φ(B).The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.
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.
Nontrivial Bloch oscillations in waveguide arrays with second-order coupling.
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.
Bloch Oscillations of Cold Atoms in a Cavity: Effects of Quantum Noise
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.
On-chip optical isolation via unidirectional Bloch oscillations in a waveguide array.
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.
Bloch oscillations of quasispin polaritons in a magneto-optically controlled atomic ensemble
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.
Stopping and time reversal of light in dynamic photonic structures via Bloch oscillations.
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)].
Micromagnetic structure of the domain wall with Bloch lines in an electric field
Borich, M. A.; Tankeev, A. P.; Smagin, V. V.
2016-07-01
The micromagnetic structure of the domain wall (DW) with periodically distributed horizontal Bloch lines in a ferromagnetic film in an external electric field has been studied. The effect of the electric field on the internal DW micromagnetic structure is caused by inhomogeneous magnetoelectric coupling. Possible scenarios of the DW internal structure transformations implemented with varying the electric fields strength have been analyzed in detail. For each scenario, static characteristics of the system, such as the energy, DW profile, DW effective thickness, and electric polarization have been calculated.
Bloch oscillating transistor as the readout element for hot electron bolometers
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.
Identification of Bloch-modes in hollow-core Photonic Crystal Fiber cladding
DEFF Research Database (Denmark)
Couny, F.; Benabid, F.; Roberts, John;
2007-01-01
length of fiber. A detailed study of the modes near the edges of the band gap shows that it is formed by the influence of three types of resonator: the glass interstitial apex, the silica strut which joins the neighboring apexes, and the air hole. The cladding electromagnetic field which survives......We report on the experimental visualization of the cladding Bloch-modes of a hollow-core photonic crystal fiber. Both spectral and spatial field information is extracted using the approach, which is based on measurement of the near-field and Fresnel-zone that results after propagation over a short...
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
Measurement of group-velocity dispersion of Bloch modes in photonic-crystal-fiber rocking filters.
Wong, G K L; Zang, L; Kang, M S; Russell, P St J
2010-12-01
We use low-coherence interferometry to measure the group-velocity dispersion (GVD) of the fast and slow Bloch modes of structural rocking filters, produced by twisting a highly birefringent photonic crystal fiber to and fro while scanning a focused CO(2) laser beam along it. The GVD curves in the vicinity of the resonant wavelength differ dramatically from those of the unperturbed fiber, suggesting that rocking filters could be used in the optimization of, e.g., four-wave mixing and supercontinuum generation. Excellent agreement is obtained between theory and experiment.
Toxicity studies of butachlor to the freshwater fish Channa punctata (Bloch).
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).
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.
Experimental reconstruction of the Berry curvature in a topological Bloch band
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.
Experimental reconstruction of the Berry curvature in a Floquet Bloch band
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.
Bloch-like surface waves in Fibonacci quasi-crystals and Thue-Morse aperiodic dielectric multilayers
Koju, Vijay; Robertson, William M.
2016-09-01
Bloch surface waves (BSWs) in periodic dielectric multilayer structures with surface defect have been extensively studied. However, it has recently been recognized that quasi-crystals and aperiodic dielectric multilayers also support Bloch-like surface waves (BLSWs). In this work, we numerically show the existence of BLSWs in Fibonacci quasi-crystals and Thue-Morse aperiodic dielectric multilayers using the prism coupling technique. We compare the surface field enhancement and penetration depth of BLSWs in these structures with that of BSWs in their periodic counterparts.
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.
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.
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.
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
Directory of Open Access Journals (Sweden)
Eleni Bisognin
2008-03-01
Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
Creating full-Bloch Bose-Einstein condensates with Raman q-plates
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.
Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate
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.
Wannier-Bloch approach to localization in high harmonics generation in solids
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...
Dynamic scattering of electron vortex beams--a Bloch wave analysis.
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.
Dynamics of Bloch State Positronium Emission from MOF Targets Studied via Rydberg TOF Spectroscopy
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).
Leblond, Hervé; Mihalache, Dumitru; 10.1103/PHYSREVA.81.033824
2011-01-01
By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.
Kadantsev, Eugene S.; Klooster, Rob; De Boeij, Paul L.; Ziegler, Tom
2007-01-01
Analytic energy gradients with respect to atomic coordinates for systems with translational invariance are formulated within the framework of Kohn-Sham Density Functional Theory. The energy gradients are implemented in the BAND program for periodic DFT calculations which directly employs a Bloch bas
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...
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.
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Rigal, B.; Kapon, E.;
We design slow and fast light photonic crystal waveguides for single-photon emission using a Bloch mode expansion and scattering matrix technique. We propose slow light designs that increase the group index-waveguide mode volume ratio for larger Purcell enhancement, and address efficient slow...
Valset, K; Tafto, J
2011-06-01
We classify the point symmetries at the different points in the Brillouin zone for the 17 two-dimensional space groups and the symmetries of the Bloch waves for the 10 two-dimensional crystallographic point groups. Simple examples involving breakdown of Friedels law, Gjonnes-Moodie lines, and reflection and refraction at interfaces are presented.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
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.
Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations
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...
Chirped dual periodic structures for photonic Bloch oscillations and Zener tunneling.
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.
Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/m Rb.
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.
Backaction-driven transport of Bloch oscillating atoms in ring cavities.
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.
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.
Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices.
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.
Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
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.
Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC
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.
Design of guided Bloch surface wave resonance bio-sensors with high sensitivity
Kang, Xiu-Bao; Wen, Li-Wei; Wang, Zhi-Guo
2017-01-01
The sensing performance of bio-sensors based on guided Bloch surface wave (BSW) resonance (GBR) is studied. GBR is realized by coupling the propagating electromagnetic wave with BSW on one side of a one-dimensional photonic crystal slab via the grating on the other side. The sensitivity of the designed bio-sensors is proportional to the grating constant when the wavelength spectrum is analyzed, and inversely proportional to the normal wave vector of the incident electromagnetic wave when the angular spectrum is resolved. For a GBR bio-sensor designed to operate near 70° angle of incidence from air, the angular sensitivity is very high, reaching 128 deg RIU-1. The sensitivity can be substantially increased by designing bio-sensors for operating at larger angles of incidence.
Sub-nanometer linewidth perfect absorption in visible band induced by Bloch surface wave
Cong, Jiawei; Liu, Wenxing; Zhou, Zhiqiang; Ren, Naifei; Ding, Guilin; Chen, Mingyang; Yao, Hongbing
2016-12-01
We demonstrate the unity absorption of visible light with an ultra-narrow 0.1 nm linewidth. It arises from the Bloch surface wave resonance in alternating TiO2/SiO2 multilayers. The total absorption and narrow linewidth are explained from the radiative and absorptive damping, which are quantitatively determined by the temporal coupled mode theory. When a silver film with proper thickness is added to the absorber, the perfect absorption is achieved with only 3 structural bilayers, in contrast with 8 bilayers required without Ag. Furthermore, significant field enhancement and an ultrahigh 2600/RIU sensing figure-of-merit are simultaneously obtained at resonance, which might facilitate applications in nonlinear optical devices and high resolution refractive index sensing.
Coexisting localized and extended optical Bloch states in a periodic deep wire array microcavity
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.
Identification of Bloch-modes in hollow-core photonic crystal fiber cladding.
Couny, F; Benabid, F; Roberts, P J; Burnett, M T; Maier, S A
2007-01-22
We report on the experimental visualization of the cladding Bloch-modes of a hollow-core photonic crystal fiber. Both spectral and spatial field nformation is extracted using the approach, which is based on measurement of the near-field and Fresnel-zone that results after propagation over a short length of fiber. A detailed study of the modes near the edges of the band gap shows that it is formed by the influence of three types of resonator: the glass interstitial apex, the silica strut which joins the neighboring apexes, and the air hole. The cladding electromagnetic field which survives the propagation is found to be spatially coherent and to contain contributions from just a few types of cladding mode.
DEFF Research Database (Denmark)
Bozhevolnyi, Sergey I.; Volkov, V.S.; Søndergaard, Thomas;
2002-01-01
We employ a collection scanning near-field optical microscope (SNOM) to image the propagation of light at telecommunication wavelengths along straight and bent regions of silicon-on-insulator photonic crystal waveguides (PCWs) formed by removing a single row of holes in the triangular 410-nm......-period lattice along the GammaM direction of the irreducible Brillouin zone. We obtain high quality SNOM images of PCWs excited in the wavelength range of 1520-1570 nm, which indicate good PCW mode confinement and low propagation loss. Using averaged cross sections of the intensity distributions before and after...... the interference between a quasihomogeneous background field and Bloch harmonics of the PCW mode, we account for spatial frequency spectra of the intensity variations and determine the propagation constant of the PCW mode at 1520 nm. The possibilities and limitations of SNOM imaging for the characterization...
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
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).
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.
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation
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 ...
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
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.
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.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
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.
Liu, Yangyang; Zeng, Xiaoge; Popovic, Milos A
2013-01-01
We experimentally demonstrate broadband waveguide crossing arrays showing ultra low loss down to $0.04\\,$dB/crossing ($0.9\\%$), matching theory, and crosstalk suppression over $35\\,$dB, in a CMOS-compatible geometry. The principle of operation is the tailored excitation of a low-loss spatial Bloch wave formed by matching the periodicity of the crossing array to the difference in propagation constants of the 1$^\\text{st}$- and 3$^\\text{rd}$-order TE-like modes of a multimode silicon waveguide. Radiative scattering at the crossing points acts like a periodic imaginary-permittivity perturbation that couples two supermodes, which results in imaginary (radiative) propagation-constant splitting and gives rise to a low-loss, unidirectional breathing Bloch wave. This type of crossing array provides a robust implementation of a key component enabling dense photonic integration.
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...
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
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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.
Grating-Coupling-Based Excitation of Bloch Surface Waves for Lab-on-Fiber Nanoprobes
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...
Pandey, Rakesh K; Singh, Ram N; Singh, Sarika; Singh, Narendra N; Das, Vijai K
2009-05-01
Pesticides are chemicals used for pest control in the agricultural fields. They finally reach the surrounding water bodies through surface runoff affecting the aquatic fauna. Dimethoate is frequently used organophosphate pesticide due to its high effectiveness and rapid breakdown into environmentally safe products. A 96 hr static acute toxicity test was carried out to determine the LC50 value of dimethoate, on the freshwater airbreathing catfish Heteropneustes fossilis (Bloch). The fish were exposed to 7 different concentrations of dimethoate (2.50, 2.75, 3.00, 3.25, 3.50, 3.75 and 4.00 mg l(-1)) for toxicity bioassay. Control (0.00 mg l(-1)) was also carried out. The data were subjected to Finney's Probit analysis and processed with Trimmed Spearman-Karber statistical software. The LC50 values for dimethoate for 24, 48, 72 and 96 hr were 3.38, 3.23, 3.08 and 2.98 mg l(-1), respectively. At higher concentration of dimethoate (3.25 mg l(-1) and above) the fish showed uncoordinated behaviour such as erratic and jerky swimming, attempt to jump out of water, frequent surfacing and gulping of air, decrease in opercular movement and copious secretion of mucus all over the body.
Abner Doubleday, Marc Bloch, and the cultural significance of baseball in rural America.
Vaught, David
2011-01-01
In 1907 baseball's promoters decreed that Civil War hero Abner Doubleday created the game in the village of Cooperstown, New York, in 1839. Baseball thus acquired a distinctly rural American origin and a romantic pastoral appeal. Skeptics have since presented irrefutable evidence that America's pastime was neither born in the United States nor was a product of rural life. But in their zeal to debunk the myth of baseball's rural beginnings, historians have fallen prey to what Annales School founder Marc Bloch famously called the "idol of origins," and all but neglected the very real phenomenon of rural baseball itself. The claim that baseball has always been "a city game for city men" does not stand up to empirical scrutiny anymore than the Doubleday myth itself, as this address demonstrates with three case studies -- Cooperstown in the 1830s, Davisville, California, in the 1880s, and Milroy, Minnesota, in the 1950s. Baseball may have been a source of rural nostalgia for city people, but it was the sport of choice for farmers and a powerful cultural agent.
The analysis of cytochrome b nucleotidic sequence for Carassius gibelio (Bloch, 1782
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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.
Differential geometric invariants for time-reversal symmetric Bloch-bundles: The "Real" case
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.
Photonic lattices in organic microcavities: Bloch states and control of lasing
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.
Establishment of a cell line from kidney of seabass, Lates calcarifer (Bloch
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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.
Effects of the projectile electronic structure on Bethe-Bloch stopping parameters for Ag
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Moussa, D., E-mail: djamelmoussa@gmail.co [USTHB, Faculte de Physique, B.P. 32, 16111 Bab-Ezzouar, Algiers (Algeria); Damache, S. [Division de Physique, CRNA, 02 Bd. Frantz Fanon, B.P. 399 Alger-gare, Algiers (Algeria); Ouichaoui, S., E-mail: souichaoui@gmail.co [USTHB, Faculte de Physique, B.P. 32, 16111 Bab-Ezzouar, Algiers (Algeria)
2010-06-15
Energy losses of protons and alpha particles in silver have been accurately measured under the same experimental conditions over the velocity range E{sub lab}=(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 . 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.
Mass Spectrum of Fermion on Bloch Branes with New Scalar-fermion Coupling
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.
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...
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.
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.
Antes, desde y para el exilio. Herencia de esta época (1935/1962 de Ernst Bloch
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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.
Tekin-Ozan, Selda; Kir, Ismail
2007-01-01
Concentrations of some heavy metals (Fe, Zn, Cu, Mn and Cr) in liver of pike (Esox lucius L., 1758) and its endoparasite [Raphidascaris acus (Bloch, 1779)] inhabiting Işikli Lake (Turkey) were analyzed using atomic absorption spectrophotometry. Only Fe and Zn were detected in R. acus and liver of fish, while levels of Cu, Mn and Cr were below detection limit (acus were 68.4 and 86.9 times higher than in the liver. Nematodes could provide reliable information about the heavy metal pollution of the lakes.
Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices.
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.
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.
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).
Liu, Yangyang; Shainline, Jeffrey M.; Zeng, Xiaoge; Popovic, Milos A.
2013-01-01
We experimentally demonstrate broadband waveguide crossing arrays showing ultra low loss down to $0.04\\,$dB/crossing ($0.9\\%$), matching theory, and crosstalk suppression over $35\\,$dB, in a CMOS-compatible geometry. The principle of operation is the tailored excitation of a low-loss spatial Bloch wave formed by matching the periodicity of the crossing array to the difference in propagation constants of the 1$^\\text{st}$- and 3$^\\text{rd}$-order TE-like modes of a multimode silicon waveguide....
Spatial differentiation of Bloch surface wave beams using an on-chip phase-shifted Bragg grating
Doskolovich, L. L.; Bezus, E. A.; Bykov, D. A.; Soifer, V. A.
2016-11-01
Bloch surface waves (BSWs) supported by the interfaces between a photonic crystal and a homogeneous medium are considered as a prospective information carrier in integrated photonic circuits. In the present work, we study the application of on-chip phase-shifted Bragg gratings for spatial differentiation of BSW beams. The presented simulation results demonstrate a high accuracy of the performed differentiation. It is shown that upon differentiation of a Gaussian BSW beam, a two-dimensional analogue of the Hermite-Gaussian mode is generated in reflection. The obtained results may find application in the design of new planar devices for analog optical information processing.
Institute of Scientific and Technical Information of China (English)
SANG Hong-Yi; LI Zhi-Yuan; GU Ben-Yuan
2005-01-01
@@ Defect modes in one-dimensional photonic crystals (PCs) can be readily detected from the solution of the transmission spectra via the standard transfer-matrix method. We adopt an analytic Bloch-mode approach to examine this problem in terms of eigenmode solutions and investigate the dispersion behaviour of localized defect modes supported by a defect layer sandwiched within two symmetric semi-infinite PCs that are made from multiple constituents. The results show that the number of defect modes grows when the dielectric constant and width of the defect layer increase.
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."
Numerical investigation of the flat band Bloch modes in a 2D photonic crystal with Dirac cones.
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.
2007-06-20
probabilities for SE at fundamental Bloch frequency into the waveguide TE10 mode with and without the scattering taking into account analyzing the ratio P rse ...the limit of τ → ∞, with N finite, the expected result P rse → 1. Also, for this limit, the integral (27) becomes a linear function of N , IN(τνB...is shown in Fig. 5 for several values of the parameter τνB. In Fig. 6, we show the dependence of the relative SE probability P rse [Eq.(42
Soliton solution for the Landau-Lifshitz equation of a one-dimensional bicomponent magnonic crystal.
Giridharan, D; Sabareesan, P; Daniel, M
2016-09-01
We investigate nonlinear localized magnetic excitations in a one-dimensional bicomponent magnonic crystal under a periodic magnetic field of spatially varying strength. The governing Landau-Lifshitz equation is transformed into a variable coefficient nonlinear Schrödinger (VCNLS) equation using stereographic projection. In general, the VCNLS equation is nonintegrable and by using Painlevé analysis, we obtain necessary conditions for the VCNLS equation to pass the Weiss-Tabor-Carnevale Painlevé test. A sufficient integrability condition is obtained by further exploring a transformation, which can map the VCNLS equation into the well-known standard nonlinear Schrödinger equation. The transformation builds a systematic connection between the solution of the standard nonlinear Schrödinger equation and VCNLS equation. The results show that the excitation of magnetization in the form of a soliton exists on the oscillatory background with a structure similar to the form of spin Bloch waves. Such a solution exists only when certain conditions on the coefficient of the VCNLS equation are satisfied. To corroborate the analytical results, we performed the numerical simulation by solving the governing VCNLS equation with integrability conditions using the split step Fourier method and the result agrees well with analytical results, and it suggests a way to control the dynamics of magnetization in the form of solitons by an appropriate spatial modulation of the nonlinearity coefficient in the governing VCNLS equation, which depends on the ferromagnetic materials which form the bicomponent magnonic crystal.
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Sun, H.Y. E-mail: hysun@165e.com; Hu, H.N.; Sun, Y.P.; Nie, X.F
2004-08-01
Influence of rotating in-plane field on vertical Bloch lines in the walls of second kind of dumbbell domains (IIDs) was investigated, and a critical in-plane field range [H{sub ip}{sup 1},H{sub ip}{sup 2}] of which vertical-Bloch lines (VBLs) annihilated in IIDs is found under rotating in-plane field (H{sub ip}{sup 1} is the maximal critical in-plane-field of which hard domains remain stable, H{sub ip}{sup 2} is the minimal critical in-plane-field of which all of the hard domains convert to soft bubbles (SBs, without VBLs)). It shows that the in-plane field range [H{sub ip}{sup 1}, H{sub ip}{sup 2}] changes with the change of the rotating angle {delta}{phi} H{sub ip}{sup 1} maintains stable, while H{sub ip}{sup 2} decreases with the decreasing of rotating angle {delta}{phi}. Comparing it with the spontaneous shrinking experiment of IIDs under both bias field and in-plane field, we presume that under the application of in-plane field there exists a direction along which the VBLs in the domain walls annihilate most easily, and it is in the direction that domain walls are perpendicular to the in-plane field.
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.
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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.
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Complex solitary waves and soliton trains in KdV and mKdV equations
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.
Tronc, P.; Kitaev, Yu. E.
2001-05-01
We determined the exact symmetries of conduction and valence Bloch states in type-I and type-II [001] (GaAs)m(AlAs)n superlattices at the Γ point and at some other symmetry points of the Brillouin zone of the superlattices and derived optical selection rules. Contrary to a result widely accepted in the envelope-function approximation (EFA), pz atomic orbitals cannot mix with px and py orbitals to build Bloch states. The phonon-assisted transitions involving the Γ point as an initial or final state are allowed both without and with taking into account the spin-orbit interaction whatever are the symmetries of the initial and final states. The electron band structure of the superlattices is discussed. Within the domain of validity of EFA (i.e., for not too small values of m and n), a detailed analysis of the Bloch-state symmetry and selection rules is provided on imposing invariance of the superlattice structure under the change of z to -z (the σz symmetry operation). It is shown that optical transitions between the conduction states arising from the Γ states of GaAs on one hand and the conduction states arising from the X states of AlAs on the other hand can be allowed from spin-orbit coupling only. The correspondence is provided between the symmetry of a Bloch state and the parity with respect to σz of its associated envelope function. The effect of an electric field parallel to the growth axis is discussed. Quantum wells do not differ from superlattices with regard to Bloch-state and envelope-function symmetries or optical selection rules. All the above results are still valid for any pseudomorphic superlattice or quantum well made of two binary compounds with zinc-blend structure and identical cations or anions, such as, for example, in the GaN/AlN system.
On the use of steady-state signal equations for 2D TrueFISP imaging.
Coolen, Bram F; Heijman, Edwin; Nicolay, Klaas; Strijkers, Gustav J
2009-07-01
To explain the signal behavior in 2D-TrueFISP imaging, a slice excitation profile should be considered that describes a variation of effective flip angles and magnetization phases after excitation. These parameters can be incorporated into steady-state equations to predict the final signal within a pixel. The use of steady-state equations assumes that excitation occurs instantaneously, although in reality this is a nonlinear process. In addition, often the flip angle variation within the slice excitation profile is solely considered when using steady-state equations, while TrueFISP is especially known for its sensitivity to phase variations. The purpose of this study was therefore to evaluate the precision of steady-state equations in calculating signal intensities in 2D TrueFISP imaging. To that end, steady-state slice profiles and corresponding signal intensities were calculated as function of flip angle, RF phase advance and pulse shape. More complex Bloch simulations were considered as a gold standard, which described every excitation within the sequence until steady state was reached. They were used to analyze two different methods based on steady-state equations. In addition, measurements on phantoms were done with corresponding imaging parameters. Although the Bloch simulations described the steady-state slice profile formation better than methods based on steady-state equations, the latter performed well in predicting the steady-state signal resulting from it. In certain cases the phase variation within the slice excitation profile did not even have to be taken into account.
Hernán Antonio Sorgentini
1999-01-01
Apología para la historia o el oficio de historiador de Marc Bloch es hoy una obra ineludible para quienes se inician en el estudio de la historia. Una nueva historia que reconoce haber experimentado un amplio proceso de renovación en el siglo XX, en el que "los Annales" fundados por Marc Bloch y Lucien Febvre han cumplido un papel central. El manuscrito interrumpido de Marc Bloch de Massimo Mastrogregori [director de la Revista di Storia della Storiografia Moderna] forma parte de las renovad...
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.
High-sensitivity label-free optical fiber optrodes based on the excitation of Bloch surface waves
Scaravilli, M.; Castaldi, G.; Cusano, A.; Galdi, V.
2016-05-01
In this study, the possibility to excite Bloch surface waves (BSWs) on the tip of a single-mode optical fiber is explored for the first time. In particular, we first show the possibility to achieve an on-tip excitation of BSWs, with optimized characteristic of the arising resonances, via an "all-fiber" grating-coupled configuration. Furthermore, envisioning novel high-performance fiber tip nanoprobes for label-free biosensing, we introduce an ad hoc design aimed at maximizing the refractive-index sensitivity. Numerical results indicate that the estimated sensitivities are comparable with those exhibited by current plasmonic lab-on-tip bio-probes, but are accompanied by a higher spectral selectivity. Therefore, this preliminary work paves the way to the development of new classes of miniaturized surface-wave optical fiber devices for low-detection-limit label-free chemical and biological sensing.
Directory of Open Access Journals (Sweden)
Maria Alvaro
2013-02-01
Full Text Available A one-dimensional photonic crystal (1DPC based on a planar stack of dielectric layers is used as an optical transducer for biosensing, upon the coupling of TE-polarized Bloch Surface Waves (BSW. The structure is tailored with a polymeric layer providing a chemical functionality facilitating the covalent binding of orienting proteins needed for a subsequent grafting of antibodies in an immunoassay detection scheme. The polymeric layer is impregnated with Cy3 dye, in such a way that the photonic structure can exhibit an emissive behavior. The BSW-coupled fluorescence shift is used as a means for detecting refractive index variations occurring at the 1DPC surface, according to a label-free concept. The proposed working principle is successfully demonstrated in real-time tracking of protein G covalent binding on the 1DPC surface within a fluidic cell.
Short-period intrinsic Stark GaN /AlGaN superlattice as a Bloch oscillator
Litvinov, V. I.; Manasson, A.; Pavlidis, D.
2004-07-01
We discuss the properties of AlGaN /GaN superlattice (SL) related to the feasibility of a terahertz-range oscillator. The distortion of the conduction-band profile by the polarization fields has been taken into account. We have calculated the conduction-band offset between the pseudomorphic AlGaN barrier and the GaN quantum well, the first miniband width and energy dispersion, as functions of Al content in the barrier. As the short-period SL miniband energy dispersion contains contributions from next to nearest neighbors, it causes anharmonic electron oscillations at the multiples of the fundamental Bloch frequency. The Al content and SL period that favor high-frequency oscillations have been determined.
Coupled Mode Equation Modeling for Out-of-Plane Gap Solitons in 2D Photonic Crystals
Dohnal, Tomas
2012-01-01
Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not generate higher harmonics, we obtain a closed curl-curl problem for the fundamental harmonic of the gap soliton. For gap solitons with frequencies inside spectral gaps and in an asymptotic vicinity of a gap edge we use a slowly varying envelope approximation based on the linear Bloch waves at the edge and slowly varying envelopes. We carry out a systematic derivation of the coupled mode equations (CMEs) which govern the envelopes. This derivation needs to be carried out in Bloch variables. The CMEs are a system of coupled nonlinear stationary Schr\\"odinger equations with an additional cross derivative term. Examples of gap soliton approximations are numerically co...
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...
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.
Directory of Open Access Journals (Sweden)
Andreas Wierschem
2007-09-01
Full Text Available The spatially periodic Kuramoto-Sivashinsky equation (pKS $$ partial_t u=-partial_x^4 u-c_3partial_x^3 u-c_2partial_x^2 u+2 deltapartial_x(cos( xu-partial_x(u^2, $$ with $u(t,xinmathbb{R}$, $tgeq 0$, $xinmathbb{R}$, is a model problem for inclined film flow over wavy bottoms and other spatially periodic systems with a long wave instability. For given $c_2,c_3inmathbb{R}$ and small $deltageq 0$ it has a one dimensional family of spatially periodic stationary solutions $u_s(cdot;c_2,c_3,delta,u_m$, parameterized by the mass $u_m=frac 1 {2pi}int_0^{2pi} u_s(x ,{ m d} x$. Depending on the parameters these stationary solutions can be linearly stable or unstable. We show that in the stable case localized perturbations decay with a polynomial rate and in a universal nonlinear self-similar way: the limiting profile is determined by a Burgers equation in Bloch wave space. We also discuss linearly unstable $u_s$, in which case we approximate the pKS by a constant coefficient KS-equation. The analysis is based on Bloch wave transform and renormalization group methods.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
van As, Liesl L; van As, Jo G
2007-05-01
During surveys of the biodiversity of fish parasites in the Okavango River and Delta, Botswana, specimens of Lamproglena von Nordmann, 1832 were found associated with the African pike Hepsetus odoe (Bloch). This Lamproglena species distinctly differs from all known species based on morphological features, in particular the cephalothorax and the maxilliped; it is described as L. hepseti n. sp. and is specific to its host, the African pike.
Tsukamoto, Shigeru; Hirose, Kikuji; Blügel, Stefan
2014-07-01
Generalized Bloch wave functions of bulk structures, which are composed of not only propagating waves but also decaying and growing evanescent waves, are known to be essential for defining the open boundary conditions in the calculations of the electronic surface states and scattering wave functions of surface and junction structures. Electronic complex band structures being derived from the generalized Bloch wave functions are also essential for studying bound states of the surface and junction structures, which do not appear in conventional band structures. We present a novel calculation method to obtain the generalized Bloch wave functions of periodic bulk structures by solving a generalized eigenvalue problem, whose dimension is drastically reduced in comparison with the conventional generalized eigenvalue problem derived by Fujimoto and Hirose [Phys. Rev. B 67, 195315 (2003)]. The generalized eigenvalue problem derived in this work is even mathematically equivalent to the conventional one, and, thus, we reduce computational cost for solving the eigenvalue problem considerably without any approximation and losing the strictness of the formulations. To exhibit the performance of the present method, we demonstrate practical calculations of electronic complex band structures and electron transport properties of Al and Cu nanoscale systems. Moreover, employing atom-structured electrodes and jellium-approximated ones for both of the Al and Si monatomic chains, we investigate how much the electron transport properties are unphysically affected by the jellium parts.
Johnson, Mathew A; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
We study the spectral stability of a family of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation $ \\partial_t v+v\\partial_x v+\\partial_x^3 v+\\delta(\\partial_x^2 v +\\partial_x^4 v)=0$, $\\delta>0$, in the Korteweg-de Vries limit $\\delta\\to 0$, a canonical limit describing small-amplitude weakly unstable thin film flow. More precisely, we carry out a rigorous singular perturbation analysis reducing the problem to the evaluation for each Bloch parameter $\\xi\\in [0,2\\pi]$ of certain elliptic integrals derived formally (on an incomplete set of frequencies/Bloch parameters, hence as necessary conditions for stability) and numerically evaluated by Bar and Nepomnyashchy \\cite{BN}, thus obtaining, up to machine error, complete conclusions about stability. The main technical difficulty is in treating the large-frequency and small Bloch-parameter regimes not studied by Bar and Nepomnyashchy \\cite{BN}, which requires techniques rather different from classical Fenichel-type analysis. The passage f...
Rapid propagation of a Bloch wave packet excited by a femtosecond ultraviolet pulse
Krasovskii, E. E.; Friedrich, C.; Schattke, W.; Echenique, P. M.
2016-11-01
Attosecond streaking spectroscopy of solids provides direct observation of the dynamics of electron excitation and transport through the surface. We demonstrate the crucial role of the exciting field in electron propagation and establish that the lattice scattering of the outgoing electron during the optical pumping leads to the wave packet moving faster than with the group velocity and faster than the free electron. We solve the time-dependent Schrödinger equation for a model of laser-assisted photoemission, with inelastic scattering treated as electron absorption and alternatively by means of random collisions. For a weak lattice scattering, the phenomenological result that the photoelectron moves with the group velocity d E /d ℏ k and traverses on average the distance equal to the mean-free path is proved to hold even at very short traveling times. This offers a novel interpretation of the delay time in streaking experiment and sheds new light on tunneling in optoelectronic devices.
Directory of Open Access Journals (Sweden)
Javier Barrera-Chica
2009-12-01
Full Text Available Objetivo. Estudiar los hábitos alimentarios de la Mayupa (Sternopygus macrurus Bloch & Schneider, 1801 en el río Sinú, Colombia. Materiales y métodos. El contenido estomacal se evaluó con el coeficiente de vacuidad, grado de llenado, grado de digestión, frecuencia de ocurrencia, frecuencia numérica, gravimetría, indice de importancia relativa (IIR y la relación longitud intestinal (LI-longitud total (LT. Resultados. Solo pocos estómagos se encontraron vacíos (CV =6.9% y el 60.0% de las presas se encontraron frescas. Se identificaron cuatro ítems alimentarios: peces, crustáceos, material vegetal y otros. Peces fue el ítem más frecuente (76.9%, abundante (48.3%, con mayor composición por peso (81.9% y con mayor importancia relativa (63.2%. Conclusiones. Los resultados obtenidos permiten inferir que la Mayupa es un pez de hábitos alimentarios carnívoros, con preferencia por los peces.
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.
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.
Cielocha, Joanna J; Jensen, Kirsten
2013-01-01
A new genus and species of lecanicephalidean cestode, Stoibocephalum arafurense n. gen., n. sp., is described from the sharkray, Rhina ancylostoma Bloch & Schneider, off northern Australia. Stoibocephalum arafurense n. gen., n. sp. is apolytic, and possesses a large, muscular, retractable apical organ, 3 pairs of excretory vessels, and testes in several columns and layers. The presence of 3 pairs of excretory vessels distinguishes this new genus from all other valid lecanicephalidean genera, except Hexacanalis Perrenoud, 1931, from which it can be distinguished based on ovary shape and egg morphology. Stoibocephalum n. gen. most closely resembles Tylocephalum Linton, 1890 but differs from that genus in its ability to completely retract its apical organ into the scolex proper. Scolex microthrix pattern and histological sections of scoleces attached in situ suggest S. arafurense n. gen., n. sp. to attach to the host's intestinal mucosa with apical organ and scolex proper surfaces, rather than just the apical organ surface. This is the third lecanicephalidean species described from the sharkray.
Pereira, Tadeu José; Silva, Gilda; Costa, Maria José; Costa, José Lino
2011-07-01
The Lusitanian toadfish, Halobatrachus didactylus (Bloch and Schneider, 1801), is a subtropical sound-producing marine teleost that inhabits estuaries and other brackish water ecosystems in its northern distribution area. The relative isolation of populations within estuaries may cause important modifications in the bio-ecology of this species. The males of this species present two morphotypes which are more accurately distinguishable during the reproductive season. In the Tagus estuary population, the two types of reproductive males were present: type I, the "characteristic" morphotype, and type II, the alternative morphotype. The opportunistic males had more developed testis while type I males had more developed accessory glands. Type I males presented more developed swimbladders and larger body size and live longer than type II males. On the contrary, type II males grew faster and matured earlier. The feeding habits of the two male morphotypes were similar during the reproductive season but differences were found between reproductive specimens and non-reproductive specimens. The diet of reproductive specimens was mainly composed of benthic prey in contrast to predominance of nectobenthic prey in the diet of non-reproductive specimens. The females of H. didactylus generally had an intermediate pattern between the two male morphotypes. The percentage of type II males tended to be higher in denser areas of the estuary. In comparison with populations from different size ecosystems, smaller ecosystems revealed important modifications on the bio-ecology of the species due to the increased competition for nesting sites and mating partners, favouring alternative male tactics.
Bingi, Jayachandra; Nair, Radhika V.; Vijayan, C.
2017-02-01
Light propagation and localization in a random structure with a periodic background is an upcoming paradigm for novel photonic applications. This paper demonstrates the phenomenon of time dependent transmittance of evanescent Bloch modes (EBM) in ZnS random photonic crystal (RPC) which forms the basis for photonic delay switching. The RPC is fabricated by colloidal self-assembly with ZnS nanospheres of size 215 nm. An anomalous reciprocity and time dependent transmission at EBM (mid band gap wavelength) are observed in coherent back scattering and transmission studies respectively. These are explained on the basis of restricted propagation of EBMs through random channels in the periodic background and enhanced field storage inside RPC. The channelized propagation of EBMs is evident from decreasing time delay of transmittance at reduced thicknesses. The proportionality between transmission time delay and incident power confirms photon (field) storage within the RPC. The results indicate that structures with systematically engineered EBM channels can work as wavelength selective delay switch and further provide a short time photon storage system under non-absorbing conditions.
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.
Buot, Felix A.; Otadoy, Roland E. S.; Rivero, Karla B.
2017-03-01
Wide ranging interest in Dirac Hamiltonian is due to the emergence of novel materials, namely, graphene, topological insulators and superconductors, the newly-discovered Weyl semimetals, and still actively-sought after Majorana fermions in real materials. We give a brief review of the relativistic Dirac quantum mechanics and its impact in the developments of modern physics. The quantum band dynamics of Dirac Hamiltonian is crucial in resolving the giant diamagnetism of bismuth and Bi-Sb alloys. Quantitative agreement of the theory with the experiments on Bi-Sb alloys has been achieved, and physically meaningful contributions to the diamagnetism has been identified. We also treat relativistic Dirac fermion as an interband dynamics in uniform magnetic fields. For the interacting Bloch electrons, the role of translation symmetry for calculating the magnetic susceptibility avoids any approximation to second order in the field. The expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results. The unified treatment of all the above calculations is based on the lattice Weyl-Wigner formulation of discrete phase-space quantum mechanics. For completeness, the magnetic susceptibility of Kondo alloys is also given since Dirac fermions in conduction band and magnetic impurities exhibit Kondo effect.
A generalized harmonic map equation for micromagnetics (abstract)
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.
Kinetic energy equations for the average-passage equation system
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.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Geochemical kinetics via the Swift-Connick equations and solution NMR
Harley, Steven J.; Ohlin, C. André; Casey, William H.
2011-07-01
Signal analysis in Nuclear Magnetic Resonance spectroscopy is among the most powerful methods to quantify reaction rates in aqueous solutions. To this end, the Swift-Connick approximations to the Bloch-McConnell equations have been used extensively to estimate rate parameters for elementary reactions. The method is primarily used for 17O NMR in aqueous solutions, but the list of geochemically relevant nuclei that can be used is long, and includes 29Si, 27Al, 19F, 13C and many others of particular interest to geochemists. Here we review the derivation of both the Swift-Connick and Bloch-McConnell equations and emphasize assumptions and quirks. For example, the equations were derived for CW-NMR, but are used with modern pulse FT-NMR and can be applied to systems that have exchange rates that are shorter than the lifetime of a typical pulse. The method requires a dilute solution where the minor reacting species contributes a negligible amount of total magnetization. We evaluate the sensitivity of results to this dilute-solution requirement and also highlight the need for chemically well-defined systems if reliable data are to be obtained. The limitations in using longitudinal relaxation to estimate reaction rate parameters are discussed. Finally, we provide examples of the application of the method, including ligand exchanges from aqua ions and hydrolysis complexes, that emphasize its flexibility. Once the basic requirements of the Swift-Connick method are met, it allows geochemists to establish rates of elementary reactions. Reactions at this scale lend themselves well to methods of computational simulation and could provide key tests of accuracy.
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.
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.
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Beginning partial differential equations
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
Ordinary differential equations
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
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.
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.
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...
La conciencia de la libertad (La filosofía moral como filosofía de la historia en Ernst Bloch)
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...
Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling.
García-Morales, Vladimir; Orlov, Alexander; Krischer, Katharina
2010-12-01
A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.
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.
Singular stochastic differential equations
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Xu, J.P. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China); Liu, S.P. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China); Guo, G.X. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China); Zhen, C.M. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China); Tang, G.D. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China); Sun, H.Y. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China); Nie, X.F. [College of Physics, Hebei Normal University, Shijiazhuang 050016 (China)]. E-mail: niexf@mail.hebtu.edu.cn
2004-12-01
The stability of vertical Bloch lines (VBLs) in the second kind of dumbbell domain (IIDs) walls in liquid phase epitaxy garnet bubble films subjected to an in-plane field at various temperatures is studied experimentally. It is found that there exists a critical in-plane field range depending on temperature, in which vertical Bloch lines (VBLs) in the second kind of IIDs walls are unstable, i.e., [Hip(1)(T),Hip(2)(T)]. Here, Hip(1)(T) is the initial critical in-plane field at which VBLs in the walls of IIDs annihilate; while Hip(2)(T) is the lowest in-plane field at which all VBLs in the walls of IIDs have annihilated completely. Also, the critical in-plane field range [Hip(1)(T),Hip(2)(T)],Hip(1)(T) and Hip(2)(T) all decrease with the temperature increasing. Hip(1)(T) and Hip(2)(T) reach zero at T0' and T0, respectively.
Differential equations for dummies
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.
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.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
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.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
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.
Differential equations I essentials
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.
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Bazeia, D; Losano, L
2016-01-01
This work reports on models described by two real scalar fields coupled with gravity in the five-dimensional spacetime, with a warped geometry involving one infinite extra dimension. Through a mechanism that smoothly changes a thick brane into a hybrid brane, one investigates the appearance of hybrid branes hosting internal structure, characterized by the splitting on the energy density and the volcano potential, induced by the parameter which controls interactions between the two scalar fields. In particular, we investigate distinct symmetric and asymmetric hybrid brane scenarios.
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-
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
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.
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Applied partial differential equations
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...
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Hyperbolic partial differential equations
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
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
Beginning partial differential equations
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
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
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.
Differential equations problem solver
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
Ordinary differential equations
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,
Uncertain differential equations
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.
Baryshev, A V; Merzlikin, A M
2014-05-10
The Bloch surface wave resonance (SWR) was visualized with the aid of plasmon absorption in a dielectric/metal/dielectric sandwich terminating a one-dimensional photonic crystal (PhC). An SWR peak in calculated spectra of such a plasmonic photonic crystal (PPhC) slab comprising a noble or base metal layer was demonstrated to be sensitive to a negligible variation of refractive index of a medium adjoining to the slab. The considered structure of PPhC slabs can be of practical importance because the metal layer is protected by a capping dielectric layer from contact with analytes and, consequently, from deterioration. We found that, in case of PPhC slabs, gold (the key element of the surface plasmon resonance-based biosensors) can be replaced by other metals. The PPhC-based sensors can be low-cost, reusable, and robust sensors having a sensitivity surpassing that of the known optical sensors.
Patterson, M.; Hughes, S.; Schulz, S.; Beggs, D. M.; White, T. P.; O'Faolain, L.; Krauss, T. F.
2009-11-01
Through a combined theoretical and experimental study of disorder-induced incoherent scattering losses in slow-light photonic crystal slab waveguides, we show the importance of Bloch mode reshaping and multiple scattering. We describe a convenient and fully three-dimensional theoretical treatment of disorder-induced extrinsic scattering, including the calculation of backscatter and out-of-plane losses per unit cell, and the extrapolation of the unit-cell loss to the loss for an entire disordered waveguide. The theoretical predictions, which are also compared with recent measurements on dispersion engineered silicon waveguides, demonstrate the failure of the Beer-Lambert law due to multiple scattering. We also explain why the previously assumed group velocity scalings of disorder-induced loss break down in general.
La conciencia de la libertad (La filosofía moral como filosofía de la historia en Ernst Bloch
Directory of Open Access Journals (Sweden)
Gimbernat, José Antonio
1991-10-01
Full Text Available 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 historización política de la libertad, heredada en parte de la tradición liberal, lo que exige a su vez una nueva definición del concepto de progreso.
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.
Directory of Open Access Journals (Sweden)
Maria Eugenia Chaves Maldonado
2016-01-01
Full Text Available In his unfinished and posthumously published book Apologie pour l’histoire, Marc Bloch bestowed on future historians a seminal legacy of critical reflections on the concept of time as the object of historical analysis. During the last decades, the concept of time in History has experienced a renewed interest by professional historians, in particular in reference to the category of anachronism. The Italian historian Carlo Ginzburg and the French art historian Georges Didi-Huberman are among those engaged in this debate. This article offers a reading of two works by these historians with the purpose of underlying the fundamental influence that Marc Bloch’s ideas on time had in Ginzburg and Didi-Hubermans’ critical interventions.
Energy Technology Data Exchange (ETDEWEB)
Zeitoun, Ph.; Oliva, E.; Fajardo, M.; Cheriaux, G.; Le, T. T. T.; Li, L.; Pitman, M.; Ros, D.; Sebban, S.; Velarde, P. [Laboratoire d' Optique Appliquee, ENSTA-PariesTech, CNRS, Ecole Poluytehcnique-PariesTech, chemin d ela huniere, Palaiseau (France); Laboratoire d' Optique Appliquee, ENSTA-PariesTech, CNRS, Ecole Poluytehcnique-PariesTech, chemin d ela huniere, Palaiseau (France); GoLP, Instituto de Plasmas e Fusao Nuclear, Laboratorio Associado, Instituto Superior Tecnico, Lisbon (Portugal); Laboratoire d' Optique Appliquee, ENSTA-PariesTech, CNRS, Ecole Poluytehcnique-PariesTech, chemin d ela huniere, Palaiseau (France); CLUPS, EA4127, Bat 106, Universite Paris-Sud, 91405 Orsay (France); Laboratoire d' Optique Appliquee, ENSTA-PariesTech, CNRS, Ecole Poluytehcnique-PariesTech, chemin d ela huniere, Palaiseau (France); Instituto de Fusion Nuclear, Universidad Politecnica de Madrid, Madrid (Spain)
2012-07-09
By seeding amplifying plasmas pumped with the so-called Transient collisionnal excitation scheme, the amplified pulse seems to be limited to an energy of several 10's of {mu}J. Aiming to attain several mJ, we study the seeding of plasma pumped by long laser pulse. Thanks to our time-dependent Maxwell-Bloch code, we demonstrate that direct seeding with femtosecond pulse is inefficient. We also study the amplification of pulse train with the drawback of re-synchronizing the pulses. We proposed and studied the amplification of high harmonic seed stretched by a grating pair, amplified finally compressed. We consider off-axis diffraction on the gratings for maximizing their efficiency. Considering the phase deformation induced by the amplification and the spectral narrowing the final pulse is 230 fs in duration and 5 mJ.
Sreejith, P; Oommen, O V
2006-04-01
The short-term action of thyroid hormone tri-iodothyronine (T3) was studied in vivo and in vitro on antioxidant enzyme activities in a teleost Anabas testudineus (Bloch). T3 injection in vivo (200 ng) in normal fish decreased the lipid peroxidation products and increased superoxide dismutase (SOD), catalase and glutathione peroxidase (GPx) activities after 30 min. T3 in vitro (10(-6) M) increased the antioxidant activities of catalase, glutathione reductase (GR), GPx and glutathione level after 15/30 min, except SOD, substantiating in vivo effects in normal fish. The results suggest a rapid regulatory effect of thyroid hormone in vivo and in vitro, in the removal of reactive oxygen species in A testudineus.
Hemanand, Th; Meitei, N Mohilal; Bandyopadhyay, Probir K; Mitra, Amlan K
2008-01-01
A new species of Henneguya parasitizing tissues affected by the ulcerative disease syndrome of a freshwater fish Anabas testudineus (Bloch) from Khiodum and Pumlen lakes of Manipur state is described. Of the fishes examined 75% were found to be infested with this myxozoan parasite. Mature spores of the new species are elongated, biconvex, and oval with bluntly rounded anterior end and gradually tapering posterior end with a caudal prolongation, measuring 12.6-15.4 (14.0+/- 1.1) microm in length. Length of the caudal prolongation is 11.2-12.6 (11.7+/- 0.6) microm. The width of the spores is 5.6-7.0 (6.3+/- 0.5) microm. The length of the polar capsules is 5.6-6.3 (5.5+/- 0.3) microm.
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.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
Applied partial differential equations
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...
Kinetic equations: computation
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.
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.
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.
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.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Functional Equations and Fourier Analysis
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.
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.
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.
Introduction to partial differential equations
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.
Directory of Open Access Journals (Sweden)
Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
Generalization of Hopf Functional Equation
Institute of Scientific and Technical Information of China (English)
无
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.
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Stochastic porous media equations
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.
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...
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....
Theory of differential equations
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
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.
Generalized estimating equations
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
Equations of mathematical physics
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
Gas Dynamics Equations: Computation
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.
Nonlocal electrical diffusion equation
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 0type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.
Test equating methods and practices
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...
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
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.
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Structural Equation Model Trees
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…
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.
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.
Standardized Referente Evapotranspiration Equation
Directory of Open Access Journals (Sweden)
M.D. Mundo–Molina
2009-04-01
Full Text Available In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude it was selected tomake comparisons. The compared equations we re: a CIANO weat her station, b Penman–Monteith ASCE (PMA, Penman–Monteith FAO 56 (PM FAO 56, Penman–Monteith estandarizado ASCE (PM Std. ASCE. The results were: a There are important differences between PMA and CIANO weather station. The differences are attributed to the nonstandardization of the equation CIANO weather station, b The coefficient of correlation between both methods was of 0,92, with a standard deviation of 1,63 mm, an average quadratic error of 0,60 mm and one efficiency in the estimation of ETo with respect to the method pattern of 87%.
Equational binary decision diagrams
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
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.
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Elements of partial differential equations
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
Stochastic differential equations and applications
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
SPECIFIC SOLUTIONS GROUNDWATER FLOW EQUATION
Syahruddin, Muhammad Hamzah
2014-01-01
Geophysic publication Groundwater flow under surface, its usually slow moving, so that in laminer flow condition can find analisys using the Darcy???s law. The combination between Darcy law and continuity equation can find differential Laplace equation as general equation groundwater flow in sub surface. Based on Differential Laplace Equation is the equation that can be used to describe hydraulic head and velocity flow distribution in porous media as groundwater. In the modeling Laplace e...
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Differential Equations with Linear Algebra
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
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Classical Diophantine equations
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, ...
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Differential equations with Mathematica
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
Trzetrzelewski, Maciej
2016-11-01
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
Dissipative Boussinesq equations
2007-01-01
40 pages, 15 figures, published in C. R. Mecanique 335 (2007) Other author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutykh; International audience; The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water fr...
Stability in Neutral Equations
1976-02-04
Martinez-Amores Division of Applied Mathematics Brown University Providence, Rhode Island 02912 and Universidad de Granada, Seccion de Matematicas , Spain S...XG w)1- 0 ~t)- >~~~ 0 suc ht j~<kIp, Ii 2 ~ o ~~~ X~ G (t) , y’ip X= 0 y 20 since equation (3.16) is satisfied. Since F = col(f,0), only the col
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.
Quantum molecular master equations
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™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 Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Ali Khan, Mohammed Safwan; Mat Jais, Abdul Manan; Hussain, Javeed; Siddiqua, Faiza; Gopala Reddy, A; Shivakumar, P; 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 assessment of antiulcer activity and Ranitidine (50 mg/kg) was employed as the standard drug. The various gastric parameters like volume of gastric juice, pH, free and total acidities, ulcer index, and levels of antioxidant enzymes like catalase, superoxide dismutase, and lipid peroxidation marker malondialdehyde were determined. AECS at concentrations of 40% and 50% w/v significantly decreased the volume of gastric juice and increased the levels of catalase while considerable decrease in free and total acidities and increase in superoxide dismutase were observed with the treatment of standard drug and AECS (50% w/v). All the test doses of AECS markedly decreased ulcer index and malondialdehyde compared to the standard drug whereas AECS 30% w/v did not alter volume of gastric juice, pH, free and total acidities, catalase, and superoxide dismutase. From these findings, it can be concluded that AECS is devoid of acid neutralizing effects at lower doses and possesses antisecretory and antiulcer activities and this could be related to its antioxidant mechanism.
Cai, S H; Lu, Y S; Wu, Z H; Jian, J C
2013-08-01
The outer membrane proteins of the marine aquatic animal pathogen, Vibrio alginolyticus, play an important role in the virulence of the bacterium and are potential candidates for vaccine development. In this study, the gene encoding an outer membrane protein-OmpU was cloned and expressed in Escherichia coli. Polyclonal antibodies were raised in rabbits against the purified recombinant OmpU, and the reaction of the antibody was confirmed by Western blotting using the isolated OmpU and the recombinant OmpU of V. alginolyticus. To analyze the immunogenicity of the recombinant OmpU, crimson snapper, Lutjanus erythropterus Bloch, were immunized by intraperitoneal injection, and antibody response was assessed by the enzyme-linked immunosorbent assay (ELISA). The results demonstrated that the recombinant OmpU produced an observable antibody response in all sera of the vaccinated fish. The vaccinated fish were challenged by virulent V. alginolyticus and observed to have high resistance to infection. These results indicate that the recombinant OmpU is an effective vaccine candidate against V. alginolyticus in L. erythropterus.
Wang, H; Xu, Lj; Lu, Lq
2016-02-01
Epidemics caused by cyprinid herpesvirus 2 (CyHV-2) in domestic cyprinid species have been reported in both European and Asian countries. Although the mechanisms remain unknown, acute CyHV-2 infections generally result in high mortality, and the surviving carps become chronic carriers displaying no external clinical signs. In this study, in situ hybridization analysis showed that CyHV-2 tended to infect peripheral blood cells during either acute or chronic infections in silver crucian carp, Carassius auratus gibelio (Bloch). Laboratory challenge experiments coupled with real-time PCR quantification assays further indicated that steady-state levels of the viral genomic copy number in fish serum exhibited a typical 'one-step' growth curve post-viral challenge. Transcriptional expression of open reading frames (ORF) 121, which was selected due to its highest transcriptional levels in almost all tested tissues, was monitored to represent the replication kinetics of CyHV-2 in peripheral blood cells. Similar kinetic curve of active viral gene transcription in blood cells was obtained as that of serum viral load, indicating that CyHV-2 replicated in peripheral blood cells as well as in other well-characterized tissues. This study should pave the way for designing non-invasive and cost-effective serum diagnostic methods for quick detection of CyHV-2 infection.
Beckmann, Peter A; Rosenberg, Jessie; Nordstrom, Kerstin; Mallory, Clelia W; Mallory, Frank B
2006-03-23
We have observed and modeled the 1H and 19F solid-state nuclear spin relaxation process in polycrystalline 3-(trifluoromethyl)phenanthrene. The relaxation rates for the two spin species were observed from 85 to 300 K at the low NMR frequencies of omega/2pi = 22.5 and 53.0 MHz where CF3 rotation, characterized by a mean time tau between hops, is the only motion on the NMR time scale. All motional time scales (omegatau 1) are observed. The 1H spins are immobile on the NMR time scale but are coupled to the 19F spins via the unlike-spin dipole-dipole interaction. The temperature dependence of the observed relaxation rates (the relaxation is biexponential) shows considerable structure and a thorough analysis of Bloch-Wangsness-Redfield theory for this coupled spin system is provided. The activation energy for CF3 rotation is 11.5 +/- 0.7 kJ/mol, in excellent agreement with the calculation in a 13-molecule cluster provided in the companion paper where the crystal structure is reported and detailed ab initio electronic structure calculations are performed [Wang, X.; Mallory F. B.; Mallory, C. W; Beckmann, P. A.; Rheingold, A. L.; Francl, M. M J. Phys. Chem. A 2006, 110, 3954].
Directory of Open Access Journals (Sweden)
Latif Taşkaya
2016-03-01
Full Text Available In this study, quality properties and shelf life for gibel carp (Carassius gibelio, Bloch 1782 marinades during stored at 4±1 °C in different sauces was investigated. The marinating process was carried out in 2.5% vinegar, 10% salt and water for 72h at 4±1 °C. After the marination process, fish were removed from the solutions, transferred in to glass jar contain with different sauces (Group A: sunflower oil and tomato paste, Group B: sunflower oil with garlic, red pepper, thyme, basil and mint and the control group: sun flower oil. Sensory, chemical, colour and microbiological analyses were performed during the storage. According the chemical analysis results TVB-N and TBA values of all groups were increased during the storage, but during the stored period did not exceed acceptible limit values. The highest TVB-N and TBA values were group A. (P<0,05. At the end of 135 days of storage, sensory analysis results pointed out that the marinades of group B did not exceed acceptible limit values (P<0,05. The overall microbial load of the fresh samples decreased through out the storage period (P<0,05. By sensory data, shelf life of sauced gibel carp marinades were 120 days (control, 105 days (group A and 135 days (group B.
Energy Technology Data Exchange (ETDEWEB)
Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Xue, Long [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Aviation Univ. of Air Force, Liaoning (China). Flight Training Base
2015-07-01
Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti
2014-03-01
Bloch oscillating transistor (BOT) is mesoscopic current amplier based on a combination of a Josephson junction or a squid connected with a large resistor and a NIS junction. We have studied the dynamics of BOT near the bifurcation threshold. This is an important feature for an amplifier as this can be utilized to improve its performance characteristics. We have measured the I - V characteristics of the BOT with different base currents (IB) over a wide range of Josephson coupling energies (EJ) . The current gain (β) is found to be increasing with increasing IB and eventually diverging. We have found a record large β = 50 in our experiment. In order to determine the common mode rejection ratio (CMRR) of a differential pair BOT we have used two BOTs fabricated on the same chip. The common mode port is connected to the bases of the two BOTs and fed with varying voltages; simultaneously emitter currents of the two BOTs are recorded. In our experiment we found a 20dB of CMRR.
Sinibaldi, Alberto; Sampaoli, Camilla; Danz, Norbert; Munzert, Peter; Sibilio, Leonardo; Sonntag, Frank; Occhicone, Agostino; Falvo, Elisabetta; Tremante, Elisa; Giacomini, Patrizio; Michelotti, Francesco
2017-06-15
We report on the use of one-dimensional photonic crystals to detect clinically relevant concentrations of ERBB2/neu/Her2 in cell lysates. ERBB2 is a pivotal breast cancer biomarker and targetable oncogenic driver associated with aggressive breast cancer subtypes. To quantitate soluble ERBB2, we developed an optical platform that combines label-free and fluorescence detection modes. Such platform makes use of a sandwich assay in which the one-dimensional photonic crystals sustaining Bloch surface waves are tailored with a monoclonal antibody for highly specific biological recognition (BSW biochip). In a second step, a second antibody to ERBB2 quantitatively detects the bound analyte. The strategy of the present approach takes advantage of the combination of label-free and fluorescence techniques, making bio-recognition more robust and sensitive. In the fluorescence operation mode, the platform can attain the limit of detection 0.3ng/mL (1.5pM) for ERBB2 in cell lysates. Such resolution meets the international guidelines and recommendations (15ng/mL) for diagnostic ERBB2 assays that in the future may help to more precisely assign therapies counteracting cancer cell proliferation and metastatic spread.
Zhao, Feng; Fessler, Jeffrey A; Wright, Steven M; Noll, Douglas C
2014-10-01
Parallel excitation requires fast and accurate B1 map estimation. Bloch-Siegert (BS) B1 mapping is very fast and accurate over a large dynamic range. When applied to multi-coil systems, however, this phase-based method may produce low signal-to-noise ratio estimates in low magnitude regions due to localized excitation patterns of parallel excitation systems. Also, the imaging time increases with the number of coils. In this work, we first propose to modify the standard BS B1 mapping sequence so that it avoids the scans required by previous B1 phase estimation methods. A regularized method is then proposed to jointly estimate the magnitude and phase of multi-coil B1 maps from BS B1 mapping data, improving estimation quality by using the prior knowledge of the smoothness of B1 magnitude and phase. Lastly, we use Cramer-Rao lower bound analysis to optimize the coil combinations, to improve the quality of the raw data for B1 estimation. The proposed methods are demonstrated by simulations and phantom experiments.
New application to Riccati equation
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.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
New Exact Solutions to NLS Equation and Coupled NLS Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2004-01-01
A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrodinger (NLS) equation and coupled NLS equations. Many kinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some are found for the first time.
The compressible adjoint equations in geodynamics: equations and numerical assessment
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.
Generalized estimating equations
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
Savvidy, G K
1998-01-01
We discuss the basic properties of the gonihedric string and the problem of its formulation in continuum. We propose a generalization of the Dirac equation and of the corresponding gamma matrices in order to describe the gonihedric string. The wave function and the Dirac matrices are infinite-dimensional. The spectrum of the theory consists of particles and antiparticles of increasing half-integer spin lying on quasilinear trajectories of different slope. Explicit formulas for the mass spectrum allow to compute the string tension and thus demonstrate the string character of the theory.
Dimensional Equations of Entropy
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.
Ordinary differential equations
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
Partial differential equations
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
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....
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.
``Riemann equations'' in bidifferential calculus
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.
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
Successfully Transitioning to Linear Equations
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…
An Extented Wave Action Equation
Institute of Scientific and Technical Information of China (English)
左其华
2003-01-01
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Abdon Atangana
2014-02-01
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of in
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Yehorchenko, Irina
2010-01-01
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.
Institute of Scientific and Technical Information of China (English)
黄虎; 丁平兴; 吕秀红
2001-01-01
The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom, thus leading to an extended mild-slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. The frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild- slope equation is more widely applicable and contains as special cases famous mild-slope equations below: the classical mild-slope equation of Berkhoff , Kirby' s mild-slope equation with current, and Dingemans' s mild-slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
$\\Lambda$ Scattering Equations
Gomez, Humberto
2016-01-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\\Lambda$ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting $\\Lambda$ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the $\\Lambda$ algorithm.
Bloch-Siemens syndrome:a case report and literature review%色素失禁症一例并文献复习
Institute of Scientific and Technical Information of China (English)
王彦; 王丽华; 曲燕; 孟现广; 杨秀莉
2016-01-01
We herein report a two-month old girl. She had rashes and blisters on trunk and limbs at birth. Dermatological examination revealed reticulate pigmented spots scattered on trunk and extremities. Some dark red papules and blisters in different size were located on both interfemus and wrists. The bilsters had thick walls and the Nikolsky's sign was negative. Most of the lesions were distributed in a splash manner. His-topathologically, the hyperkeratesis, acanthosis and epidermal vesicles filled with eosinophils were found in epidermis, and a small number of lymphocytes and eosinophils infiltration in the superficial dermis capillary were reported. Based on the clinical and histological findings, the final diagnosis was neonatal Bloch-Sie-mens syndrome.%患儿,女,2个月。因躯干及四肢皮疹2个月就诊。皮肤科检查：躯干及四肢皮肤弥漫分布网状色素沉着斑。双股内侧、手腕部见暗红色大小不一丘疹、水疱,水疱壁厚,尼氏征阴性,部分水疱结痂。皮疹呈泼溅状分布。组织病理示：表皮角化过度,棘层增厚,表皮内见多房性水疱,疱液中可见大量嗜酸性粒细胞。真皮浅层毛细血管周围可见少量淋巴细胞及嗜酸性粒细胞浸润。诊断：新生儿色素失禁症。
The Riccati Differential Equation and a Diffusion-Type Equation
Suazo, Erwin; Vega-Guzman, Jose M
2008-01-01
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equation with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary functions and certain integrals involving a characteristic function, which should be found as an analytic or numerical solution of the second order linear differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding nonhomogeneous equation is also found.
Comparison between characteristics of mild slope equations and Boussinesq equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Boussinesq-type equations and mild-slope equations are compared in terms of their basic forms and characteristics. It is concluded that linear mild-slope equations on dispersion relation are better than non-linear Boussinesq equations. In addition, Berkhoff experiments are computed and compared by the two models, and agreement between model results and available experimental data is found to be quite reasonable, which demonstrates the two models' capacity to simulate wave transformation. However they can deal with different physical processes respectively, and they have their own characteristics.
Institute of Scientific and Technical Information of China (English)
余建; 伍鹏程
2016-01-01
In this paper,the boundedness and compactness of the composite differential prior operator were studied,which was used to support the mapping,from Bloch space to the weighted space. And we obtained the necessary and sufficient conditions for the boundedness and compactness of this opera-tor.%从算子的性质出发，研究Bloch空间到加权型空间的复合微分前置算子的有界性和紧性，得到了算子有界性和紧性的充分必要条件。
Algebraic Approaches to Partial Differential Equations
Xu, Xiaoping
2012-01-01
Partial differential equations are fundamental tools in mathematics,sciences and engineering. This book is mainly an exposition of the various algebraic techniques of solving partial differential equations for exact solutions developed by the author in recent years, with emphasis on physical equations such as: the Calogero-Sutherland model of quantum many-body system in one-dimension, the Maxwell equations, the free Dirac equations, the generalized acoustic system, the Kortweg and de Vries (KdV) equation, the Kadomtsev and Petviashvili (KP) equation, the equation of transonic gas flows, the short-wave equation, the Khokhlov and Zabolotskaya equation in nonlinear acoustics, the equation of geopotential forecast, the nonlinear Schrodinger equation and coupled nonlinear Schrodinger equations in optics, the Davey and Stewartson equations of three-dimensional packets of surface waves, the equation of the dynamic convection in a sea, the Boussinesq equations in geophysics, the incompressible Navier-Stokes equations...
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Surface Gap Soliton Ground States for the Nonlinear Schr\\"{o}dinger Equation
Dohnal, Tomáš; Reichel, Wolfgang
2010-01-01
We consider the nonlinear Schr\\"{o}dinger equation $(-\\Delta +V(x))u = \\Gamma(x) |u|^{p-1}u$, $x\\in \\R^n$ with $V(x) = V_1(x) \\chi_{\\{x_1>0\\}}(x)+V_2(x) \\chi_{\\{x_10\\}}(x)+\\Gamma_2(x) \\chi_{\\{x_1<0\\}}(x)$ and with $V_1, V_2, \\Gamma_1, \\Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\\min \\sigma(-\\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\\equiv V_1, \\Gamma\\equiv \\Gamma_1$ and $V\\equiv V_2, \\Gamma\\equiv \\Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\\tfrac{d^2}{dx^2} +V_1(x)$ an...
Introduction to partial differential equations
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Energy Conservation Equations of Motion
Vinokurov, Nikolay A
2015-01-01
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Partial Differential Equations of Physics
Geroch, Robert
1996-01-01
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of differential equations so formulated. Examples of such features include hyperbolicity of the equations, constraints and their roles (e.g., in connection with the initial-value formulation), how diffeomorphism freedom is manifest, and how interactions betwee...
Integrable Equations on Time Scales
Gurses, Metin; Guseinov, Gusein Sh.; Silindir, Burcu
2005-01-01
Integrable systems are usually given in terms of functions of continuous variables (on ${\\mathbb R}$), functions of discrete variables (on ${\\mathbb Z}$) and recently in terms of functions of $q$-variables (on ${\\mathbb K}_{q}$). We formulate the Gel'fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over $q...
Hyperbolic Methods for Einstein's Equations
Directory of Open Access Journals (Sweden)
Reula Oscar
1998-01-01
Full Text Available 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.
The generalized Airy diffusion equation
Directory of Open Access Journals (Sweden)
Frank M. Cholewinski
2003-08-01
Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.
Delay equations and radiation damping
Chicone, C.; Kopeikin, S. M.; Mashhoon, B.; Retzloff, D. G.
2001-06-01
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we identify this invariant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not contained in the local equations of motion.
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
Solutions of relativistic radial quasipotential equations
Energy Technology Data Exchange (ETDEWEB)
Minh, V.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1985-11-01
A systematic approach to the investigation of relativistic radial quasipotential equations is developed. The quasipotential equations can be interpreted either as linear equations in finite differences of fourth and second orders, respectively, or as differential equations of infinite order.