Two dimensional kinetic analysis of electrostatic harmonic plasma waves

Energy Technology Data Exchange (ETDEWEB)

Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R. [Instituto de Física, UFRGS, 91501-970 Porto Alegre, RS (Brazil); Yoon, P. H. [IPST, University of Maryland, College Park, Maryland 20742 (United States); SSR, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of)

2016-06-15

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.

On the connection between the hydrogen atom and the harmonic oscillator: the continuum case

International Nuclear Information System (INIS)

Kibler, M.; Negadi, T.

1983-05-01

The connection between a three-dimensional nonrelativistic hydrogen atom with positive energy and a four-dimensional isotropic harmonic oscillator with repulsive potential is established by applying Jordan-Schwinger boson calculus to the algebra of the Laplace-Runge-Lenz-Pauli vector. The spectrum generating group SO(4,2) both for the bound and free states of the three-dimensional hydrogen atom arises as a quotient of the group Sp(8,R) associated to a four-dimensional isotropic harmonic oscillator with constraint

The two-capacitor problem revisited: a mechanical harmonic oscillator model approach

International Nuclear Information System (INIS)

Lee, Keeyung

2009-01-01

The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that exactly half the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be exactly half the supplied energy whether that is caused by the Joule heat or by the radiation. This paper, which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem, is suitable for all undergraduate levels

Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects

International Nuclear Information System (INIS)

Ghosh, Subir; Majhi, Bibhas Ranjan

2008-01-01

We study complexified harmonic oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) who initiated the study of these Crypto-gauge invariant models that can be related to PT-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints (in contrast to Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) where one deals with a single constraint) with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator

Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry

CERN Document Server

Buccella, F; Savoy, C A

1972-01-01

The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).

The su(1, 1) dynamical algebra from the Schroedinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator

International Nuclear Information System (INIS)

Martinez, D; Flores-Urbina, J C; Mota, R D; Granados, V D

2010-01-01

We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.

The quantum harmonic oscillator on a circle and a deformed quantum field theory

International Nuclear Information System (INIS)

Rego-Monteiro, M.A.

2001-05-01

We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)

The Two-Beam Free Electron Laser Oscillator

CERN Document Server

Thompson, Neil R

2004-01-01

A one-dimensional model of a free-electron laser operating simultaneously with two electron beams of different energies [1] is extended to an oscillator configuration. The electron beam energies are chosen so that an harmonic of the lower energy beam is at the fundamental radiation wavelength of the higher energy beam. Potential benefits over a single-beam free-electron laser oscillator are discussed.

Magnetoresistance oscillations of two-dimensional electron systems in lateral superlattices with structured unit cells

Science.gov (United States)

Gerhardts, Rolf R.

2015-11-01

Model calculations for commensurability oscillations of the low-field magnetoresistance of two-dimensional electron systems (2DES) in lateral superlattices, consisting of unit cells with an internal structure, are compared with recent experiments. The relevant harmonics of the effective modulation potential depend not only on the geometrical structure of the modulated unit cell, but also strongly on the nature of the modulation. While higher harmonics of an electrostatically generated surface modulation are exponentially damped at the position of the 2DES about 90 nm below the surface, no such damping appears for strain-induced modulation generated, e.g., by the deposition of stripes of calixarene resist on the surface before cooling down the sample.

An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

International Nuclear Information System (INIS)

Arcos-Olalla, Rafael; Reyes, Marco A.; Rosu, Haret C.

2012-01-01

We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.

An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

Energy Technology Data Exchange (ETDEWEB)

Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)

2012-10-01

We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.

Parametric Resonance in a Time-Dependent Harmonic Oscillator

Directory of Open Access Journals (Sweden)

P. N. Nesterov

2013-01-01

Full Text Available In this paper, we study the phenomenon of appearance of new resonances in a timedependent harmonic oscillator under an oscillatory decreasing force. The studied equation belongs to the class of adiabatic oscillators and arises in connection with the spectral problem for the one-dimensional Schr¨odinger equation with Wigner–von Neumann type potential. We use a specially developed method for asymptotic integration of linear systems of differential equations with oscillatory decreasing coefficients. This method uses the ideas of the averaging method to simplify the initial system. Then we apply Levinson’s fundamental theorem to get the asymptotics for its solutions. Finally, we analyze the features of a parametric resonance phenomenon. The resonant frequencies of perturbation are found and the pointwise type of the parametric resonance phenomenon is established. In conclusion, we construct an example of a time-dependent harmonic oscillator (adiabatic oscillator in which the parametric resonances, mentioned in the paper, may occur.

The macroscopic harmonic oscillator and quantum measurements

International Nuclear Information System (INIS)

Hayward, R.W.

1982-01-01

A quantum mechanical description of a one-dimensional macroscopic harmonic oscillator interacting with its environment is given. Quasi-coherent states are introduced to serve as convenient basis states for application of a density matrix formalism to characterize the system. Attention is given to the pertinent quantum limits to the precision of measurement of physical observables that may provide some information on the nature of a weak classical force interacting with the oscillator. A number of ''quantum nondemolition'' schemes proposed by various authors are discussed. (Auth.)

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

Science.gov (United States)

Steely, Sidney L.

1993-01-01

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Exact complex integrals in two dimensions for shifted harmonic ...

Indian Academy of Sciences (India)

We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.

Quantization of the damped harmonic oscillator revisited

Energy Technology Data Exchange (ETDEWEB)

Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Fresneda, R., E-mail: fresneda@gmail.co [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)

2011-04-11

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: We prove the local equivalence of two damped harmonic oscillator models. We find different high energy behaviors between the two models. Based on the local equivalence, we make a simple construction of the coherent states.

Quantization of the damped harmonic oscillator revisited

International Nuclear Information System (INIS)

Baldiotti, M.C.; Fresneda, R.; Gitman, D.M.

2011-01-01

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: → We prove the local equivalence of two damped harmonic oscillator models. → We find different high energy behaviors between the two models. → Based on the local equivalence, we make a simple construction of the coherent states.

Quantum oscillations in quasi-two-dimensional conductors

CERN Document Server

Galbova, O

2002-01-01

The electronic absorption of sound waves in quasi-two-dimensional conductors in strong magnetic fields, is investigated theoretically. A longitudinal acoustic wave, propagating along the normal n-> to the layer of quasi-two-dimensional conductor (k-> = left brace 0,0,k right brace; u-> = left brace 0,0,u right brace) in magnetic field (B-> = left brace 0, 0, B right brace), is considered. The quasiclassical approach for this geometry is of no interest, due to the absence of interaction between electromagnetic and acoustic waves. The problem is of interest in strong magnetic field when quantization of the charge carriers energy levels takes place. The quantum oscillations in the sound absorption coefficient, as a function of the magnetic field, are theoretically observed. The experimental study of the quantum oscillations in quasi-two-dimensional conductors makes it possible to solve the inverse problem of determining from experimental data the extrema closed sections of the Fermi surface by a plane p sub z = ...

Chimera states in two-dimensional networks of locally coupled oscillators

Science.gov (United States)

Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.

2018-02-01

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera

Introduction to classical and quantum harmonic oscillators

CERN Document Server

Bloch, Sylvan C

2013-01-01

From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con

Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator

International Nuclear Information System (INIS)

Belendez, Augusto; Pascual, Carolina

2007-01-01

The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A

SU(1,2) invariance in two-dimensional oscillator

Energy Technology Data Exchange (ETDEWEB)

Krivonos, Sergey [Bogoliubov Laboratory of Theoretical Physics,Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Nersessian, Armen [Yerevan State University,1 Alex Manoogian St., Yerevan, 0025 (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)

2017-02-01

Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756, with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written in terms of the oscillator variables.

Interbasis expansions for isotropic harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)

2012-03-12

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.

Phase-space treatment of the driven quantum harmonic oscillator

Indian Academy of Sciences (India)

A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...

Fundamental and Harmonic Oscillations in Neighboring Coronal Loops

Science.gov (United States)

Li, Hongbo; Liu, Yu; Vai Tam, Kuan

2017-06-01

We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.

Eigenstates of the higher power of the annihilation operator of two-parameter deformed harmonic oscillator

International Nuclear Information System (INIS)

Wang Jisuo; Sun Changyong; He Jinyu

1996-01-01

The eigenstates of the higher power of the annihilation operator a qs k (k≥3) of the two-parameter deformed harmonic oscillator are constructed. Their completeness is demonstrated in terms of the qs-integration

On the quantization of a nonlinear oscillator with quasi-harmonic behaviour

International Nuclear Information System (INIS)

Ranada, M.F.; Carinena, J.F.; Satander, M.

2006-01-01

Full text: (author)The quantum version of a non-linear oscillator, depending of a parameter λ, is studied. This λ-dependent system can be considered deformation of the harmonic oscillator in the sense that for λ→0 all the characteristics of the linear oscillator are recovered. This is a problem of quantization of a system with position-dependent mass and with a λ-dependent nonpolynominal rational potential. The quantization problem is solved using existence of a Killing vector, the λ-dependent Schroedinger equation is exactly solved and λ-dependent eigenenergies and eigenfunctions are obtained. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as deformations of the standard Hermite polynomials. In the second part, it is proved the superintegrability of the two-dimensional system

Complex dynamical invariants for two-dimensional complex potentials

Indian Academy of Sciences (India)

Abstract. Complex dynamical invariants are searched out for two-dimensional complex poten- tials using rationalization method within the framework of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. It is found that the cubic oscillator and shifted harmonic oscillator ...

Rabi oscillation between states of a coupled harmonic oscillator

International Nuclear Information System (INIS)

Park, Tae Jun

2003-01-01

Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves

On the connection between the hydrogen atom and the harmonic oscillator: the zero-energy case

International Nuclear Information System (INIS)

Kibler, M.; Negali, T.

1983-09-01

The connection between the three-dimensional hydrogen atom and a four-dimensional harmonic oscillator obtained in previous works, from an hybridization of the infinitesimal Pauli approach to the hydrogen system with the Schwinger approach to spherical and hyperbolical angular momenta, is worked out in the case of the zero-energy point of the hydrogen atom. This leads to the equivalence of the three-dimensional hydrogen problem with a four-dimensional free-particle problem involving a constraint condition. For completeness, the latter results is also derived by using the Kustaanheimo-Stiefel transformation introduced in celestial mechanics. Finally, it is shown how the Lie algebra of SO(4,2) quite naturally arises for the whole spectrum (discrete + continuum + zero-energy point) of the three-dimensional hydrogen atom from the introduction of the constraint condition into the Lie algebra of Sp(8,R) associated to the four-dimensional harmonic oscillator

Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

International Nuclear Information System (INIS)

Nogueira, Pedro H F; Castro, Antonio S de

2016-01-01

The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)

SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÖDINGER

Directory of Open Access Journals (Sweden)

T B Prayitno

2012-02-01

Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master Schrödinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution can’t be normalized.   Keywords : harmonic oscillator, nonlinear Schrödinger.

Harmonically trapped dipolar fermions in a two-dimensional square lattice

DEFF Research Database (Denmark)

Larsen, Anne-Louise G.; Bruun, Georg

2012-01-01

We consider dipolar fermions in a two-dimensional square lattice and a harmonic trapping potential. The anisotropy of the dipolar interaction combined with the lattice leads to transitions between phases with density order of different symmetries. We show that the attractive part of the dipolar...

On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator

International Nuclear Information System (INIS)

Dubois, Daniel M.

2008-01-01

A fundamental mathematical formalism related to the Quantum Potential factor, Q, is presented in this paper. The Schroedinger equation can be transformed to two equations depending on a group velocity and a density of presence of the particle. A factor, in these equations, was called ''Quantum Potential'' by D. Bohm and B. Hiley. In 1999, I demonstrated that this Quantum Potential, Q, can be split in two Quantum Potentials, Q 1 , and Q 2 , for which the relation, Q=Q 1 +Q 2 , holds. These two Quantum Potentials depend on a fundamental new variable, what I called a phase velocity, u, directly related to the probability density of presence of the wave-particle, given by the modulus of the wave function. This paper gives some further developments for explaining the Quantum Potential for oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator. It is shown that the two Quantum Potentials play a central role in the interpretation of quantum mechanics. A breakthrough in the formalism of the Quantum Mechanics could be provoked by the physical properties of these Quantum Potentials. The probability density of presence of the oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator is directly depending on the ratio Q 2 /Q 1 of the two Quantum Potentials. In the general case, the energy of these Gaussian wave packets is not constant, but is oscillating. The energy is given by the sum of the kinetic energy, T, the potential energy, V, and the two Quantum Potentials: E=T+V+Q 1 +Q 2 . For some conditions, given in the paper, the energy can be a constant. The first remarkable result is the fact that the first Quantum Potential, Q 1 , is related to the ground state energy, E 0 , of the Quantum Harmonic Oscillator: Q 1 =h-bar ω/2=E 0 . The second result is related to the property of the second Quantum Potential, Q 2 , which plays the role of an anti-potential, Q 2 =-V(x), where V is the harmonic oscillator potential. This Quantum Potential

Hyperchaotic circuit with damped harmonic oscillators

DEFF Research Database (Denmark)

Lindberg, Erik; Murali, K.; Tamasevicius, A.

2001-01-01

A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...... by means of numerical integration of the appropriate differential equations....

Non-singular spiked harmonic oscillator

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Guardiola, R.

1990-01-01

A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)

Non-unique monopole oscillations of harmonically confined Yukawa systems

Science.gov (United States)

Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael

2008-11-01

Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)

Harmonic oscillator states with integer and non-integer orbital angular momentum

International Nuclear Information System (INIS)

Land, Martin

2011-01-01

We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

Science.gov (United States)

Verreault, René

2017-08-01

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

High-order harmonic generation from a two-dimensional band structure

Science.gov (United States)

Jin, Jian-Zhao; Xiao, Xiang-Ru; Liang, Hao; Wang, Mu-Xue; Chen, Si-Ge; Gong, Qihuang; Peng, Liang-You

2018-04-01

In the past few years, harmonic generation in solids has attracted tremendous attention. Recently, some experiments of two-dimensional (2D) monolayer or few-layer materials have been carried out. These studies demonstrated that harmonic generation in the 2D case shows a strong dependence on the laser's orientation and ellipticity, which calls for a quantitative theoretical interpretation. In this work, we carry out a systematic study on the harmonic generation from a 2D band structure based on a numerical solution to the time-dependent Schrödinger equation. By comparing with the 1D case, we find that the generation dynamics can have a significant difference due to the existence of many crossing points in the 2D band structure. In particular, the higher conduction bands can be excited step by step via these crossing points and the total contribution of the harmonic is given by the mixing of transitions between different clusters of conduction bands to the valence band. We also present the orientation dependence of the harmonic yield on the laser polarization direction.

Infinite-time and finite-time synchronization of coupled harmonic oscillators

International Nuclear Information System (INIS)

Cheng, S; Ji, J C; Zhou, J

2011-01-01

This paper studies the infinite-time and finite-time synchronization of coupled harmonic oscillators with distributed protocol in the scenarios with and without a leader. In the absence of a leader, the convergence conditions and the final trajectories that each harmonic oscillator follows are developed. In the presence of a leader, it is shown that all harmonic oscillators can achieve the trajectory of the leader in finite time. Numerical simulations of six coupled harmonic oscillators are given to show the effects of the interaction function parameter, algebraic connectivity and initial conditions on the convergence time.

Spectral inverse problem for q-deformed harmonic oscillator

Indian Academy of Sciences (India)

The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this ...

An exactly solvable three-dimensional nonlinear quantum oscillator

International Nuclear Information System (INIS)

Schulze-Halberg, A.; Morris, J. R.

2013-01-01

Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states

An exactly solvable three-dimensional nonlinear quantum oscillator

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2013-11-15

Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.

Creation and annihilation operators, symmetry and supersymmetry of the 3D isotropic harmonic oscillator

International Nuclear Information System (INIS)

Mota, R D; Granados, V D; Queijeiro, A; Garcia, J; Guzman, L

2003-01-01

We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

International Nuclear Information System (INIS)

Borzov, V. V.; Damaskinsky, E. V.

2014-01-01

In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators

Poincare' maps of impulsed oscillators and two-dimensional dynamics

International Nuclear Information System (INIS)

Lupini, R.; Lenci, S.; Gardini, L.; Urbino Univ.

1996-01-01

The Poincare' map of one-dimensional linear oscillators subject to periodic, non-linear and time-delayed impulses is shown to reduce to a family of plane maps with possible non-uniqueness of the inverse. By restricting the analysis to a convenient form of the impulse function, a variety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical curves of two-dimensional endomorphisms are used to identify the structure of absorbing areas and their bifurcations

Quantum mechanical treatment of a constrained particle on two dimensional sphere

Energy Technology Data Exchange (ETDEWEB)

Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com; Panahi, H., E-mail: t-panahi@guilan.ac.ir

2016-12-15

In this work, we study the motion of a particle on two dimensional sphere. By writing the Schrodinger equation, we obtain the wave function and energy spectra for three dimensional harmonic oscillator potential plus trigonometric Rosen–Morse non-central potential. By letting three special cases for intertwining operator, we investigate the energy spectra and wave functions for Smorodinsky–Winternitz potential model.

Quantum theory of damped harmonic oscillator | Antia | Global ...

African Journals Online (AJOL)

The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...

Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry

International Nuclear Information System (INIS)

Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.

2008-01-01

We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties

Ginzburg-Landau-Gor close-quote kov theory of magnetic oscillations in a type-II two-dimensional superconductor

International Nuclear Information System (INIS)

Bruun, G.M.; Nicopoulos, V.N.; Johnson, N.F.

1997-01-01

We investigate de Haas endash van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor close-quote kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eighth order against an exact numerical solution of the corresponding Bogoliubov endash de Gennes equations. The perturbation theory is found to describe well the onset of superconductivity close to the transition point H c2 . Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA oscillations below H c2 . Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore, we have investigated the recently debated issue of the possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement. copyright 1997 The American Physical Society

Two dimensional (4,0) supergravity in harmonic superspace. The action and the matter couplings

International Nuclear Information System (INIS)

Lhallabi, T.; Saidi, E.H.

1988-08-01

The superfield formulation of the two dimensional (4,0) supergravity is developed using the harmonic superspace techniques. The different sets of constraints are given and their solutions are expressed in terms of a SU(2) self dual torsion superfield and harmonic prepotentials. The pure auxiliary (4,0) Einstein action generalizing the (2,0) one is written down and the most general (4,0) matter couplings are given. (author). 24 refs

Harmonic oscillator in Snyder space

Indian Academy of Sciences (India)

The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...

Exact solution of a quantum forced time-dependent harmonic oscillator

Science.gov (United States)

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

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Harmonic and Anharmonic Behaviour of a Simple Oscillator

Science.gov (United States)

O'Shea, Michael J.

2009-01-01

We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…

From the harmonic oscillator to the A-D-E classification of conformal models

International Nuclear Information System (INIS)

Itzykson, C.

1988-01-01

Arithmetical aspects of the solution of systems involving dimensional statistical models and conformal field theory. From this perspective, the analysis of the harmonic oscillator, the free particle in a box, the rational billards is effectuated. Moreover, the description of the classification of minimal conformal models and Weiss-Lumino-Witten models, based on the simplest affine algebra is also given. Attempts to interpret and justify the appearance of A-D-E classification of algebra in W-Z-W model are made. Extensions of W-Z-W model, based on SU(N) level one, and the ways to deal with rank two Lie groups, using the arithmetics of quadratic intergers, are described

The relativistic harmonic oscillator reconsidered

International Nuclear Information System (INIS)

Hofsaess, T.

1978-01-01

The bound states of scalar quarks interacting through a scalar harmonic oscillator are investigated. In the presence of this interaction the dressed quark propagator differs substantially from the free one. This leads to a Bethe Salpeter equation which does not allow for any stable bound states of positive mass. (orig.) [de

Harmonic oscillations, chaos and synchronization in systems consisting of Van der Pol oscillator coupled to a linear oscillator

International Nuclear Information System (INIS)

Woafo, P.

1999-12-01

This paper deals with the dynamics of a model describing systems consisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is found that our model shows period doubling and period-m sudden transitions to chaos. Synchronization of two and more systems in their chaotic regime is presented. (author)

Controllability in tunable chains of coupled harmonic oscillators

DEFF Research Database (Denmark)

Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David

2018-01-01

any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can......We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....

Controllability in tunable chains of coupled harmonic oscillators

Science.gov (United States)

Buchmann, L. F.; Mølmer, K.; Petrosyan, D.

2018-04-01

We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N -1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach any desired Gaussian state requires at most 3 N (N -1 )/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides.

Controllability in tunable chains of coupled harmonic oscillators

DEFF Research Database (Denmark)

Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David

2018-01-01

We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....

Comparative analysis of gyrotron backward-wave oscillators operating at different cyclotron harmonics

International Nuclear Information System (INIS)

Yeh, Y.S.; Chang, T.H.; Wu, T.S.

2004-01-01

A comparative analysis between the fundamental and second cyclotron harmonics of gyrotron backward-wave oscillators (gyro-BWOs) is presented. The simulation results reveal that nonlinear field contraction is a common feature for both harmonic interactions. Besides, the electron transit angle, used to characterize the axial modes of the fundamental harmonic TE 11 mode at the start-oscillation conditions, is found to be applicable even for the second harmonic TE 21 mode. Each axial mode of either the fundamental harmonic TE 11 or the second harmonic TE 21 modes is maintained at a constant value of the electron transit angle while changing the operating parameters, such as magnetic field and beam voltage. Extensive numerical calculations are conducted for the start-oscillation currents and tuning properties. Moreover, single-mode operating regimes are suggested where the second harmonic TE 21 gyro-BWO could generate a considerable output power, comparing with the fundamental harmonic TE 11 gyro-BWO

Coulomb crystallites from harmonically confined charged bosons in two dimensions

International Nuclear Information System (INIS)

Mese, A I; Okan, S E; Capuzzi, P; Akdeniz, Z; Tosi, M P

2008-01-01

We exploit rotational-symmetry breaking in the one-body density to examine the formation of structures in systems of N strongly coupled charged bosons with logarithmic repulsions inside isotropic two-dimensional harmonic traps, with N in the range from 2 to 7. The results serve as a map for ordered arrangements of vortices in a trapped Bose-Einstein condensate. Two types of N-body wavefunctions are assumed: (i) a permanent |ψ WM > of N identical Gaussian orbitals centred at variationally determined sites, and (ii) a permanent |ψ SM > of N orthogonal orbitals built from harmonic-oscillator energy eigenstates. With increasing coupling strength, the bosons in the |ψ WM > orbitals localize into polygonal-ringlike crystalline patterns ('Wigner molecules'), whereas the wavefunctions |ψ SM / describe low energy excited states containing delocalized bosons as in supersolid crystallites ('supermolecules'). For N = 2 at strong coupling both states describe a Wigner dimer

An alternative pseudo-harmonics methodology; application to the reactors two-dimensional calculations

International Nuclear Information System (INIS)

Abreu, M.P. de.

1988-01-01

An alternative pseudo-harmonics method for two-dimensional reactor calculations is presented together with some one-energy group results, namely, eigenvalue and flux reconstruction. A brief description of the Standard and Modified versions of the method is presented for critical purposes, i.e., it was intended to discuss the previously developed versions and in some sense to improve the solution of the K-th eigenvalue and flux terms of the corresponding expansions. Intense and localized perturbations, where a significant imbalance between neutron production and destruction rates exists, were simulated. Since convergence in flux and eigenvalue were achieved for all test-cases, there is a tendency to consider the alternative method to be very promising for two-dimensional calculations. (author)

Introduction to Classical and Quantum Harmonic Oscillators

International Nuclear Information System (INIS)

Latal, H

1997-01-01

As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)

On oscillation and nonoscillation of two-dimensional linear differential systems

Czech Academy of Sciences Publication Activity Database

Lomtatidze, A.; Šremr, Jiří

2013-01-01

Roč. 20, č. 3 (2013), s. 573-600 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : two-dimensional system of linear ODE * oscillation * nonoscillation Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0025/gmj-2013-0025.xml?format=INT

On oscillation and nonoscillation of two-dimensional linear differential systems

Czech Academy of Sciences Publication Activity Database

Lomtatidze, A.; Šremr, Jiří

2013-01-01

Roč. 20, č. 3 (2013), s. 573-600 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : two-dimensional system of linear ODE * oscillation * nonoscillation Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0025/gmj-2013-0025. xml ?format=INT

A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space

International Nuclear Information System (INIS)

Bagchi, B.

1995-01-01

In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.))

Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the classical harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)

2011-09-19

We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.

Time-dependent coupled harmonic oscillators: classical and quantum solutions

International Nuclear Information System (INIS)

Macedo, D.X.; Guedes, I.

2014-01-01

In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)

Generating transverse response explicitly from harmonic oscillators

Science.gov (United States)

Yao, Yuan; Tang, Ying; Ao, Ping

2017-10-01

We obtain stochastic dynamics from a system-plus-bath mechanism as an extension of the Caldeira-Leggett (CL) model in the classical regime. An effective magnetic field and response functions with both longitudinal and transverse parts are exactly generated from the bath of harmonic oscillators. The effective magnetic field and transverse response are antisymmetric matrices: the former is explicitly time-independent corresponding to the geometric magnetism, while the latter can have memory. The present model can be reduced to previous representative examples of stochastic dynamics describing nonequilibrium processes. Our results demonstrate that a system coupled with a bath of harmonic oscillators is a general approach to studying stochastic dynamics, and provides a method to experimentally implement an effective magnetic field from coupling to the environment.

Excitation of high numbers harmonics by flows of oscillators in a periodic potential

International Nuclear Information System (INIS)

Buts, V.A.; Marekha, V.I.; Tolstoluzhsky, A.P.

2005-01-01

It is shown that the maximum of radiation spectrum of nonrelativistic oscillators, which move into a periodically inhomogeneous potential, can be in the region of high numbers harmonics. Spectrum of such oscillators radiation becomes similar to the radiation spectrum of relativistic oscillators. The equations, describing the non-linear self-consistent theory of excitations, of high numbers harmonics by ensemble of oscillators are formulated and its numerical analysis is conducted. The numerical analysis has confirmed the capability of radiation of high numbers of harmonics. Such peculiarity of radiation allows t expect of creation of nonrelativistic FEL

Energy spectrum inverse problem of q -deformed harmonic oscillator and WBK approximation

International Nuclear Information System (INIS)

Sang, Nguyen Anh; Thuy, Do Thi Thu; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

2016-01-01

Using the connection between q-deformed harmonic oscillator and Morse-like anharmonic potential we investigate the energy spectrum inverse problem. Consider some energy levels of energy spectrum of q -deformed harmonic oscillator are known, we construct the corresponding Morse-like potential then find out the deform parameter q . The application possibility of using the WKB approximation in the energy spectrum inverse problem was discussed for the cases of parabolic potential (harmonic oscillator), Morse-like potential ( q -deformed harmonic oscillator). so we consider our deformed-three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. For practical problems, we propose the deformed- three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. (paper)

A harmonic oscillator having “volleyball damping”

Science.gov (United States)

Mickens, R. E.; Oyedeji, K.; Rucker, S. A.

2006-05-01

Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

International Nuclear Information System (INIS)

Mota, R D; Xicotencatl, M A; Granados, V D

2004-01-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse

Jordan Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Science.gov (United States)

Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.

2004-02-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Energy Technology Data Exchange (ETDEWEB)

Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)

2004-02-20

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T

2008-01-01

A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient

Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. I. Gaussian-white case

NARCIS (Netherlands)

Steffen, T; Tanimura, Y

The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by

On quantum harmonic oscillator being subjected to absolute

Indian Academy of Sciences (India)

In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing ...

A Look at Damped Harmonic Oscillators through the Phase Plane

Science.gov (United States)

Daneshbod, Yousef; Latulippe, Joe

2011-01-01

Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…

The Aerodynamic Behavior of a Harmonically Oscillating Finite Sweptback Wing in Supersonic Flow

National Research Council Canada - National Science Library

Chang, Chieh-Chien

1951-01-01

By an extension of Evvard's "diaphragm" concept outside the wing tip, the present paper presents two approximate methods for calculating the aerodynamic behavior of harmonically oscillating, sweptback...

Harmonic oscillator on a lattice

International Nuclear Information System (INIS)

Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.

1983-01-01

The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)

Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

International Nuclear Information System (INIS)

Zhang Fulin; Song Ci; Chen Jingling

2009-01-01

The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum L. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed

First, Second Quantization and Q-Deformed Harmonic Oscillator

International Nuclear Information System (INIS)

Van Ngu, Man; Vinh, Ngo Gia; Lan, Nguyen Tri; Viet, Nguyen Ai; Thanh, Luu Thi Kim

2015-01-01

Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed. (paper)

A new analytical approximation to the Duffing-harmonic oscillator

International Nuclear Information System (INIS)

Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.

2009-01-01

In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.

Density Profiles, Energy, and Oscillation Strength of a Quantum Dot in Two Dimensions with a Harmonic Oscillator External Potential using an Orbital-free Energy Functional Based on Thomas–Fermi Theory

Directory of Open Access Journals (Sweden)

Suhufa Alfarisa

2016-03-01

Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free density functional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.

Combined analytical-numerical procedure to solve multigroup spherical harmonics equations in two-dimensional r-z geometry

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1986-01-01

In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)

(1 + 1) Newton-Hooke group for the simple and damped harmonic oscillator

Science.gov (United States)

Brzykcy, Przemysław

2018-03-01

It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillator is indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the orbit method. An in-depth analysis of the coadjoint orbits of the (1 + 1) dimensional Newton-Hooke group is presented. Furthermore, it is argued that the physical interpretation is carried by a specific realisation of the Lie algebra of smooth functions on a phase space rather than by an abstract Lie algebra.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

International Nuclear Information System (INIS)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.

2015-01-01

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

Energy Technology Data Exchange (ETDEWEB)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

2015-11-15

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

Laguerre polynomials by a harmonic oscillator

Science.gov (United States)

Baykal, Melek; Baykal, Ahmet

2014-09-01

The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.

Bispectral analysis of harmonic oscillations measured using beam emission spectroscopy and magnetic probes in CHS

International Nuclear Information System (INIS)

Oishi, Tetsutarou; Yoshinuma, Mikirou; Ida, Katsumi; Akiyama, Tsuyoshi; Minami, Takashi; Nagaoka, Kenichi; Shimizu, Akihiro; Okamura, Shoichi; Kado, Shinichiro

2008-01-01

The coherent MHD oscillation, which consists of the fundamental frequency of several kilohertz and its higher harmonics, (harmonic oscillation: HO) has been observed in Compact Helical System. HO consists of two pairs of harmonic series. One is located in the core region near the ι=0.5 rational surface (denoted as 'HO (core)'), the other is located in the edge region near the ι=1.0 rational surface (denoted as 'HO (edge)'). In the present study, bispectral analysis is applied to the fluctuation data, for which HO is measured by beam emission spectroscopy (BES) and using magnetic probes. The analysis has revealed that fundamental mode of HO in both the magnetic and core density fluctuations have phase correlation with the harmonics including fundamental oscillation, while HO in edge density fluctuation does not have such phase correlation. Mode numbers of HOs are identical for harmonic components having different frequencies, i.e., m/n=-2/1 for HO (core) and m/n=-1/1 for HO (edge). It suggests that the generation of harmonics cannot be interpreted simply as mode coupling because the summation rule for the wavenumber is not satisfied, even though the bicoherence value is significant. The bicoherence value and relative amplitude of higher harmonics correlate with each other, which suggests that bicoherence indicates the degree of distortion of the signals. (author)

A quantum mechanical model of Rabi oscillations between two interacting harmonic oscillator modes and the interconversion of modes in a Penning trap

International Nuclear Information System (INIS)

Kretzschmar, Martin

1999-01-01

When a Penning trap is operated with an additional quadrupole driving field with a frequency that equals a suitable combination (sum or difference) of the frequencies of the fundamental modes of motion (modified cyclotron, magnetron and axial frequency), then a periodic conversion of the participating modes into each other is observed, strongly resembling the Rabi oscillations in a 2-level atom driven by a laser field tuned to the transition frequency. This investigation attempts to understand on a fundamental level how and why the motion of a classical particle in a macroscopic apparatus can be truely analogous to the oscillations of states of quantum mechanical 2-level systems (2-level atom or magnetic resonance). Ion motion in a Penning trap with an additional quadrupole driving field is described in a quantum mechanical frame work. The Heisenberg equations of motion for the creation and annihilation operators of the interacting oscillators have been explicitly solved, the time development operator of the Schroedinger picture has been determined. The driving field provides for two types of intermode interaction: Type I preserves the total number of excitation quanta present in the two interacting modes, the system oscillates between the modes with a frequency corresponding to the Rabi frequency in two-level systems. Type II preserves the difference of the numbers of excitation quanta present in the two interacting modes, it causes the ion motion to become unbounded. The two types of interaction are associated in a natural way with a SU(2) and a SU(1,1) Lie algebra. The three generators of these algebras form a vector operator that we denote as the Bloch vector operator. The Hilbert space decomposes in a natural way into invariant subspaces, finite dimensional in the case of type I interaction (SU(2)-algebra) and infinite dimensional in the case of type II interaction (SU(1,1)-algebra). The physics of the 2-level atom in the laser field can be described in the 2

Sobolev Spaces Associated to the Harmonic Oscillator

Indian Academy of Sciences (India)

We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator H = − + | x | 2 . Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.

Action-angle variables for the harmonic oscillator : ambiguity spin x duplication spin

International Nuclear Information System (INIS)

Oliveira, C.R. de; Malta, C.P.

1983-08-01

The difficulties of obtaining for the harmonic oscillator a well defined unitary transformation to action-angle variables were overcome by M. Moshinsky and T.H. Seligman through the introduction of a spinlike variable (ambiguity spin) from a classical point of view. The difficulty of defining a unitary phase operator for the harmonic oscillator was overcome by Roger G. Newton also through the introduction of a spinlike variable (named duplication spin by us) but within a quantum framework. The relation between the ambiguity spin and the duplication spin by introducing these two types of spins in the canonical transformation to action-angle variables is investigated. Doing this it is possible to obtain both well defined unitary transformation and phase operator. (Author) [pt

Laguerre polynomials by a harmonic oscillator

International Nuclear Information System (INIS)

Baykal, Melek; Baykal, Ahmet

2014-01-01

The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)

Quantum entanglement in coupled harmonic oscillator systems: from micro to macro

International Nuclear Information System (INIS)

Kao, Jhih-Yuan; Chou, Chung-Hsien

2016-01-01

We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number. (paper)

Spin–orbit coupling induced magnetoresistance oscillation in a dc biased two-dimensional electron system

International Nuclear Information System (INIS)

Wang, C M; Lei, X L

2014-01-01

We study dc-current effects on the magnetoresistance oscillation in a two-dimensional electron gas with Rashba spin-orbit coupling, using the balance-equation approach to nonlinear magnetotransport. In the weak current limit the magnetoresistance exhibits periodical Shubnikov-de Haas oscillation with changing Rashba coupling strength for a fixed magnetic field. At finite dc bias, the period of the oscillation halves when the interbranch contribution to resistivity dominates. With further increasing current density, the oscillatory resistivity exhibits phase inversion, i.e., magnetoresistivity minima (maxima) invert to maxima (minima) at certain values of the dc bias, which is due to the current-induced magnetoresistance oscillation. (paper)

Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems

Science.gov (United States)

Abdul-Rahman, Houssam

2018-03-01

For disordered harmonic oscillator systems over the d-dimensional lattice, we consider the problem of finding the bipartite entanglement of the uniform ensemble of the energy eigenstates associated with a particular number of modes. Such an ensemble defines a class of mixed, non-Gaussian entangled states that are labeled, by the energy of the system, in an increasing order. We develop a novel approach to find the exact logarithmic negativity of this class of states. We also prove entanglement bounds and demonstrate that the low energy states follow an area law.

Two new types of solvability of the one-dimensional anharmonic oscillators

International Nuclear Information System (INIS)

Znojil, M.

1989-01-01

In the Schroedinger picture, we propose a new modification of the so-called Hill-determinant technique. It is shown to guarantee a proper matching of the two underlying power series Ψ(x) at x=0. In the Heisenberg picture, an evolution of the same one-dimensional polynomially anharmonic oscillator is considered. A modified Peano-Baker method is applied and shown to define the explicit solutions by recurrences. 11 refs

Time-dependent Hartree approximation and time-dependent harmonic oscillator model

International Nuclear Information System (INIS)

Blaizot, J.P.

1982-01-01

We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)

'quantumness' measures in the decohering harmonic oscillator

Indian Academy of Sciences (India)

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of ...

Universal and Deterministic Manipulation of the Quantum State of Harmonic Oscillators: A Route to Unitary Gates for Fock State Qubits

International Nuclear Information System (INIS)

Santos, Marcelo Franca

2005-01-01

We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state

Dynamical class of a two-dimensional plasmonic Dirac system.

Science.gov (United States)

Silva, Érica de Mello

2015-10-01

A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

Science.gov (United States)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Directory of Open Access Journals (Sweden)

A. M. El-Naggar

2015-11-01

Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.

Self-oscillations of a two-dimensional shear flow with forcing and dissipation

Science.gov (United States)

López Zazueta, A.; Zavala Sansón, L.

2018-04-01

Two-dimensional shear flows continuously forced in the presence of dissipative effects are studied by means of numerical simulations. In contrast with most previous studies, the forcing is confined in a finite region, so the behavior of the system is characterized by the long-term evolution of the global kinetic energy. We consider regimes with 1 limited to develop only one vortical instability by choosing an appropriate width of the forcing band. The most relevant regime is found for Reλ > 36, in which the energy maintains a regular oscillation around a reference value. The flow configuration is an elliptical vortex tilted with respect to the forcing axis, which oscillates steadily also. Second, the flow is allowed to develop two Kelvin-Helmholtz billows and eventually more complicated structures. The regimes of the one-vortex case are observed again, except for Reλ > 135. At these values, the energy oscillates chaotically as the two vortices merge, form dipolar structures, and split again, with irregular periodicity. The self-oscillations are explained as a result of the alternate competition between forcing and dissipation, which is verified by calculating the budget terms in the energy equation. The relevance of the forcing-vs.-dissipation competition is discussed for more general flow systems.

Pisot q-coherent states quantization of the harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)

2013-03-15

We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0oscillator.

On quantum harmonic oscillator being subjected to absolute ...

Indian Academy of Sciences (India)

On quantum harmonic oscillator being subjected to absolute potential state. SWAMI NITYAYOGANANDA. Ramakrishna Mission Ashrama, R.K. Beach, Visakhapatnam 530 003, India. E-mail: nityayogananda@gmail.com. MS received 1 May 2015; accepted 6 May 2016; published online 3 December 2016. Abstract.

The determination of the Dirac density matrix of the d-dimensional harmonic oscillator for an arbitrary number of closed shells

International Nuclear Information System (INIS)

Howard, I.A.; March, N.H.; Nieto, L.M.

2002-01-01

In 1959, March and Young (Nucl. Phys. 12 237) rewrote the equation of motion for the Dirac density matrix γ(x, x 0 ) in terms of sum and difference variables. Here, γ(r-bar, r-bar 0 ) for the d-dimensional isotropic harmonic oscillator for an arbitrary number of closed shells is shown to satisfy, using the variables vertical bar r-bar + r-bar 0 vertical bar/2 and vertical bar r-bar - r-bar 0 vertical bar/2, a generalized partial differential equation embracing the March-Young equation for d=1. As applications, we take in turn the cases d=1, 2, 3 and 4, and obtain both the density matrix γ (r-bar, r-bar 0 ) and the diagonal density ρ(r)=γ(r-bar, r-bar 0 ) vertical bar r-bar 0 =r-bar, this diagonal element already being known to satisfy a third-order linear homogeneous differential equation for d=1 through 3. Some comments are finally made on the d-dimensional kinetic energy density, which is important for first-principles density functional theory in allowing one to bypass one-particle Schroedinger equations (the so-called Slater-Kohn-Sham equations). (author)

Three-dimensional oscillator and Coulomb systems reduced from Kaehler spaces

International Nuclear Information System (INIS)

Nersessian, Armen; Yeranyan, Armen

2004-01-01

We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kaehler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kaehler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid originate. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to a monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is a non-Kaehler one. Finally, we extend these results to the family of Kaehler spaces with conic singularities

Coherent states for the time dependent harmonic oscillator: the step function

International Nuclear Information System (INIS)

Moya-Cessa, Hector; Fernandez Guasti, Manuel

2003-01-01

We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for a continuous treatment that differs from former studies that involve the matching of two time independent solutions at the time when the step occurs

Information cloning of harmonic oscillator coherent states

Indian Academy of Sciences (India)

We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use ...

Mehler's formulae for isotropic harmonic oscillator wave functions and application in the Green function calculus

International Nuclear Information System (INIS)

Caetano Neto, E.S.

1976-01-01

A stationary Green function is calculated for the Schroedinger Hamiltonian of the multidimensional isotropic harmonic oscillator and for physical systems, which may, somehow, have their Hamiltonian reduced to one in the form of a harmonic oscillator, for any dimension [pt

Forced harmonic oscillations of the Euler-Bernoulli beam with resistance forces

Directory of Open Access Journals (Sweden)

Yuriy S. Krutiy

2015-12-01

Full Text Available The important issue in the oscillation theory is the study of resistance impact on oscillatory processes. Unlike the calculations of free oscillations, that reside in determination of natural frequencies and waveshapes and unlike the calculations of forced oscillations far away from resonance, that are performing without reference to friction, the oscillations researches in vicinity of resonance need accounting of friction forces. Special attention is paid to forced transverse fluctuations in beams as an important technical problem for engineering and building. Aim: The aim of the work is constructing of analytical solution of the problem of forced transverse vibrations of a straight rod with constant cross-section, which is under the influence of the harmonic load taking into account external and internal resistances. Materials and Methods: The internal resistance is taken into account using the corrected hypothesis of Kelvin-Voigt which reflects the empirically proven fact about the frequency-independent internal friction in the material. The external friction is also considered as frequency-independent. Results: An analytical solution is built for the differential equation of forced transverse oscillations of a straight rod with constant cross-section which is under the influence of the harmonic load taking into account external and internal resistances. As a result, analytically derived formulae are presented which describe the forced dynamic oscillations and the dynamic internal forces due to the harmonic load applied to the rod thus reducing the problem with any possible fixed ends to the search of unknown integration constants represented in a form of initial parameters.

Three-dimensional analysis of nonlinear plasma oscillation

International Nuclear Information System (INIS)

Miano, G.

1990-01-01

In an underdense plasma a large-amplitude plasma oscillation may be produced by the beating of two external and colinear electromagnetic waves with a frequency difference approximately equal to the plasma frequency - plasma beat wave (PBW) resonant mechanism. The plasma oscillations are driven by the ponderomotive force arising from the beating of the two imposed electromagnetic waves. In this paper two pump electromagnetic waves with arbitrary transverse profiles have been considered. The plasma is described by using the three dimensinal weakly relativistic fluid equations. The nonlinear plasma oscillation dynamics is studied by using the eulerian description, the averaging and the multiple time scale methods. Unlike the linear theory a strong cross field coupling between longitudinal ans transverse electric field components of the plasma oscillation comes out, resulting in a nonlinear phase change and energy transfer between the two components. Unlike the one-dimensional nonlinear theory, the nonlinear frequency shift is caused by relativistic effects as well as by convective effects and electromagnetic field generated from the three dimensional plasma oscillation. The large amplitude plasma oscillation dynamics produced by a bunched relativistic electron beam with arbitrary transverse profile - plasma wave field (PWF) - or by a high power single frequency short electromagnetic pulse with arbitrary transverse profile - electromagnetic plasma wake field (EPWF) - may be described by means of the present theory. (orig.)

Chemical potential of one-dimensional simple harmonic oscillators

International Nuclear Information System (INIS)

Mungan, Carl E

2009-01-01

Expressions for the chemical potential of an Einstein solid, and of ideal Fermi and Bose gases in an external one-dimensional oscillatory trap, are calculated by two different methods and are all found to share the same functional form. These derivations are easier than traditional textbook calculations for an ideal gas in an infinite three-dimensional square well. Furthermore, the results indicate some important features of chemical potential that could promote student learning in an introductory course in statistical mechanics at the undergraduate level.

A non-orthogonal harmonic-oscillator basis for three-body problems

International Nuclear Information System (INIS)

Agrello, D.A.; Aguilera-Navarro, V.C.; Chacon, E.

1979-01-01

A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12 C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author) [pt

On the moment of inertia of a quantum harmonic oscillator

International Nuclear Information System (INIS)

Khamzin, A. A.; Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.

2013-01-01

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.

Maximal Regularity of the Discrete Harmonic Oscillator Equation

Directory of Open Access Journals (Sweden)

Airton Castro

2009-01-01

Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.

Nonlinear analysis of a cross-coupled quadrature harmonic oscillator

DEFF Research Database (Denmark)

Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens

2005-01-01

The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...

A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems

Science.gov (United States)

Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.

2018-05-01

The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

Science.gov (United States)

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Information measures of a deformed harmonic oscillator in a static electric field

Science.gov (United States)

Nascimento, J. P. G.; Ferreira, F. A. P.; Aguiar, V.; Guedes, I.; Costa Filho, Raimundo N.

2018-06-01

The Shannon entropy and the Fischer information are calculated for an harmonic oscillator in the presence of an applied electric field (ε) in a space with metrics given by gxx-1/2 = 1 + γx. For that metric the harmonic oscillator can be mapped into a Morse potential in an Euclidean space. For ε = 0, the ground state energy decreases when γ increases. However, for certain values of ε the energy decrease can be canceled out. The dependence of the uncertainties, the entropy, and the information on the parameters γ and ε are shown.

Third harmonic generation by Bloch-oscillating electrons in a quasioptical array

International Nuclear Information System (INIS)

Ghosh, A.W.; Wanke, M.C.; Allen, S.J.; Wilkins, J.W.

1999-01-01

We compute the third harmonic field generated by Bloch-oscillating electrons in a quasioptical array of superlattices under THz irradiation. The third harmonic power transmitted oscillates with the internal electric field, with nodes associated with Bessel functions in eEd/ℎω. The nonlinear response of the array causes the output power to be a multivalued function of the incident laser power. The output can be optimized by adjusting the frequency of the incident pulse to match one of the Fabry-Pacute erot resonances in the substrate. Within the transmission-line model of the array, the maximum conversion efficiency is 0.1%. copyright 1999 American Institute of Physics

Symmetries and conservation laws of the damped harmonic oscillator

Indian Academy of Sciences (India)

symmetries are expressed in the form of generators. We have studied the ..... For λ = 0, Iβ=1 represents the total energy of the harmonic oscillator with Uβ=1 as the time .... Ind. J. Pure Appl. Phys. 43, 479 (2005); Classical and quantum me-.

Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap

International Nuclear Information System (INIS)

Sowinski, Tomasz; Brewczyk, Miroslaw; Gajda, Mariusz; RzaPzewski, Kazimierz

2010-01-01

We study dynamics of two interacting ultracold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the δ-like potential, we study the time evolution of an initially separable state of two particles. The corresponding time-dependent single-particle density matrix is obtained and diagonalized, and single-particle orbitals are found. This allows us to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled, then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.

Variational and perturbative schemes for a spiked harmonic oscillator

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Estevez, G.A.; Guardiola, R.

1989-01-01

A variational analysis of the spiked harmonic-oscillator Hamiltonian operator -d 2 /dx 2 + x 2 + l(l+1)/x 2 + λ |x| -α , where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schroedinger equation for the linear harmonic-oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provides accurate approximations for the ground-state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large-coupling pertubative-expansion is carried out and the contributions up to fourth order to the ground-state energy are explicitly evaluated. Numerical results are compared for the special case α=5/2. (author) [pt

Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps

Science.gov (United States)

Pendrill, Ann-Marie; Eager, David

2015-01-01

Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…

Coherent states of general time-dependent harmonic oscillator

Indian Academy of Sciences (India)

Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...

Two dimensional code for modeling of high ione cyclotron harmonic fast wave heating and current drive

International Nuclear Information System (INIS)

Grekov, D.; Kasilov, S.; Kernbichler, W.

2016-01-01

A two dimensional numerical code for computation of the electromagnetic field of a fast magnetosonic wave in a tokamak at high harmonics of the ion cyclotron frequency has been developed. The code computes the finite difference solution of Maxwell equations for separate toroidal harmonics making use of the toroidal symmetry of tokamak plasmas. The proper boundary conditions are prescribed at the realistic tokamak vessel. The currents in the RF antenna are specified externally and then used in Ampere law. The main poloidal tokamak magnetic field and the ''kinetic'' part of the dielectric permeability tensor are treated iteratively. The code has been verified against known analytical solutions and first calculations of current drive in the spherical torus are presented.

A simple mechanical model for the isotropic harmonic oscillator

International Nuclear Information System (INIS)

Nita, Gelu M

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels.

Zeta functions for the spectrum of the non-commutative harmonic oscillators

CERN Document Server

Ichinose, T

2004-01-01

This paper investigates the spectral zeta function of the non-commutative harmonic oscillator studied in \\cite{PW1, 2}. It is shown, as one of the basic analytic properties, that the spectral zeta function is extended to a meromorphic function in the whole complex plane with a simple pole at $s=1$, and further that it has a zero at all non-positive even integers, i.e. at $s=0$ and at those negative even integers where the Riemann zeta function has the so-called trivial zeros. As a by-product of the study, both the upper and the lower bounds are also given for the first eigenvalue of the non-commutative harmonic oscillator.

A Generalized Time-Dependent Harmonic Oscillator at Finite Temperature

International Nuclear Information System (INIS)

Majima, H.; Suzuki, A.

2006-01-01

We show how a generalized time-dependent harmonic oscillator (GTHO) is extended to a finite temperature case by using thermo field dynamics (TFD). We derive the general time-dependent annihilation and creation operators for the system, and obtain the time-dependent quasiparticle annihilation and creation operators for the GTHO by using the temperature-dependent Bogoliubov transformation of TFD. We also obtain the thermal state as a two-mode squeezed vacuum state in the time-dependent case as well as in the time-independent case. The general formula is derived to calculate the thermal expectation value of operators

Predicting chaos in memristive oscillator via harmonic balance method.

Science.gov (United States)

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-10-15

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

International Nuclear Information System (INIS)

Chou, Chia-Chun

2016-01-01

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

Replicate periodic windows in the parameter space of driven oscillators

Energy Technology Data Exchange (ETDEWEB)

Medeiros, E.S., E-mail: esm@if.usp.br [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil); Souza, S.L.T. de [Universidade Federal de Sao Joao del-Rei, Campus Alto Paraopeba, Minas Gerais (Brazil); Medrano-T, R.O. [Departamento de Ciencias Exatas e da Terra, Universidade Federal de Sao Paulo, Diadema, Sao Paulo (Brazil); Caldas, I.L. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)

2011-11-15

Highlights: > We apply a weak harmonic perturbation to control chaos in two driven oscillators. > We find replicate periodic windows in the driven oscillator parameter space. > We find that the periodic window replication is associated with the chaos control. - Abstract: In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.

ABC of ladder operators for rationally extended quantum harmonic oscillator systems

Science.gov (United States)

Cariñena, José F.; Plyushchay, Mikhail S.

2017-07-01

The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.

The resonating group method in an harmonic oscillator basis

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.

1987-05-01

The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

Science.gov (United States)

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

Science.gov (United States)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Land-cover separability analysis of MODIS time-series data using a combined simple harmonic oscillator and a mean reverting stochastic process

CSIR Research Space (South Africa)

Grobler, TL

2012-06-01

Full Text Available . The Fourier transform and maximum-likelihood parameter estimation are used to estimate the harmonic and noise parameters of the colored simple harmonic oscillator. Two case studies in South Africa show that reliable class differentiation can be obtained...

Thermal state of the general time-dependent harmonic oscillator

Indian Academy of Sciences (India)

Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator ...

Sticky orbits of a kicked harmonic oscillator

International Nuclear Information System (INIS)

Lowenstein, J H

2005-01-01

We study a Hamiltonian dynamical system consisting of a one-dimensional harmonic oscillator kicked impulsively in 4:1 resonance with its natural frequency, with the amplitude of the kick proportional to a sawtooth function of position. For special values of the coupling parameter, the dynamical map W relating the phase-space coordinates just prior to each kick acts locally as a piecewise affine map K on a square with rational rotation number p/q. For λ = 2cos2πp/q a quadratic irrational, a recursive return-map structure allows us to completely characterize the orbits of the map K. The aperiodic orbits of this system are sticky in the sense that they spend all of their time wandering pseudo-chaotically (with strictly zero Lyapunov exponent) in the vicinity of self-similar archipelagos of periodic islands. The same recursive structure used locally for K gives us the asymptotic scaling features of long orbits of W on the infinite plane. For some coupling parameters the orbits remain bounded, but for others the distance from the origin increases as a logarithm or power of the time. In the latter case, we find examples of sub-diffusive, diffusive, super-diffusive, and ballistic power-law behavior

Three-dimensional harmonic control of a nuclear reactor

International Nuclear Information System (INIS)

Potapenko, P.T.

1989-01-01

Algorithms for neutron flux control based on harmonic three-dimensional core are considered. The essence of the considered approach includes determination of harmonics amplitudes by signals self-powered detectors placed in reactor channels and reconstruction of neutron field distribution over the reactor core volume using the data obtained. Neutron field harmonic control is shown to be reduced to independent measurement and calculation of height harmonics in channels using techniques developed for channel power control

Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)

2011-02-11

The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)

Coherent harmonic production using a two-section undulator FEL

Energy Technology Data Exchange (ETDEWEB)

Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others

1995-12-31

We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.

Density functional theory investigation of two-dimensional dipolar fermions in a harmonic trap

International Nuclear Information System (INIS)

Ustunel, Hande; Abedinpour, Saeed H; Tanatar, B

2014-01-01

We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems

New construction of coherent states for generalized harmonic oscillators

International Nuclear Information System (INIS)

El Baz, M.; Hassouni, Y.; Madouri, F.

2001-08-01

A dynamical algebra A q , englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type A q is discussed. The construction following this method is carried out for the special case. (author)

The Wigner distribution function for the one-dimensional parabose oscillator

International Nuclear Information System (INIS)

Jafarov, E; Lievens, S; Jeugt, J Van der

2008-01-01

In the beginning of the 1950s, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the so-called Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. In this paper, we consider which definition for such a distribution function could be used in the case of non-canonical quantum mechanics. We then explicitly compute two different expressions for this distribution function for the case of the parabose oscillator. Both expressions turn out to be multiple sums involving (generalized) Laguerre polynomials. Plots then show that the Wigner distribution function for the ground state of the parabose oscillator is similar in behaviour to the Wigner distribution function of the first excited state of the canonical quantum oscillator

Hall field-induced magnetoresistance oscillations of a two-dimensional electron system

International Nuclear Information System (INIS)

Kunold, A.; Torres, M.

2008-01-01

We develop a model of the nonlinear response to a dc electrical current of a two-dimensional electron system (2DES) placed on a magnetic field. Based on the exact solution to the Schroedinger equation in arbitrarily strong electric and magnetic fields, and separating the relative and guiding center coordinates, a Kubo-like formula for the current is worked out as a response to the impurity scattering. Self-consistent expressions determine the longitudinal and Hall components of the electric field in terms of the dc current. The differential resistivity displays strong Hall field-induced oscillations, in agreement with the main features of the phenomenon observed in recent experiments

The forced harmonic oscillator with damping and thermal effects

International Nuclear Information System (INIS)

Menezes Franca, H. de; Thomaz, M.T.

1984-01-01

Nonperturbative quantum mechanical solutions of the forced harmonic oscillator with radiation reaction damping are obtained from previous analysis based on Stochastic Electrodynamics. The transition to excited states is shown to be to coherent states which follow the classical trajectory. The quantum Wigner distribution in phase space is constructed. All the results are extended to finite temperatures. (Author) [pt

Flipping-shuttle oscillations of bright one- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with Rabi mixing

Science.gov (United States)

Sakaguchi, Hidetsugu; Malomed, Boris A.

2017-10-01

We analyze the possibility of macroscopic quantum effects in the form of coupled structural oscillations and shuttle motion of bright two-component spin-orbit-coupled striped (one-dimensional, 1D) and semivortex (two-dimensional, 2D) matter-wave solitons, under the action of linear mixing (Rabi coupling) between the components. In 1D, the intrinsic oscillations manifest themselves as flippings between spatially even and odd components of striped solitons, while in 2D the system features periodic transitions between zero-vorticity and vortical components of semivortex solitons. The consideration is performed by means of a combination of analytical and numerical methods.

Study of the phase delay in the amplitude-modulated harmonic oscillator

International Nuclear Information System (INIS)

Krupska, Aldona; Krupski, Marcin

2003-01-01

The delayed response of a damped harmonic oscillator (RLC circuit) to a slow periodic disturbance is presented. This communication is supplementary to the paper published recently (Krupska et al 2001 Eur. J. Phys. 22 133-8)

Kraus representation of a damped harmonic oscillator and its application

International Nuclear Information System (INIS)

Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki

2004-01-01

By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity

Oscillations of the positive column plasma due to ionization wave propagation and two-dimensional structure of striations

International Nuclear Information System (INIS)

Golubovskii, Yu B; Kozakov, R V; Wilke, C; Behnke, J; Nekutchaev, V O

2004-01-01

Time and space resolved measurements of the plasma potential in axial and radial directions in S- and P-striations in neon are performed. The measurements in different radial positions were carried out with high spatial resolution by means of simultaneous displacement of electrodes relative to the stationary probe. The plasma potential was found to be a superposition of the potentials of ionization wave and plasma oscillations relative to the electrodes. A method of decomposition of the measured spatio-temporal structure of the potential in components associated with the plasma oscillations and ionization wave propagation is proposed. A biorthogonal decomposition of the spatio-temporal structure of the potential is performed. A comparison of the decomposition results obtained by the two methods is made. The experiments revealed a two-dimensional structure of the potential field in an ionization wave. Qualitative discussions of the reasons for the occurrence of this two-dimensional structure are presented based on the analysis of the kinetic equation and the equation for the potential

A study on boiling water reactor regional stability from the viewpoint of higher harmonics

International Nuclear Information System (INIS)

Takeuchi, Yutaka; Takigawa, Yukio; Uematsu, Hitoshi

1994-01-01

A quantitative study on a mechanism for boiling water reactor regional stability has been carried out from the viewpoint of higher harmonics. In the mechanism, the gain decrease in the void-to-power transfer function can be explained by the higher harmonics mode subcriticality. It is shown that the thermal-hydraulic feedback effect can compensate for the gain decrease, and regional oscillation can be sustained that way. For quantitative evaluations, a three-dimensional higher harmonics analysis model has been developed. The results show that the first azimuthal harmonics subcriticality has a relatively small value under a regionally unstable condition. Comparing the subcriticality and the steady-state power distribution, it is shown that the distribution exists whose first azimuthal harmonics subcriticality takes a small value. A method of decomposition for the oscillated power responses into the harmonics modes is presented. The results show that the corewide oscillation power response consists almost entirely of the fundamental mode, and the regional oscillation power response consists almost entirely of the first azimuthal harmonics mode. This indicates that regional oscillation is a phenomenon in which the first azimuthal harmonics mode oscillates on the basis of the fundamental mode

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

KAUST Repository

Kilpatrick, Zachary P.

2009-10-29

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave. © Springer Science + Business Media, LLC 2009.

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

KAUST Repository

Kilpatrick, Zachary P.; Bressloff, Paul C.

2009-01-01

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave. © Springer Science + Business Media, LLC 2009.

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)

2006-09-22

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

International Nuclear Information System (INIS)

Guasti, Manuel Fernandez

2006-01-01

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system

A quantum harmonic oscillator and strong chaos

International Nuclear Information System (INIS)

Oprocha, Piotr

2006-01-01

It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

International Nuclear Information System (INIS)

Morales, J.; Ovando, G.; Pena, J. J.

2010-01-01

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

A method of solving simple harmonic oscillator Schroedinger equation

Science.gov (United States)

Maury, Juan Carlos F.

1995-01-01

A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

Science.gov (United States)

López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.

2012-08-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

International Nuclear Information System (INIS)

López-Ruiz, F F; Guerrero, J; Aldaya, V; Cossío, F

2012-01-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

Initial conditions and robust Newton-Raphson for harmonic balance analysis of free-running oscillators

NARCIS (Netherlands)

Virtanen, J.E.; Maten, ter E.J.W.; Beelen, T.G.J.; Honkala, M.; Hulkkonen, M.

2011-01-01

Poor initial conditions for Harmonic Balance (HB) analysis of freerunning oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for

Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes

Science.gov (United States)

Takahashi, Daisuke A.; Ohashi, Keisuke; Fujimori, Toshiaki; Nitta, Muneto

2017-08-01

Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonic trap are known to possess a hidden 2D Schrödinger symmetry, that is, the Schrödinger symmetry modified by a trapping potential. Spontaneous breaking of this symmetry gives rise to a breathing motion of the BEC, whose oscillation frequency is robustly determined by the strength of the harmonic trap. In this paper, we demonstrate that the concept of the 2D Schrödinger symmetry can be applied to predict the nature of three-dimensional (3D) collective modes propagating along a condensate confined in an elongated trap. We find three kinds of collective modes whose existence is robustly ensured by the Schrödinger symmetry, which are physically interpreted as one breather mode and two Kelvin-ripple complex modes, i.e., composite modes in which the vortex core and the condensate surface oscillate interactively. We provide analytical expressions for the dispersion relations (energy-momentum relation) of these modes using the Bogoliubov theory [D. A. Takahashi and M. Nitta, Ann. Phys. 354, 101 (2015), 10.1016/j.aop.2014.12.009]. Furthermore, we point out that these modes can be interpreted as "quasi-massive-Nambu-Goldstone (NG) modes", that is, they have the properties of both quasi-NG and massive NG modes: quasi-NG modes appear when a symmetry of a part of a Lagrangian, which is not a symmetry of a full Lagrangian, is spontaneously broken, while massive NG modes appear when a modified symmetry is spontaneously broken.

Phase-space treatment of the driven quantum harmonic oscillator

Indian Academy of Sciences (India)

2017-02-22

Feb 22, 2017 ... i.e., ρ(θ,q ,p |q,p,t) is a measure of the interference effects associated ... an oscillating electric field, when the initial state is cho- sen as a .... The conclusive effect is that. A±(q,p,t) ...... wave functions ±(q,p,t) stem from the time depen- dence of ..... define a two-dimensional cell in phase space, which is centred ...

Initial conditions and robust Newton-Raphson for harmonic balance analysis of free-running oscillators

NARCIS (Netherlands)

Virtanen, J.E.; Maten, ter E.J.W.; Honkala, M.; Hulkkonen, M.; Günther, M.; Bartel, A.; Brunk, M.; Schoeps, S.; Striebel, M.

2012-01-01

Poor initial conditions for Harmonic Balance (HB) analysis of free-running oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for

Quantum harmonic oscillators with wave functions having a fixed logarithmic derivative at the equilibrium position

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Ley Koo, E.

The exact solution of the Schrodinger equation for the systems and the boundary condition stated in the title is constructed. The familiar cases of the ordinary harmonic oscillator and the half oscillator are immediately identified. The connection with the double oscillator is also established and is helpful to understand the energy spectrum of the latter. Similar connections can be used to study other partial oscillators. (Author) [pt

Two-dimensional time dependent Riemann solvers for neutron transport

International Nuclear Information System (INIS)

Brunner, Thomas A.; Holloway, James Paul

2005-01-01

A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem

Surface harmonics method for two-dimensional time-dependent neutron transport problems of square-lattice nuclear reactors

Energy Technology Data Exchange (ETDEWEB)

Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A. [National Research Centre Kurchatov Institute, Kurchatov Sq. 1, Moscow (Russian Federation)

2013-07-01

Time-dependent equations of the Surface Harmonics Method (SHM) have been derived from the time-dependent neutron transport equation with explicit representation of delayed neutrons for solving the two-dimensional time-dependent problems. These equations have been realized in the SUHAM-TD code. The TWIGL benchmark problem has been used for verification of the SUHAM-TD code. The results of the study showed that computational costs required to achieve necessary accuracy of the solution can be an order of magnitude less than with the use of the conventional finite difference method (FDM). (authors)

A two-center-oscillator-basis as an alternative set for heavy ion processes

International Nuclear Information System (INIS)

Tornow, V.; Reinhard, P.G.; Drechsel, D.

1977-01-01

The two-center-oscillator-basis, which is constructed from harmonic oscillator wave functions developing about two different centers, suffers from numerical problems at small center separations due to the overcompleteness of the set. In order to overcome these problems we admix higer oscillator wave functions before the orthogonalization, or antisymmetrization resp. This yields a numerically stable basis set at each center separation. The results obtained for the potential energy suface are comparable with the results of more elaborate models. (orig.) [de

Quantization of a free particle interacting linearly with a harmonic oscillator

International Nuclear Information System (INIS)

Mainiero, Thomas; Porter, Mason A.

2007-01-01

We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic

Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

International Nuclear Information System (INIS)

Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.

2009-01-01

The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed

From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry

Energy Technology Data Exchange (ETDEWEB)

Latini, D., E-mail: latini@fis.uniroma3.it [Department of Mathematics and Physics and INFN, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy); Riglioni, D. [Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy)

2016-10-14

The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed. - Highlights: • We construct a discrete quantum version of the harmonic oscillator. • We solve the spectral problem on the lattice. • We introduce the coalgebra symmetry in real discrete Quantum Mechanics (rdQM). • The coalgebra is used to extend the system to higher dimensions preserving its superintegrability. • We explicitly write down a discrete version of both the angular momentum and the Demkov–Fradkin Tensor.

Complex-potential description of the damped harmonic oscillator

International Nuclear Information System (INIS)

Exner, P.

1981-01-01

Multidimensional damped harmonic oscillator is treated by means of a non-selfadjoint Hamiltonian with complex potential. The latter is chosen as V(x)=xx(A-iW)x with positive matrices A, W, By a perturbation-theory argument, the corresponding Hamiltonian H=-1/2Δ+V with the natural domain is shown to be closed and such that Vsub(t)=exp(-iHt) is a continuous contractive semigroup. Explicit integral-operator form of Vsub(t) is found by use of Lie-Trotter formula [ru

On the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential

Czech Academy of Sciences Publication Activity Database

Novák, Radek

2015-01-01

Roč. 54, č. 11 (2015), s. 4142-4153 ISSN 0020-7748 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : pseudospectrum * harmonic oscillator * imaginary qubic potential * PT-symmetry * semiclassical method Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015

Modelling of oscillations in two-dimensional echo-spectra of the Fenna-Matthews-Olson complex

International Nuclear Information System (INIS)

Hein, Birgit; Kreisbeck, Christoph; Kramer, Tobias; Rodríguez, Mirta

2012-01-01

Recent experimental observations of time-dependent beatings in the two-dimensional echo-spectra of light-harvesting complexes at ambient temperatures have opened up the question of whether coherence and wave-like behaviour play a significant role in photosynthesis. We carry out a numerical study of the absorption and echo-spectra of the Fenna-Matthews-Olson (FMO) complex in Chlorobium tepidum and analyse the requirements in the theoretical model needed to reproduce beatings in the calculated spectra. The energy transfer in the FMO pigment-protein complex is theoretically described by an exciton Hamiltonian coupled to a phonon bath which accounts for the pigments' electronic and vibrational excitations, respectively. We use the hierarchical equations of motions method to treat the strong couplings in a non-perturbative way. We show that the oscillations in the two-dimensional echo-spectra persist in the presence of thermal noise and static disorder. (paper)

Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation

Science.gov (United States)

Cardoso, Wesley B.; Salasnich, Luca; Malomed, Boris A.

2017-05-01

We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self-focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad stability areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

Bose gases in one-dimensional harmonic trap

Indian Academy of Sciences (India)

dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in ...

Coupled harmonic oscillators and their quantum entanglement

Science.gov (United States)

Makarov, Dmitry N.

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis.

Science.gov (United States)

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2017-03-01

In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.

Use of an untuned cavity for absolute power measurements of the harmonics above 100 GHz from an IMPATT oscillator

Science.gov (United States)

Llewellyn-Jones, D. T.; Knight, R. J.; Gebbie, H. A.

1980-07-01

A new technique of measuring absolute power exploiting an untuned cavity and Fourier spectroscopy has been used to examine the power spectrum of the harmonics and other overtones produced by a 95 GHz IMPATT oscillator. The conditions which favor the production of a rich harmonic spectrum are not those which maximize the fundamental power. Under some conditions of mismatch at the fundamental frequency it is possible to produce over 200 microW of harmonic power in the 100-200 GHz region comparable with the fundamental power from the oscillator.

On the effects of a screw dislocation and a linear potential on the harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Bueno, M.J.; Furtado, C., E-mail: furtado@fisica.ufpb.br; Bakke, K., E-mail: kbakke@fisica.ufpb.br

2016-09-01

Quantum effects on the harmonic oscillator due to the presence of a linear scalar potential and a screw dislocation are investigated. By searching for bound states solutions, it is shown that an Aharonov-Bohm-type effect for bound states and a restriction of the values of the angular frequency of the harmonic oscillator can be obtained, where the allowed values are determined by the topology of the screw dislocation and the quantum numbers associated with the radial modes and the angular momentum. As particular cases, the angular frequency and the energy levels associated with the ground state and the first excited state of the system are obtained.

An easy trick to a periodic solution of relativistic harmonic oscillator

Directory of Open Access Journals (Sweden)

Jafar Biazar

2014-04-01

Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.

Microwave-Induced Magneto-Oscillations and Signatures of Zero-Resistance States in Phonon-Drag Voltage in Two-Dimensional Electron Systems.

Science.gov (United States)

Levin, A D; Momtaz, Z S; Gusev, G M; Raichev, O E; Bakarov, A K

2015-11-13

We observe the phonon-drag voltage oscillations correlating with the resistance oscillations under microwave irradiation in a two-dimensional electron gas in perpendicular magnetic field. This phenomenon is explained by the influence of dissipative resistivity modified by microwaves on the phonon-drag voltage perpendicular to the phonon flux. When the lowest-order resistance minima evolve into zero-resistance states, the phonon-drag voltage demonstrates sharp features suggesting that current domains associated with these states can exist in the absence of external dc driving.

Schwinger's formula and the partition function for the bosonic and fermionic harmonic oscillators

International Nuclear Information System (INIS)

Albuquerque, L.C. de; Farina, C.; Rabello, S.J.

1994-01-01

We use Schwinger's formula, introduced by himself in the early fifties to compute effective actions for Qed, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic oscillators. (author)

Origin of Hund's multiplicity rule in quasi-two-dimensional two-electron quantum dots

International Nuclear Information System (INIS)

Sako, Tokuei; Paldus, Josef; Diercksen, Geerd H. F.

2010-01-01

The origin of Hund's multiplicity rules has been studied for a system of two electrons confined by a quasi-two-dimensional harmonic-oscillator potential by relying on a full configuration interaction wave function and Cartesian anisotropic Gaussian basis sets. In terms of appropriate normal-mode coordinates the wave function factors into a product of the center-of-mass and the internal components. The 1 Π u singlet state and the 3 Π u triplet state represent the energetically lowest pair of states to which Hund's multiplicity rule applies. They are shown to involve excitations into different degrees of freedom, namely, into the center-of-mass angular mode and the internal angular mode for the singlet and triplet states, respectively. The presence of an angular nodal line in the internal space allows then the triplet state to avoid the singularity in the electron-electron interaction potential, leading to the energy lowering of the triplet state relative to its counterpart singlet state.

Optimal control of a harmonic oscillator: Economic interpretations

Science.gov (United States)

Janová, Jitka; Hampel, David

2013-10-01

Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Wang, Jie

2015-01-01

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Wang, Jie, E-mail: wangjie@iun.edu [Department of Computer Information Systems, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2015-07-15

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.

The generation of two-dimensional vortices by transverse oscillation of a soap film

International Nuclear Information System (INIS)

Afenchenko, V.O.; Ezersky, A.B.; Kiyashko, S.V.; Rabinovich, M.I.; Weidman, P.D.

1998-01-01

An experimental investigation of the dynamics of horizontal soap films stretched over circular or square boundaries undergoing periodic transverse oscillations at frequencies in the range 20 - 200 Hz is reported. Concomitant with modes of transverse flexural oscillations, it was observed that two-dimensional vortices in the plane of the film are excited. The vortices may be either (i) large, scaling with the size of the cavity or (ii) small, localized at a wavelength or half-wavelength of the membrane modes. In the experiments a stable generation of one, two, hor-ellipsis, ten pairs of counter-rotating vortices were observed in finite regions of amplitude-frequency parameter space. The circulation strength of vortices in a given vortex pattern increases with increasing external forcing and with decreasing soap film thickness. A theoretical model based on the wave-boundary interaction of excited Marangoni waves reveals a vorticity generation mechanism active in vibrating soap films. This model shows that vorticity is generated throughout the entire liquid volume by viscous diffusion, and qualitatively reproduces many steady vortex patterns observed in the experiment. However, the model cannot explain the existence of the sometimes intense vortices observed far from the film boundary that do not appear to be generated by diffusive processes. copyright 1998 American Institute of Physics

Many-dimensional anisotropic anharmonic oscillator

International Nuclear Information System (INIS)

Turbiner, A.V.

1987-01-01

Precision calculation of energies of several first states at d=2 and first 17 states at d=3 has been performed within the framework of a unique method based on ''nonlinearization'' method for d-dimension anisotropic an harmonic oscillator. Spectrum behaviour within the limit d → ∞ has been investigated and problems of the given approach accuracy have been studied. For the first time properties of nodal surfaces of the given task have been investigated. Routine perturbation theory in degrees of a perturbation parameter has been constructed for several first states

The optimal performance of a quantum refrigeration cycle working with harmonic oscillators

International Nuclear Information System (INIS)

Lin Bihong; Chen Jincan; Hua Ben

2003-01-01

The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily

Coherent control of third-harmonic-generation by a waveform-controlled two-colour laser field

International Nuclear Information System (INIS)

Chen, W-J; Chen, W-F; Pan, C-L; Lin, R-Y; Lee, C-K

2013-01-01

We investigate generation of the third harmonic (TH; λ = 355 nm) signal by two-colour excitation (λ = 1064 nm and its second harmonic, λ = 532 nm) in argon gas, with emphasis on the influence of relative phases and intensities of the two-colour pump on the third-order nonlinear frequency conversion process. Perturbative nonlinear optics predicts that the TH signal will oscillate periodically with the relative phases of the two-colour driving laser fields due to the interference of TH signals from a direct third-harmonic-generation (THG) channel and a four-wave mixing (FWM) channel. For the first time, we show unequivocal experimental evidence of this effect. A modulation level as high as 0.35 is achieved by waveform control of the two-colour laser field. The modulation also offers a promising way to retrieve the relative phase value of the two-colour laser field. (letter)

Free harmonic oscillators, Jack polynomials, and Calogero-Sutherland systems

International Nuclear Information System (INIS)

Gurappa, N.; Panigrahi, Prasanta K.

2000-01-01

The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous nonsymmetric eigenfunctions of the A N-1 Cherednik operators, from which the eigenfunctions of the CSM and SM are constructed, and the monomials. This construction allows us to simultaneously diagonalize both CSM and SM (after gauging away the Hamiltonians by suitable measures) and also enables us to write down a harmonic oscillator algebra involving the Cherednik operators, which yields the raising and lowering operators for both of these models. The connections of the CSM with free oscillators and the SM with free particles on a circle are established in a novel way. We also point out the subtle differences between the excitations of the CSM and the SM

An analogue of the Berry phase for simple harmonic oscillators

Science.gov (United States)

Suslov, S. K.

2013-03-01

We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.

Oscillation mode transformation of edge magnetoplasmons in two-dimensional electron system on liquid-helium surface

International Nuclear Information System (INIS)

Yamanaka, Shuji; Yayama, Hideki; Arai, Toshikazau; Anju Sawada, Anju; Fukuda, Akira

2013-01-01

We measured the resonance spectra of edge magnetoplasmon (EMP) oscillations in a two-dimensional (2D) electron system located on a liquid-helium surface below 1.1 K. Systematic measurements of the resonance frequency and the damping rate as a function of the lateral confinement electric field strength shows clear evidence of the oscillation mode transformation. A pronounced change corresponding to the mode transformation was observed in the damping rate. When 2D electrons are confined in a strong lateral electric field, the damping is weak. As the lateral confinement electric field is reduced below a certain threshold value, an abrupt enhancement of the damping rate is observed. We hypothesize that the weak damping mode in the strong lateral confinement electric field is the compressive density oscillation of the electrons near the edge (conventional EMP) and the strong damping mode in the weak confinement field is the coupled mode of conventional EMP and the boundary displacement wave (BDW). The observation of the strong damping in the BDW-EMP coupled mode is a manifestation of the nearly incompressible feature of strongly interacting classical electrons, which agrees with earlier theoretical predictions.

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

International Nuclear Information System (INIS)

Chae, Jongchul; Litvinenko, Yuri E.

2017-01-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D 2 and H α lines.

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

Energy Technology Data Exchange (ETDEWEB)

Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)

2017-08-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.

Stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable duffing oscillator and bifurcation of moment equation

International Nuclear Information System (INIS)

Zhang Guangjun; Xu Jianxue; Wang Jue; Yue Zhifeng; Zou Hailin

2009-01-01

In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.

Mechanism of equivalent electric dipole oscillation for high-order harmonic generation from grating-structured solid-surface by femtosecond laser pulse

Energy Technology Data Exchange (ETDEWEB)

Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn

2017-07-12

Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.

West Coast Swing Dancing as a Driven Harmonic Oscillator Model

Science.gov (United States)

Ferrara, Davon; Holzer, Marie; Kyere, Shirley

The study of physics in sports not only provides valuable insight for improved athletic performance and injury prevention, but offers undergraduate students an opportunity to engage in both short- and long-term research efforts. In this project, conducted by two non-physics majors, we hypothesized that a driven harmonic oscillator model can be used to better understand the interaction between two west coast swing dancers since the stiffness of the physical connection between dance partners is a known factor in the dynamics of the dance. The hypothesis was tested by video analysis of two dancers performing a west coast swing basic, the sugar push, while changing the stiffness of the physical connection. The difference in stiffness of the connection from the ideal was estimated by the leader; the position with time data from the video was used to measure changes in the amplitude and phase difference between the leader and follower. While several aspects of our results agree with the proposed model, some key characteristics do not, possibly due to the follower relying on visual leads. Corresponding author and principal investigator.

The Harmonic Oscillator–A Simplified Approach

Directory of Open Access Journals (Sweden)

L. R. Ganesan

2008-01-01

Full Text Available Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator method etc. A method which is much shorter, mathematically simpler is presented here.

Harmonically excited orbital variations

International Nuclear Information System (INIS)

Morgan, T.

1985-01-01

Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs

Bateman's dual system revisited: quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator

International Nuclear Information System (INIS)

Blasone, Massimo; Jizba, Petr

2004-01-01

By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a system are constructed and discussed entirely in the framework of the classical theory. The corresponding geometric (Pancharatnam) phase is calculated and found to be directly related to the ground-state energy of the 1D linear harmonic oscillator to which the 2D system reduces under appropriate constraint

Two-dimensional analysis of motion artifacts, including flow effects

International Nuclear Information System (INIS)

Litt, A.M.; Brody, A.S.; Spangler, R.A.; Scott, P.D.

1990-01-01

The effects of motion on magnetic resonance images have been theoretically analyzed for the case of a point-like object in simple harmonic motion and for other one-dimensional trajectories. The authors of this paper extend this analysis to a generalized two-dimensional magnetization with an arbitrary motion trajectory. The authors provide specific solutions for the clinically relevant cases of the cross-sections of cylindrical objects in the body, such as the aorta, which has a roughly one-dimensional, simple harmonic motion during respiration. By extending the solution to include inhomogeneous magnetizations, the authors present a model which allows the effects of motion artifacts and flow artifacts to be analyzed simultaneously

About the functions of the Wigner distribution for the q-deformed harmonic oscillator model

International Nuclear Information System (INIS)

Atakishiev, N.M.; Nagiev, S.M.; Djafarov, E.I.; Imanov, R.M.

2005-01-01

Full text : A q-deformed model of the linear harmonic oscillator in the Wigner phase-space is studied. It was derived an explicit expression for the Wigner probability distribution function, as well as the Wigner distribution function of a thermodynamic equilibrium for this model

Quantum energy teleportation with a linear harmonic chain

International Nuclear Information System (INIS)

Nambu, Yasusada; Hotta, Masahiro

2010-01-01

A protocol of quantum energy teleportation is proposed for a one-dimensional harmonic chain. A coherent-state positive operator-valued measure (POVM) measurement is performed on coupled oscillators of the chain in the ground state accompanied by energy infusion to the system. This measurement consumes a part of the ground-state entanglement. Depending on the measurement result, a displacement operation is performed on a distant oscillator accompanied by energy extraction from the zero-point fluctuation of the oscillator. We find that the amount of consumed entanglement is bounded from below by a positive value that is proportional to the amount of teleported energy.

Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

Science.gov (United States)

Osherovich, V. A.; Fainberg, J.

2018-01-01

We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

Harmonic uniflow engine

Science.gov (United States)

Bennett, Charles L.

2016-03-22

A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. When released, the inlet valve head undergoes a single oscillation past the equilibrium position to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.

Two-dimensional electron states bound to an off-plane donor in a magnetic field

International Nuclear Information System (INIS)

Bruno-Alfonso, A; Candido, L; Hai, G-Q

2010-01-01

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

Quantum infinite square well with an oscillating wall

International Nuclear Information System (INIS)

Glasser, M.L.; Mateo, J.; Negro, J.; Nieto, L.M.

2009-01-01

A linear matrix equation is considered for determining the time dependent wave function for a particle in a one-dimensional infinite square well having one moving wall. By a truncation approximation, whose validity is checked in the exactly solvable case of a linearly contracting wall, we examine the cases of a simple harmonically oscillating wall and a non-harmonically oscillating wall for which the defining parameters can be varied. For the latter case, we examine in closer detail the dependence on the frequency changes, and we find three regimes: an adiabatic behabiour for low frequencies, a periodic one for high frequencies, and a chaotic behaviour for an intermediate range of frequencies.

Higher dimensional models of cross-coupled oscillators and application to design

KAUST Repository

Elwakil, Ahmed S.; Salama, Khaled N.

2010-01-01

We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.

Higher dimensional models of cross-coupled oscillators and application to design

KAUST Repository

Elwakil, Ahmed S.

2010-06-01

We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.

Elementary derivation of the quantum propagator for the harmonic oscillator

Science.gov (United States)

Shao, Jiushu

2016-10-01

Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.

Spontaneous decoherence of coupled harmonic oscillators confined in a ring

Science.gov (United States)

Gong, ZhiRui; Zhang, ZhenWei; Xu, DaZhi; Zhao, Nan; Sun, ChangPu

2018-04-01

We study the spontaneous decoherence of coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry-breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the gauge couplings between the center-of-mass and the relative degrees of freedoms, which actually originate from the symmetries of the ring geometry and the corresponding nontrivial boundary conditions. In particular, such spontaneous decoherence does not occur at all at the thermodynamic limit because the nontrivial boundary conditions become the trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has a chance for its quantum properties to degrade even without applying an external symmetry-breaking field or surrounding environment.

The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states

Directory of Open Access Journals (Sweden)

A Rabeie and

2015-01-01

Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation

Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap

DEFF Research Database (Denmark)

Salami Dehkharghani, Amin; Bellotti, Filipe Furlan; Zinner, Nikolaj Thomas

2017-01-01

are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using...... a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different...

Improved time-dependent harmonic oscillator method for vibrationally inelastic collisions

International Nuclear Information System (INIS)

DePristo, A.E.

1985-01-01

A quantal solution to vibrationally inelastic collisions is presented based upon a linear expansion of the interaction potential around the time-dependent classical positions of all translational and vibrational degrees of freedom. The full time-dependent wave function is a product of a Gaussian translational wave packet and a multidimensional harmonic oscillator wave function, both centered around the appropriate classical position variables. The computational requirements are small since the initial vibrational coordinates are the equilibrium values in the classical trajectory (i.e., phase space sampling does not occur). Different choices of the initial width of the translational wave packet and the initial classical translational momenta are possible, and two combinations are investigated. The first involves setting the initial classical momenta equal to the quantal expectation value, and varying the width to satisfy normalization of the transition probability matrix. The second involves adjusting the initial classical momenta to ensure detailed balancing for each set of transitions, i→f and f→i, and varying the width to satisfy normalization. This choice illustrates the origin of the empirical correction of using the arithmetic average momenta as the initial classical momenta in the forced oscillator approximation. Both methods are tested for the collinear collision systems CO 2 --(He, Ne), and are found to be accurate except for near-resonant vibration--vibration exchange at low initial kinetic energies

Red Shift and Broadening of Backward Harmonic Radiation from Electron Oscillations Driven by Femtosecond Laser Pulse

International Nuclear Information System (INIS)

Tian Youwei; Yu Wei; Lu Peixiang; Senecha, Vinod K; Han, Xu; Deng Degang; Li Ruxin; Xu Zhizhan

2006-01-01

The characteristics of backward harmonic radiation due to electron oscillations driven by a linearly polarized fs laser pulse are analysed considering a single electron model. The spectral distributions of the electron's backward harmonic radiation are investigated in detail for different parameters of the driver laser pulse. Higher order harmonic radiations are possible for a sufficiently intense driving laser pulse. We have shown that for a realistic pulsed photon beam, the spectrum of the radiation is red shifted as well as broadened because of changes in the longitudinal velocity of the electrons during the laser pulse. These effects are more pronounced at higher laser intensities giving rise to higher order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that by increasing the laser pulse width the broadening of the high harmonic radiations can be controlled

The fractional oscillator process with two indices

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

Energy Technology Data Exchange (ETDEWEB)

Radice, David, E-mail: david.radice@aei.mpg.de [Max Planck Institute für Gravitationsphysik, Albert Einstein Institute, Potsdam (Germany); Abdikamalov, Ernazar [TAPIR, California Institute of Technology, Pasadena, CA (United States); Rezzolla, Luciano [Max Planck Institute für Gravitationsphysik, Albert Einstein Institute, Potsdam (Germany); Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA (United States); Ott, Christian D. [TAPIR, California Institute of Technology, Pasadena, CA (United States)

2013-06-01

Recent work by McClarren and Hauck (2010) [31] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations.

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

International Nuclear Information System (INIS)

Radice, David; Abdikamalov, Ernazar; Rezzolla, Luciano; Ott, Christian D.

2013-01-01

Recent work by McClarren and Hauck (2010) [31] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations

Semi-classical quantization non-manifestly using the method of harmonic balance

International Nuclear Information System (INIS)

Stepanov, S.S.; Tutik, R.S.; Yaroshenko, A.P.; Schlippe, W. von.

1990-01-01

Based on the ideas of the harmonic balance method and h-expansion a semi-classical procedure for deriving approximations to the energy levels of one-dimensional quantum systems is developed. The procedure is applied to treat the perturbed oscillator potentials. 12 refs.; 2 tabs

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

International Nuclear Information System (INIS)

Majima, H.; Suzuki, A.

2011-01-01

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-γx) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+(γ)/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)=1/2 k(x±y/2) 2 specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: → A method of quantizing dissipative systems is presented. → In order to obtain the method, we apply Bateman's dual system approach. → A formula for a transition amplitude is derived. → We use the formula to study the instability of the dissipative systems.

Magnetohydrodynamic waves in two-dimensional prominences embedded in coronal arcades

International Nuclear Information System (INIS)

Terradas, J.; Soler, R.; Díaz, A. J.; Oliver, R.; Ballester, J. L.

2013-01-01

Solar prominence models used so far in the analysis of MHD waves in two-dimensional structures are quite elementary. In this work, we calculate numerically magnetohydrostatic models in two-dimensional configurations under the presence of gravity. Our interest is in models that connect the magnetic field to the photosphere and include an overlying arcade. The method used here is based on a relaxation process and requires solving the time-dependent nonlinear ideal MHD equations. Once a prominence model is obtained, we investigate the properties of MHD waves superimposed on the structure. We concentrate on motions purely two-dimensional, neglecting propagation in the ignorable direction. We demonstrate how, by using different numerical tools, we can determine the period of oscillation of stable waves. We find that vertical oscillations, linked to fast MHD waves, are always stable and have periods in the 4-10 minute range. Longitudinal oscillations, related to slow magnetoacoustic-gravity waves, have longer periods in the range of 28-40 minutes. These longitudinal oscillations are strongly influenced by the gravity force and become unstable for short magnetic arcades.

Symmetries of cyclic work distributions for an isolated harmonic oscillator

International Nuclear Information System (INIS)

Ford, Ian J; Minor, David S; Binnie, Simon J

2012-01-01

We have calculated the distribution of work W done on a 1D harmonic oscillator that is initially in canonical equilibrium at temperature T, then thermally isolated and driven by an arbitrary time-dependent cyclic spring constant κ(t), and demonstrated that it satisfies P(W) = exp (βW)P( − W), where β = 1/k B T, in both classical and quantum dynamics. This differs from the celebrated Crooks relation of nonequilibrium thermodynamics, since the latter relates distributions for forward and backward protocols of driving. We show that it is a special case of a symmetry that holds for non-cyclic work processes on the isolated oscillator, and that consideration of time reversal invariance shows it to be consistent with the Crooks relation. We have verified that the symmetry holds in both classical and quantum treatments of the dynamics, but that inherent uncertainty in the latter case leads to greater fluctuations in work performed for a given process. (paper)

Semiclassical analysis of long-wavelength multiphoton processes: The periodically driven harmonic oscillator

International Nuclear Information System (INIS)

Fox, Ronald F.; Vela-Arevalo, Luz V.

2002-01-01

The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances

Vibrational spectra and thermal rectification in three-dimensional anharmonic lattices

International Nuclear Information System (INIS)

Lan Jinghua; Li Baowen

2007-01-01

We study thermal rectification in a three-dimensional model consisting of two segments of anharmonic lattices. One segment consists of layers of harmonic oscillator arrays coupled to a substrate potential, which is a three-dimensional Frenkel-Kontorova model, and the other segment is a three-dimensional Fermi-Pasta-Ulam model. We study the vibrational bands of the two lattices analytically and numerically, and find that, by choosing the system parameters properly, the rectification can be as high as a few thousands, which is high enough to be observed in experiment. Possible experiments in nanostructures are discussed

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

DEFF Research Database (Denmark)

Loft, Niels Jakob; Salami Dehkharghani, Amin; Mehta, N. P.

2015-01-01

We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in t...

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

International Nuclear Information System (INIS)

Nutku, Yavuz

2003-01-01

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems

Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap

Science.gov (United States)

Dehkharghani, A. S.; Bellotti, F. F.; Zinner, N. T.

2017-07-01

In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose-Bose and the Fermi-Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose-Fermi mixtures we find pronounced odd-even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.

Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

International Nuclear Information System (INIS)

Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

2009-01-01

In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

Symmetries of the quantum damped harmonic oscillator

International Nuclear Information System (INIS)

Guerrero, J; López-Ruiz, F F; Aldaya, V; Cossío, F

2012-01-01

For the non-conservative Caldirola–Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg–Weyl algebra can be found. The inclusion of the standard time evolution generator (which is not a symmetry) as a symmetry in this algebra, in a unitary manner, requires a non-trivial extension of this basic algebra and hence of the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman dual system, which now includes a new particle acting as an energy reservoir. In addition, the Caldirola–Kanai dissipative system can be retrieved by imposing constraints. The algebra of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. As opposed to other approaches, where it is claimed that the spectrum of the Bateman Hamiltonian is complex and discrete, we obtain that it is real and continuous, with infinite degeneracy in all regimes. (paper)

Three-dimensional analysis of harmonic generation in high-gain free-electron lasers

International Nuclear Information System (INIS)

Huang, Zhirong; Kim, Kwang-Je

2000-01-01

In a high-gain free-electron laser (FEL) employing a planar undulator, strong bunching at the fundamental wavelength can drive substantial bunching and power levels at the harmonic frequencies. In this paper we investigate the three-dimensional evolution of harmonic radiation based on the coupled Maxwell-Klimontovich equations that take into account nonlinear harmonic interactions. Each harmonic field is a sum of a linear amplification term and a term driven by nonlinear harmonic interactions. After a certain stage of exponential growth, the dominant nonlinear term is determined by interactions of the lower nonlinear harmonics and the fundamental radiation. As a result, the gain length, transverse profile, and temporal structure of the first few harmonics are eventually governed by those of the fundamental. Transversely coherent third-harmonic radiation power is found to approach 1% of the fundamental power level for current high-gain FEL projects

One dimensional Dirac-Moshinsky oscillator-like system and isospectral partners

International Nuclear Information System (INIS)

Contreras-Astorga, A

2015-01-01

Two different exactly solvable systems are constructed using the supersymmetric quantum mechanics formalism and a pseudoscalar one-dimensional version of the Dirac- Moshinsky oscillator as a departing system. One system is built using a first-order SUSY transformation. The second is obtained through the confluent supersymmetry algorithm. The two of them are explicitly designed to have the same spectrum as the departing system and pseudoscalar potentials. (paper)

Approximation of sums of oscillating summands in certain physical problems

International Nuclear Information System (INIS)

Karatsuba, Ekatherina A.

2004-01-01

The motion of a one-dimensional harmonic oscillator caused by recurring pushes in the absence of friction is considered. In particular, two cases are studied: the case when the pushes become more frequent and the other one when the pushes become less frequent. By means of an application of the Hardy-Littlewood-Vinogradov-Van der Corput theorem on the approximation of exponential sums by shorter ones, new asymptotic formulas for the solution of the problem are obtained

Edge harmonic oscillations at the density pedestal in the H-mode discharges in CHS Heliotron measured using beam emission spectroscopy and magnetic probe

Energy Technology Data Exchange (ETDEWEB)

Kado, S. [High Temperature Plasma Center, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8568 (Japan)]. E-mail: kado@q.t.u-tokyo.ac.jp; Oishi, T. [School of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Yoshinuma, M. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Ida, K. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Takeuchi, M. [Department of Energy Engineering and Science, Nagoya University, Nagoya 464-8603 (Japan); Toi, K. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Akiyama, T. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Minami, T. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Nagaoka, K. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Shimizu, A. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Okamura, S. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Tanaka, S. [School of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan)

2007-06-15

Edge harmonic oscillations (EHO) offer the potential to relax the H-mode pedestal in a tokamak, thus avoiding edge localised modes (ELM). The mode structure of the EHO in CHS was investigated using a poloidal array of beam emission spectroscopy (BES) and a magnetic probe array. The EHO exhibited a peculiar characteristic in which the first, second and third harmonics show the same wavenumber, suggesting that the propagation velocities are different. Change in the phase of higher harmonics at the time when that of the first harmonic is zero can be described as a variation along the (m, n) = (-2, 1) mode structure, though the EHO lies on the {iota} = 1 surface. This behavior leads to an oscillation that exhibits periodic dependence of shape on spatial position.

Two dimensional unstable scar statistics.

Energy Technology Data Exchange (ETDEWEB)

Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)

2006-12-01

This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.

Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Bizimana, Laurie A.; Brazard, Johanna; Carbery, William P.; Gellen, Tobias; Turner, Daniel B., E-mail: dturner@nyu.edu [Department of Chemistry, New York University, 100 Washington Square East, New York, New York 10003 (United States)

2015-10-28

Coherent multidimensional optical spectroscopy is an emerging technique for resolving structure and ultrafast dynamics of molecules, proteins, semiconductors, and other materials. A current challenge is the quality of kinetics that are examined as a function of waiting time. Inspired by noise-suppression methods of transient absorption, here we incorporate shot-by-shot acquisitions and balanced detection into coherent multidimensional optical spectroscopy. We demonstrate that implementing noise-suppression methods in two-dimensional electronic spectroscopy not only improves the quality of features in individual spectra but also increases the sensitivity to ultrafast time-dependent changes in the spectral features. Measurements on cresyl violet perchlorate are consistent with the vibronic pattern predicted by theoretical models of a highly displaced harmonic oscillator. The noise-suppression methods should benefit research into coherent electronic dynamics, and they can be adapted to multidimensional spectroscopies across the infrared and ultraviolet frequency ranges.

Is there a lower bound energy in the harmonic oscillator interacting with a heat bath?

International Nuclear Information System (INIS)

Arevalo Aguilar, L.M.; Almeida, N.G. de; Villas-Boas, C.J.

2003-01-01

In this Letter we investigate the lower bound energy of the usual Hamiltonian employed in Quantum Optics to model the interaction between a harmonic oscillator and a reservoir without the rotating wave approximation. We show that this model has serious inconsistencies and then we discuss the origin of these inconsistencies

Simultaneous operation of a free-electron laser on two harmonically related wavelengths

International Nuclear Information System (INIS)

Burke, A.T.; Ride, S.K.

1992-01-01

The interaction of light waves at the fundamental and the third harmonic frequencies in a free-electron laser (FEL) oscillator is explored using the 1-D finite pulse mode-code BFELP. The code, which assumes that only the TEM 00 transverse mode is present at both harmonic frequencies, tracks the temporally-finite pulse electric field amplitudes of the fundamental and the third harmonic which interact with an rf-linac-generated electron micropulse inside a wiggler. The evolution of the pulse profiles, with possibly different mirror reflectivities at each frequency, after many passes through the wiggler and the optical resonator, has been generated for various initial conditions. Results include pulse-dependent third-harmonic coherent-spontaneous emission (CSE) with, and without, multiple-pass interference effects; the effects of sidebands at the fundamental on third-harmonic CSE; and, lasing competition between the fundamental and third harmonic in overlapping spatial regions of the electron micropulse

On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress

International Nuclear Information System (INIS)

Bocko, M.F.; Onofrio, R.

1996-01-01

Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. copyright 1996 The American Physical Society

Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

DEFF Research Database (Denmark)

Jensen, Arne; Yajima, Kenji

We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....

Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

DEFF Research Database (Denmark)

Jensen, Arne; Yajima, Kenji

2010-01-01

We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with an algebraic growth rate, which increases indefinitely when the growth rate of perturbations at infinity decreases from the near quadratic to the near linear ones....

Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

International Nuclear Information System (INIS)

Belendez, A.; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A.

2008-01-01

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities

Constructive influence of noise flatness and friction on the resonant behavior of a harmonic oscillator with fluctuating frequency.

Science.gov (United States)

Laas, Katrin; Mankin, Romi; Rekker, Astrid

2009-05-01

The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.

Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1977-01-01

A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

Hyperspherical Harmonics Expansion on Lagrange Meshes for Bosonic Systems in One Dimension

International Nuclear Information System (INIS)

Timofeyuk, N. K.; Baye, D.

2017-01-01

A one-dimensional system of bosons interacting with contact and single-Gaussian forces is studied with an expansion in hyperspherical harmonics. The hyper radial potentials are calculated using the link between the hyperspherical harmonics and the single-particle harmonic-oscillator basis while the coupled hyper radial equations are solved with the Lagrange-mesh method. Extensions of this method are proposed to achieve good convergence with small numbers of mesh points for any truncation of hyper momentum. The convergence with hyper momentum strongly depends on the range of the two-body forces: it is very good for large ranges but deteriorates as the range decreases, being the worst for the contact interaction. In all cases, the lowest-order energy is within 4.5% of the exact solution and shows the correct cubic asymptotic behaviour at large boson numbers. Details of the convergence studies are presented for 3, 5, 20 and 100 bosons. A special treatment for three bosons was found to be necessary. For single-Gaussian interactions, the convergence rate improves with increasing boson number, similar to what happens in the case of three-dimensional systems of bosons. (author)

Simultaneous negative refraction and focusing of fundamental frequency and second-harmonic fields by two-dimensional photonic crystals

Energy Technology Data Exchange (ETDEWEB)

Zhang, Jun [School of Physics, Beijing Institute of Technology and Beijing Key Laboratory of Fractional Signals and Systems, Beijing 100081 (China); College of Physics and Electronic Engineering, Henan Normal University, 453007 Xinxiang, Henan (China); Zhang, Xiangdong, E-mail: zhangxd@bit.edu.cn [School of Physics, Beijing Institute of Technology and Beijing Key Laboratory of Fractional Signals and Systems, Beijing 100081 (China)

2015-09-28

Simultaneous negative refraction for both the fundamental frequency (FF) and second-harmonic (SH) fields in two-dimensional nonlinear photonic crystals have been found through both the physical analysis and exact numerical simulation. By combining such a property with the phase-matching condition and strong second-order susceptibility, we have designed a SH lens to realize focusing for both the FF and SH fields at the same time. Good-quality non-near field images for both FF and SH fields have been observed. The physical mechanism for such SH focusing phenomena has been disclosed, which is different from the backward SH generation as has been pointed out in the previous investigations. In addition, the effect of absorption losses on the phenomena has also been discussed. Thus, potential applications of these phenomena to biphotonic microscopy technique are anticipated.

Mutual phase-locking of planar nano-oscillators

Directory of Open Access Journals (Sweden)

K. Y. Xu

2014-06-01

Full Text Available Characteristics of phase-locking between Gunn effect-based planar nano-oscillators are studied using an ensemble Monte Carlo (EMC method. Directly connecting two oscillators in close proximity, e.g. with a channel distance of 200 nm, only results in incoherent oscillations. In order to achieve in-phase oscillations, additional considerations must be taken into account. Two coupling paths are shown to exist between oscillators. One coupling path results in synchronization and the other results in anti-phase locking. The coupling strength through these two paths can be adjusted by changing the connections between oscillators. When two identical oscillators are in the anti-phase locking regime, fundamental components of oscillations are cancelled. The resulting output consists of purely second harmonic oscillations with a frequency of about 0.66 THz. This type of second harmonic generation is desired for higher frequency applications since no additional filter system is required. This transient phase-locking process is further analyzed using Adler's theory. The locking range is extracted, and a criterion for the channel length difference required for realizing phased arrays is obtained. This work should aid in designing nano-oscillator arrays for high power applications and developing directional transmitters for wireless communications.

Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field

International Nuclear Information System (INIS)

Yuece, Cem

2003-01-01

In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained

Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons

Energy Technology Data Exchange (ETDEWEB)

Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2014-09-02

A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.

Self-organization and oscillation of negatively charged dust particles in a 2-dimensional dusty plasma

Energy Technology Data Exchange (ETDEWEB)

Song, Y.L. [College of Science, China Agricultural University, Beijing 100083 (China); Huang, F., E-mail: huangfeng@cau.edu.cn [College of Science, China Agricultural University, Beijing 100083 (China); Chen, Z.Y., E-mail: chenzy@mail.buct.edu.cn [Department of Physics, Beijing University of Chemical Technology, Beijing 100029 (China); State Key Laboratory of Laser Propulsion & Application, Beijing 101416 (China); Liu, Y.H. [School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025 (China); Yu, M.Y. [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027 (China); Institute for Theoretical Physics I, Ruhr University, D-44801 Bochum (Germany)

2016-02-22

Negatively charged dust particles immersed in 2-dimensional dusty plasma system are investigated by molecular dynamics simulations. The effects of the confinement potential and attraction interaction potential on dust particle self-organization are studied in detail and two typical dust particle distributions are obtained when the system reaches equilibrium. The average radial velocity (ARV), average radial force (ARF) and radial mean square displacement are employed to analyze the dust particles' dynamics. Both ARVs and ARFs exhibit oscillation behaviors when the simulation system reaches equilibrium state. The relationships between the oscillation and confinement potential and attraction potential are studied in this paper. The simulation results are qualitatively similar to experimental results. - Highlights: • Self-organization and oscillation of a 2-dimensional dusty plasma is investigated. • Effect of the confinement potential on dust self-organization and oscillation is given. • Effect of the attraction potential on dust self-organization and oscillation is studied.

Self-organization and oscillation of negatively charged dust particles in a 2-dimensional dusty plasma

International Nuclear Information System (INIS)

Song, Y.L.; Huang, F.; Chen, Z.Y.; Liu, Y.H.; Yu, M.Y.

2016-01-01

Negatively charged dust particles immersed in 2-dimensional dusty plasma system are investigated by molecular dynamics simulations. The effects of the confinement potential and attraction interaction potential on dust particle self-organization are studied in detail and two typical dust particle distributions are obtained when the system reaches equilibrium. The average radial velocity (ARV), average radial force (ARF) and radial mean square displacement are employed to analyze the dust particles' dynamics. Both ARVs and ARFs exhibit oscillation behaviors when the simulation system reaches equilibrium state. The relationships between the oscillation and confinement potential and attraction potential are studied in this paper. The simulation results are qualitatively similar to experimental results. - Highlights: • Self-organization and oscillation of a 2-dimensional dusty plasma is investigated. • Effect of the confinement potential on dust self-organization and oscillation is given. • Effect of the attraction potential on dust self-organization and oscillation is studied.

Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

International Nuclear Information System (INIS)

Rezende, J.

1983-01-01

We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)

Mechanism of equivalent electric dipole oscillation for high-order harmonic generation from grating-structured solid-surface by femtosecond laser pulse

Science.gov (United States)

Wang, Yang; Song, Hai-Ying; Liu, H. Y.; Liu, Shi-Bing

2017-07-01

We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.

Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator

Science.gov (United States)

Doll, Moritz; Gannot, Oran; Wunsch, Jared

2018-02-01

Let H denote the harmonic oscillator Hamiltonian on R}^d,} perturbed by an isotropic pseudodifferential operator of order 1. We consider the Schrödinger propagator {U(t)=e^{-itH},} and find that while sing-supp Tr U(t) \\subset 2 π Z as in the unperturbed case, there exists a large class of perturbations in dimensions {d ≥ 2 for which the singularities of {Tr U(t)} at nonzero multiples of {2 π} are weaker than the singularity at t = 0. The remainder term in the Weyl law is of order {o(λ^{d-1})} , improving in these cases the {o(λ^{d-1})} remainder previously established by Helffer-Robert.

Shapes of nuclear configurations in a cranked harmonic oscillator model

International Nuclear Information System (INIS)

Troudet, T.; Arvieu, R.

1980-05-01

The shapes of nuclear configurations are calculated using Slater determinants built with cranked harmonic oscillator single particle states. The nuclear forces role is played by a volume conservation condition (of the potential or of the density) in a first part. In a second part, we have used the finite range, density dependent interaction of Cogny. A very simple classification of configurations emerges in the first part, the relevant parameter being the equatorial eccentricity of the nuclear density. A critical equatorial eccentricity is obtained which governs the accession to the case for which the nucleus is oblate and symmetric around its axis of rotation. Nuclear configurations calculated in the second part observe remarkably well these behaviors

Three-dimensional features on oscillating microbubbles streaming flows

Science.gov (United States)

Rossi, Massimiliano; Marin, Alvaro G.; Wang, Cheng; Hilgenfeldt, Sascha; Kähler, Christian J.

2013-11-01

Ultrasound-driven oscillating micro-bubbles have been used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting and manipulation of microparticles. A common configuration consists in side-bubbles, created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration results in bubbles with a semi-cylindrical shape that creates a streaming flow generally considered quasi two-dimensional. However, recent experiments performed with three-dimensional velocimetry methods have shown how microparticles can present significant three-dimensional trajectories, especially in regions close to the bubble interface. Several reasons will be discussed such as boundary effects of the bottom/top wall, deformation of the bubble interface leading to more complex vibrational modes, or bubble-particle interactions. In the present investigation, precise measurements of particle trajectories close to the bubble interface will be performed by means of 3D Astigmatic Particle Tracking Velocimetry. The results will allow us to characterize quantitatively the three-dimensional features of the streaming flow and to estimate its implications in practical applications as particle trapping, sorting or mixing.

Tunable Soft X-Ray Oscillators

International Nuclear Information System (INIS)

Wurtele, Jonathan; Gandhi, Punut; Gu, X.-W.; Fawley, William M.; Reinsch, Matthia; Penn, Gregory; Kim, K.-J.; Lindberg, Ryan; Zholents, Alexander

2010-01-01

A concept for a tunable soft x-ray free electron laser (FEL) photon source is presented and studied numerically. The concept is based on echo-enabled harmonic generation (EEHG), wherein two modulator-chicane sections impose high harmonic structure with much greater efficacy as compared to conventional high harmonic FELs that use only one modulator-chicane section. The idea proposed here is to replace the external laser power sources in the EEHG modulators with FEL oscillators, and to combine the bunching of the beam with the production of radiation. Tunability is accomplished by adjusting the magnetic chicanes while the two oscillators remain at a fixed frequency. This scheme eliminates the need to develop coherent sources with the requisite power, pulse length, and stability requirements by exploiting the MHz bunch repetition rates of FEL continuous wave (CW) sources driven by superconducting (SC) linacs. We present time-dependent GINGER simulation results for an EEHG scheme with an oscillator modulator at 43 nm employing 50percent reflective dielectric mirrors and a second modulator employing an external, 215-nm drive laser. Peak output of order 300 MW is obtained at 2.7 nm, corresponding to the 80th harmonic of 215 nm. An alternative single-cavity echo-oscillator scheme based on a 13.4 nm oscillator is investigated with time-independent simulations that a 180-MW peak power at final wavelength of 1.12 nm. Three alternate configurations that use separate bunches to produce the radiation for EEHG microbunching are also presented. Our results show that oscillator-based soft x-ray FELs driven by CWSC linacs are extremely attractive because of their potential to produce tunable radiation at high average power together with excellent longitudinal coherence and narrow spectral bandwidth.

Tunable Soft X-Ray Oscillators

Energy Technology Data Exchange (ETDEWEB)

Wurtele, Jonathan; Gandhi, Punut; Gu, X-W; Fawley, William M; Reinsch, Matthia; Penn, Gregory; Kim, K-J; Lindberg, Ryan; Zholents, Alexander

2010-09-17

A concept for a tunable soft x-ray free electron laser (FEL) photon source is presented and studied numerically. The concept is based on echo-enabled harmonic generation (EEHG), wherein two modulator-chicane sections impose high harmonic structure with much greater efficacy as compared to conventional high harmonic FELs that use only one modulator-chicane section. The idea proposed here is to replace the external laser power sources in the EEHG modulators with FEL oscillators, and to combine the bunching of the beam with the production of radiation. Tunability is accomplished by adjusting the magnetic chicanes while the two oscillators remain at a fixed frequency. This scheme eliminates the need to develop coherent sources with the requisite power, pulse length, and stability requirements by exploiting the MHz bunch repetition rates of FEL continuous wave (CW) sources driven by superconducting (SC) linacs. We present time-dependent GINGER simulation results for an EEHG scheme with an oscillator modulator at 43 nm employing 50percent reflective dielectric mirrors and a second modulator employing an external, 215-nm drive laser. Peak output of order 300 MW is obtained at 2.7 nm, corresponding to the 80th harmonic of 215 nm. An alternative single-cavity echo-oscillator scheme based on a 13.4 nm oscillator is investigated with time-independent simulations that a 180-MW peak power at final wavelength of 1.12 nm. Three alternate configurations that use separate bunches to produce the radiation for EEHG microbunching are also presented. Our results show that oscillator-based soft x-ray FELs driven by CWSC linacs are extremely attractive because of their potential to produce tunable radiation at high average power together with excellent longitudinal coherence and narrow spectral bandwidth.

Dimensional reduction in Bose-Einstein-condensed alkali-metal vapors

International Nuclear Information System (INIS)

Salasnich, L.; Reatto, L.; Parola, A.

2004-01-01

We investigate the effects of dimensional reduction in atomic Bose-Einstein condensates (BECs) induced by a strong harmonic confinement in the cylindric radial direction or in the cylindric axial direction. The former case corresponds to a transition from three dimensions (3D) to 1D in cigar-shaped BECs, while the latter case corresponds to a transition from 3D to 2D in disk-shaped BECs. We analyze the first sound velocity in axially homogeneous cigar-shaped BECs and in radially homogeneous disk-shaped BECs. We consider also the dimensional reduction in a BEC confined by a harmonic potential both in the radial direction and in the axial direction. By using a variational approach, we calculate monopole and quadrupole collective oscillations of the BEC. We find that the frequencies of these collective oscillations are related to the dimensionality and to the repulsive or attractive interatomic interaction

Three-Dimensional Geometry of Collagenous Tissues by Second Harmonic Polarimetry.

Science.gov (United States)

Reiser, Karen; Stoller, Patrick; Knoesen, André

2017-06-01

Collagen is a biological macromolecule capable of second harmonic generation, allowing label-free detection in tissues; in addition, molecular orientation can be determined from the polarization dependence of the second harmonic signal. Previously we reported that in-plane orientation of collagen fibrils could be determined by modulating the polarization angle of the laser during scanning. We have now extended this method so that out-of-plane orientation angles can be determined at the same time, allowing visualization of the 3-dimensional structure of collagenous tissues. This approach offers advantages compared with other methods for determining out-of-plane orientation. First, the orientation angles are directly calculated from the polarimetry data obtained in a single scan, while other reported methods require data from multiple scans, use of iterative optimization methods, application of fitting algorithms, or extensive post-optical processing. Second, our method does not require highly specialized instrumentation, and thus can be adapted for use in almost any nonlinear optical microscopy setup. It is suitable for both basic and clinical applications. We present three-dimensional images of structurally complex collagenous tissues that illustrate the power of such 3-dimensional analyses to reveal the architecture of biological structures.

Three-dimensional simulation of thermal harmonic lasing free electron laser with detuning of the fundamental

Science.gov (United States)

Salehi, E.; Maraghechi, B.; Mirian, N. S.

2016-03-01

Detuning of the fundamental is a way to enhance harmonic generation. By this method, the wiggler is composed of two segments in such a way that the fundamental resonance of the second segment to coincide with the third harmonic of the first segment of the wiggler to generate extreme ultraviolet radiation and x-ray emission. A set of coupled, nonlinear, and first-order differential equations in three dimensions describing the evolution of the electron trajectories and the radiation field with warm beam is solved numerically by CYRUS 3D code in the steady-state for two models (1) seeded free electron laser (FEL) and (2) shot noise on the electron beam (self-amplified spontaneous emission FEL). Thermal effects in the form of longitudinal velocity spread are considered. Three-dimensional simulation describes self-consistently the longitudinal spatial dependence of radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. The evolutions of the transverse modes are investigated for the fundamental resonance and the third harmonic. Also, the effective modes of the third harmonic are studied. In this paper, we found that detuning of the fundamental with shot noise gives more optimistic result than the seeded FEL.

Three-dimensional simulation of thermal harmonic lasing free electron laser with detuning of the fundamental

International Nuclear Information System (INIS)

Salehi, E.; Maraghechi, B.; Mirian, N. S.

2016-01-01

Detuning of the fundamental is a way to enhance harmonic generation. By this method, the wiggler is composed of two segments in such a way that the fundamental resonance of the second segment to coincide with the third harmonic of the first segment of the wiggler to generate extreme ultraviolet radiation and x-ray emission. A set of coupled, nonlinear, and first-order differential equations in three dimensions describing the evolution of the electron trajectories and the radiation field with warm beam is solved numerically by CYRUS 3D code in the steady-state for two models (1) seeded free electron laser (FEL) and (2) shot noise on the electron beam (self-amplified spontaneous emission FEL). Thermal effects in the form of longitudinal velocity spread are considered. Three-dimensional simulation describes self-consistently the longitudinal spatial dependence of radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. The evolutions of the transverse modes are investigated for the fundamental resonance and the third harmonic. Also, the effective modes of the third harmonic are studied. In this paper, we found that detuning of the fundamental with shot noise gives more optimistic result than the seeded FEL.

Three-dimensional simulation of thermal harmonic lasing free electron laser with detuning of the fundamental

Energy Technology Data Exchange (ETDEWEB)

Salehi, E. [Department of Physics, Amirkabir University of Technology, 15875-4413 Tehran (Iran, Islamic Republic of); Maraghechi, B., E-mail: behrouz@aut.ac.ir [Department of Physics, Amirkabir University of Technology, 15875-4413 Tehran (Iran, Islamic Republic of); School of Particle and Accelerator Physics, Institute for Research in Fundamental Sciences (IPM), 19395-5531 Tehran (Iran, Islamic Republic of); Mirian, N. S. [School of Particle and Accelerator Physics, Institute for Research in Fundamental Sciences (IPM), 19395-5531 Tehran (Iran, Islamic Republic of); UVSOR Facility (UVSOR), Institute for Molecular Science, Myodaiji, Okazaki 444-8585 (Japan)

2016-03-15

Detuning of the fundamental is a way to enhance harmonic generation. By this method, the wiggler is composed of two segments in such a way that the fundamental resonance of the second segment to coincide with the third harmonic of the first segment of the wiggler to generate extreme ultraviolet radiation and x-ray emission. A set of coupled, nonlinear, and first-order differential equations in three dimensions describing the evolution of the electron trajectories and the radiation field with warm beam is solved numerically by CYRUS 3D code in the steady-state for two models (1) seeded free electron laser (FEL) and (2) shot noise on the electron beam (self-amplified spontaneous emission FEL). Thermal effects in the form of longitudinal velocity spread are considered. Three-dimensional simulation describes self-consistently the longitudinal spatial dependence of radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. The evolutions of the transverse modes are investigated for the fundamental resonance and the third harmonic. Also, the effective modes of the third harmonic are studied. In this paper, we found that detuning of the fundamental with shot noise gives more optimistic result than the seeded FEL.

A comparison of left ventricular mass between two-dimensional echocardiography, using fundamental and tissue harmonic imaging, and cardiac MRI in patients with hypertension

International Nuclear Information System (INIS)

Alfakih, Khaled; Bloomer, Tim; Bainbridge, Samantha; Bainbridge, Gavin; Ridgway, John; Williams, Gordon; Sivananthan, Mohan

2004-01-01

Purpose: To compare left ventricular mass (LVM) as measured by two-dimensional (2D) echocardiography using two different calculation methods: truncated ellipse (TE) and area length (AL), in both fundamental and tissue harmonic imaging frequencies, to LVM as measured by, the current gold standard, cardiac magnetic resonance imaging (MRI). Turbo gradient echo (TGE) pulse sequence was utilized for MRI. Materials and methods: Thirty-two subjects with history of hypertension were recruited. The images were acquired, contours were traced and the LVM was calculated for all four different echocardiography methods as well as for the cardiac MRI method. The intra-observer variabilities were calculated. The four different echocardiography methods were compared to cardiac MRI using the method described by Bland and Altman. Results: Twenty-five subjects had adequate paired data sets. The mean LVM as measured by cardiac MRI was 162±55 g and for the four different echocardiography methods were: fundamental AL 165±55 g, harmonic AL 168±53 g, fundamental TE 148±50 g, harmonic TE 149±45 g. The intra-observer variability for cardiac MRI method, expressed as bias ± 1 standard deviation of the difference (S.D.D.), was 2.3±9.2 g and for the four different echocardiography methods were: fundamental TE 0.4±26.8 g, fundamental AL 0.6±27.0 g, harmonic TE 6.7±21.8 g, harmonic AL 6.4±22.9 g. The mean LVM for the AL method was closest to the cardiac MRI technique, while TE underestimated LVM. The 95% limits of agreement were consistently wide for all the 2D echocardiography modalities when compared with the cardiac MRI technique. Conclusion: The intra-observer variability in measurements of 2D echocardiographic LVM, together with the wide limits of agreement when compared to the gold standard (cardiac MRI) are sufficiently large to make serial estimates of LVM, of single patients or small groups of subjects, by 2D echocardiography, unreliable

High-order harmonics generation from overdense plasmas

International Nuclear Information System (INIS)

Quere, F.; Thaury, C.; Monot, P.; Martin, Ph.; Geindre, J.P.; Audebert, P.; Marjoribanks, R.

2006-01-01

Complete test of publication follows. When an intense laser beam reflects on an overdense plasma generated on a solid target, high-order harmonics of the incident laser frequency are observed in the reflected beam. This process provides a way to produce XUV femtosecond and attosecond pulses in the μJ range from ultrafast ultraintense lasers. Studying the mechanisms responsible for this harmonic emission is also of strong fundamental interest: just as HHG in gases has been instrumental in providing a comprehensive understanding of basic intense laser-atom interactions, HHG from solid-density plasmas is likely to become a unique tool to investigate many key features of laser-plasma interactions at high intensities. We will present both experimental and theoretical evidence that two mechanisms contribute to this harmonic emission: - Coherent Wake Emission: in this process, harmonics are emitted by plasma oscillations in te overdense plasma, triggered in the wake of jets of Brunel electrons generated by the laser field. - The relativistic oscillating mirror: in this process, the intense laser field drives a relativistic oscillation of the plasma surface, which in turn gives rise to a periodic phase modulation of the reflected beam, and hence to the generation of harmonics of the incident frequency. Left graph: experimental harmonic spectrum from a polypropylene target, obtained with 60 fs laser pulses at 10 19 W/cm 2 , with a very high temporal contrast (10 10 ). The plasma frequency of this target corresponds to harmonics 15-16, thus excluding the CWE mechanism for the generation of harmonics of higher orders. Images on the right: harmonic spectra from orders 13 et 18, for different distances z between the target and the best focus. At the highest intensity (z=0), harmonics emitted by the ROM mechanism are observed above the 15th order. These harmonics have a much smaller spectral width then those due to CWE (below the 15th order). These ROM harmonics vanish as soon

Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics

DEFF Research Database (Denmark)

Nørrelykke, Simon F; Flyvbjerg, Henrik

2011-01-01

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...

Modeling stock return distributions with a quantum harmonic oscillator

Science.gov (United States)

Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

2017-11-01

We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

International Nuclear Information System (INIS)

Ayvaz, Muzaffer; Demiralp, Metin

2011-01-01

In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics

Science.gov (United States)

Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei

2013-01-01

At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

Dynamics of harmonically-confined systems: Some rigorous results

Energy Technology Data Exchange (ETDEWEB)

Wu, Zhigang, E-mail: zwu@physics.queensu.ca; Zaremba, Eugene, E-mail: zaremba@sparky.phy.queensu.ca

2014-03-15

In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the response of the system to external perturbations which can be either static or dynamic in nature. We prove an extended Harmonic Potential Theorem which is useful in determining the damping of the centre of mass motion when the system is prepared initially in a highly nonequilibrium state. We also study the response of the gas to a dynamic external potential whose position is made to oscillate sinusoidally in a given direction. We show in this case that either the energy absorption rate or the centre of mass dynamics can serve as a probe of the optical conductivity of the system. -- Highlights: •We derive various rigorous results on the dynamics of harmonically-confined atomic gases. •We derive an extension of the Harmonic Potential Theorem. •We demonstrate the link between the energy absorption rate in a harmonically-confined system and the optical conductivity.

Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

Directory of Open Access Journals (Sweden)

A.F. EL-Bassiouny

2006-01-01

Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.

Oscillations of the crystal-melt interface caused by harmonic oscillations of the pulling rate for the cylindrical phase of crystal growth

Science.gov (United States)

Vasil'ev, M. G.

2017-02-01

A technique for measuring the crystal cross-sectional area with a weight sensor based on the difference between its readings at the extreme rod positions in the stepwise and continuous modes of modulation of the pulling rate is proposed for the low-thermal gradient Czochralski method. A change in the crystallization rate at harmonic oscillations of the pulling rate is estimated with the aim of conserving the quality of the growing crystal for this measurement method.

Oscillator potential for the four-dimensional Hall effect

International Nuclear Information System (INIS)

Mardoyan, Levon; Nersessian, Armen

2005-01-01

We suggest an exactly solvable model of an oscillator on a four-dimensional sphere interacting with an SU(2) Yang monopole. We show that the properties of the model essentially depend on the monopole charge

Few helium atoms in quasi two-dimensional space

International Nuclear Information System (INIS)

Kilic, Srecko; Vranjes, Leandra

2003-01-01

Two, three and four 3 He and 4 He atoms in quasi two-dimensional space above graphite and cesium surfaces and in 'harmonic' potential perpendicular to the surface have been studied. Using some previously examined variational wave functions and the Diffusion Monte Carlo procedure, it has been shown that all molecules: dimers, trimers and tetramers, are bound more strongly than in pure two- and three-dimensional space. The enhancement of binding with respect to unrestricted space is more pronounced on cesium than on graphite. Furthermore, for 3 He 3 ( 3 He 4 ) on all studied surfaces, there is an indication that the configuration of a dimer and a 'free' particle (two dimers) may be equivalently established

Relativistic corrections to one-particle neutron levels in the harmonic oscillator well

International Nuclear Information System (INIS)

Yanavichyus, A.I.

1983-01-01

Relativistic corrections to mass and potential energy for one-particle levels in the harmonic oscillator well are calculated in the first approximation of the perturbation theory. These corrections are, mainly negliqible, but they sharply increase with growth of the head and orbital quantum numbers. For the state 1s the relativistic correction is of the order of 0.01 MeV, and for 3p it is equal to 0.4 MeV. Thus, the relativistic correction for certain states approaches the energy of spin-orbital interactions and it should be taken into account in calculating the energy of one-particle levels

Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

International Nuclear Information System (INIS)

Yang Yong-Ge; Xu Wei; Sun Ya-Hui; Gu Xu-Dong

2016-01-01

This paper aims to investigate the stochastic response of the van der Pol (VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary. (paper)

Resolving a puzzle concerning fluctuation theorems for forced harmonic oscillators in non-Markovian heat baths

International Nuclear Information System (INIS)

Chaudhury, Srabanti; Chatterjee, Debarati; Cherayil, Binny J

2008-01-01

A harmonic oscillator that evolves under the action of both a systematic time-dependent force and a random time-correlated force can do work w. This work is a random quantity, and Mai and Dhar have recently shown, using the generalized Langevin equation (GLE) for the oscillator's position x, that it satisfies a fluctuation theorem. In principle, the same result could have been derived from the Fokker–Planck equation (FPE) for the probability density function, P(x,w,t), for the oscillator being at x at time t, having done work w. Although the FPE equivalent to the above GLE is easily constructed and solved, one finds, unexpectedly, that its predictions for the mean and variance of w do not agree with the fluctuation theorem. We show that to resolve this contradiction, it is necessary to construct an FPE that includes the velocity of the oscillator, v, as an additional variable. The FPE for P(x,v,w,t) does indeed yield expressions for the mean and variance of w that agree with the fluctuation theorem

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

Science.gov (United States)

Park, DaeKil

2018-06-01

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.

Multicascade X-Ray Free-Electron Laser with Harmonic Multiplier and Two-Frequency Undulator

Science.gov (United States)

Zhukovsky, K. V.

2018-06-01

The feasibility of generation of powerful x-ray radiation by a cascade free-electron laser (FEL) with amplification of higher harmonics using a two-frequency undulator is studied. To analyze the FEL operation, a complex phenomenological single-pass FEL model is developed and used. It describes linear and nonlinear generation of harmonics in the FEL with seed laser that takes into account initial electron beam noise and describes all main losses of each harmonic in each FEL cascade. The model is also calibrated against and approved by the experimental FEL data and available results of three-dimensional numerical simulation. The electron beam in the undulator is assumed to be matched and focused, and the dynamics of power in the singlepass FEL with cascade harmonic multipliers is investigated to obtain x-ray laser radiation in the FEL having the shortest length, beam energy, and frequency of the seed laser as low as possible. In this context, the advantages of the two-frequency undulator used for generation of harmonics are demonstrated. The evolution of harmonics in a multicascade FEL with multiplication of harmonics is investigated. The operation of the cascade FEL at the wavelength λ = 1.14 nm, generating 30 MW already on 38 m with the seed laser operating at a wavelength of 11.43 nm corresponding to the maximal reflectivity of the multilayered mirror MoRu/Be coating is investigated. In addition, the operation of the multicascade FEL with accessible seed UVlaser operating at a wavelength of 157 nm (F2 excimer UV-laser) and electron beam with energy of 0.5 GeV is investigated. X-ray radiation simulated in it at the wavelength λ 3.9 nm reaches power of 50 MW already at 27 m, which is by two orders of magnitude shorter than 3.4 km of the x-ray FEL recently put into operation in Europe.

Nonlinear oscillations of the FitzHugh-Nagumo equations under combined external and two-frequency parametric excitations

International Nuclear Information System (INIS)

Tatchim Bemmo, D.; Siewe Siewe, M.; Tchawoua, C.

2011-01-01

The continuous FitzHugh-Nagumo (FHN for short) model is transformed into modified van der Pol oscillator with asymmetry under external and two-frequency parametric excitations. At the first, the dependence of the solutions on a combined external and two-frequency parametric stimulus forcing is investigated. By using the multiple scale method, ranges of applied current and/or parametric forcing in which nonlinear oscillations are observed are described. Second, when the multiple scale method cannot be used, we numerically prove that in the modified van der Pol oscillator with asymmetry under external and two-frequency parametric excitations, chaos and periodic solution depending on the combination between different frequencies of the model should appear. We also show that the amplitude of the oscillations can be reduced or increased. To do this, we perform the study of the FHN model by choosing a range of parameters exhibiting Hopf bifurcation and two qualitative different regimes in phase portrait. - Highlights: → We model both external and two-frequency parametric excitations in FHN equations. → We examine effects of harmonic forcing on coupled nonlinear oscillator. → Jump and hysteresis phenomena are observed in the dynamical response. → By increasing the constant stimulus we obtain limit cycle. → Some combinations of frequencies produce limit cycle and chaos for other.

Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps

DEFF Research Database (Denmark)

Salami Dehkharghani, Amin; Volosniev, A. G.; Zinner, N. T.

2016-01-01

Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the case of equal mass fermions or bosons with two or more...... internal degrees of freedom, one can map the problem onto the well-known Heisenberg spin models. However, many interesting physical systems contain mixtures of particles with different masses. Therefore, a generalization of the recent strong-coupling techniques would be highly desirable....... This is particularly important since such problems are generally considered non-integrable and thus the hugely successful Bethe ansatz approach cannot be applied. Here we discuss some initial steps towards this goal by investigating small ensembles of one-dimensional harmonically trapped particles where pairwise...

Exploration of near the origin and the asymptotic behaviors of the Kohn-Sham kinetic energy density for two-dimensional quantum dot systems with parabolic confinement

Science.gov (United States)

Jana, Subrata; Samal, Prasanjit

2018-01-01

The behaviors of the positive definite Kohn-Sham kinetic energy density near the origin and at the asymptotic region play a major role in designing meta-generalized gradient approximations (meta-GGAs) for exchange in low-dimensional quantum systems. It is shown that near the origin of the parabolic quantum dot, the Kohn-Sham kinetic energy differs from its von Weizsäcker counterpart due to the p orbital contributions, whereas in the asymptotic region, the difference between the above two kinetic energy densities goes as ˜ρ/(r ) r2 . All these behaviors have been explored using the two-dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients are then studied by making use of the above findings. Also, the asymptotic conditions for the exchange energy density and the potential at the meta-GGA level are proposed using the corresponding behaviors of the two kinetic energy densities.

Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

Institute of Scientific and Technical Information of China (English)

Liu Li; Zhang Liang-Ying; Cao Li

2009-01-01

The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Orustein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3)Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.

Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

International Nuclear Information System (INIS)

Li, Liu; Li, Cao; Liang-Ying, Zhang

2009-01-01

The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ 3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Ornstein–Uhlenbeck (O-U) noises. 2) Changing the value of τ 3 , the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model. (general)

A daily oscillation in the fundamental frequency and amplitude of harmonic syllables of zebra finch song.

Directory of Open Access Journals (Sweden)

William E Wood

Full Text Available Complex motor skills are more difficult to perform at certain points in the day (for example, shortly after waking, but the daily trajectory of motor-skill error is more difficult to predict. By undertaking a quantitative analysis of the fundamental frequency (FF and amplitude of hundreds of zebra finch syllables per animal per day, we find that zebra finch song follows a previously undescribed daily oscillation. The FF and amplitude of harmonic syllables rises across the morning, reaching a peak near mid-day, and then falls again in the late afternoon until sleep. This oscillation, although somewhat variable, is consistent across days and across animals and does not require serotonin, as animals with serotonergic lesions maintained daily oscillations. We hypothesize that this oscillation is driven by underlying physiological factors which could be shared with other taxa. Song production in zebra finches is a model system for studying complex learned behavior because of the ease of gathering comprehensive behavioral data and the tractability of the underlying neural circuitry. The daily oscillation that we describe promises to reveal new insights into how time of day affects the ability to accomplish a variety of complex learned motor skills.

Expansion of a Bose-Einstein condensate formed on a joint harmonic and one-dimensional optical-lattice potential

International Nuclear Information System (INIS)

Adhikari, Sadhan K

2003-01-01

We study the expansion of a Bose-Einstein condensate trapped in a combined optical-lattice and axially-symmetric harmonic potential using the numerical solution of the mean-field Gross-Pitaevskii equation. First, we consider the expansion of such a condensate under the action of the optical-lattice potential alone. In this case the result of numerical simulation for the axial and radial sizes during expansion is in agreement with two experiments by Morsch et al (2002 Phys. Rev. A 66 021601(R) and 2003 Laser Phys. 13 594). Finally, we consider the expansion under the action of the harmonic potential alone. In this case the oscillation, and the disappearance and revival of the resultant interference pattern is in agreement with the experiment by Mueller et al (2003 J. Opt. B: Quantum Semiclass. Opt. 5 S38)

Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

Energy Technology Data Exchange (ETDEWEB)

Zhu, Jinghao; Zhang, Jing; Li, Yuan; Zhang, Yong; Fang, Zhengji; Zhao, Peide, E-mail: pdzhao@eyou.com, E-mail: pdzhao@hebut.edu.cn [School of Science, Hebei University of Technology, Beichen Campus, Tianjin 300401 (China); Li, Erping, E-mail: liep@zju.edu.cn [Institute of High Performance Computing, Fusionopolis, 1 Fusionopolis Way, No. 16-16 Connexis, Singapore 138632 (Singapore)

2015-11-15

A quantized impedance is proposed to theoretically establish the relationship between the atomic eigenfrequency and the intrinsic frequency of the one-dimensional oscillator in this paper. The classical oscillator is modified by the idea that the electron transition is treated as a charge-discharge process of a suggested capacitor with the capacitive energy equal to the energy level difference of the jumping electron. The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency. The quantized resistance reflects that the damping coefficient of the oscillator is the mean collision frequency of the transition electron. In addition, the first and third order electric susceptibilities based on the oscillator are accordingly quantized. Our simulation of the hydrogen atom emission spectrum based on the proposed method agrees well with the experimental one. Our results exhibits that the one-dimensional oscillator with the quantized impedance may become useful in the estimations of the refractive index and one- or multi-photon absorption coefficients of some nonmagnetic media composed of hydrogen-like atoms.

Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom

Science.gov (United States)

Plenio, M. B.; Hartley, J.; Eisert, J.

2004-03-01

We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally.

Harmonic engine

Science.gov (United States)

Bennett, Charles L [Livermore, CA

2009-10-20

A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.

Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator

Science.gov (United States)

Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan

2018-01-01

The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.

Coupled Langmuir oscillations in 2-dimensional quantum plasmas

International Nuclear Information System (INIS)

Akbari-Moghanjoughi, M.

2014-01-01

In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits

High-order harmonics from bow wave caustics driven by a high-intensity laser

International Nuclear Information System (INIS)

Pirozhkov, A.S.; Kando, M.; Esirkepov, T.Zh.

2012-01-01

We propose a new mechanism of high-order harmonic generation during an interaction of a high-intensity laser pulse with underdense plasma. A tightly focused laser pulse creates a cavity in plasma pushing electrons aside and exciting the wake wave and the bow wave. At the joint of the cavity wall and the bow wave boundary, an annular spike of electron density is formed. This spike surrounds the cavity and moves together with the laser pulse. Collective motion of electrons in the spike driven by the laser field generates high-order harmonics. A strong localization of the electron spike, its robustness to oscillations imposed by the laser field and, consequently, its ability to produce high-order harmonics is explained by catastrophe theory. The proposed mechanism explains the experimental observations of high-order harmonics with the 9 TW J-KAREN laser (JAEA, Japan) and the 120 TW Astra Gemini laser (CLF RAL, UK) [A. S. Pirozhkov, et al., arXiv:1004.4514 (2010); A. S. Pirozhkov et al, AIP Proceedings, this volume]. The theory is corroborated by high-resolution two-and three-dimensional particle-in-cell simulations.

Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

Science.gov (United States)

Volegov, P. L.; Danly, C. R.; Fittinghoff, D.; Geppert-Kleinrath, V.; Grim, G.; Merrill, F. E.; Wilde, C. H.

2017-11-01

Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this paper, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.

Nonlinear effects in microwave photoconductivity of two-dimensional electron systems

International Nuclear Information System (INIS)

Ryzhii, V; Suris, R

2003-01-01

We present a model for microwave photoconductivity of two-dimensional electron systems in a magnetic field which describes the effects of strong microwave and steady-state electric fields. Using this model, we derive an analytical formula for the photoconductivity associated with photon- and multi-photon-assisted impurity scattering as a function of the frequency and power of microwave radiation. According to the developed model, the microwave conductivity is an oscillatory function of the frequency of microwave radiation and the cyclotron frequency which becomes zero at the cyclotron resonance and its harmonics. It exhibits maxima and minima (with absolute negative conductivity) at microwave frequencies somewhat different from the resonant frequencies. The calculated power dependence of the amplitude of the microwave photoconductivity oscillations exhibits pronounced sublinear behaviour similar to a logarithmic function. The height of the microwave photoconductivity maxima and the depth of its minima are nonmonotonic functions of the electric field. The possibility of a strong widening of the maxima and minima due to a strong sensitivity of their parameters on the electric field and the presence of strong long-range electric-field fluctuations is pointed to. The obtained dependences are consistent with the results of the experimental observations

Water flow patterns induced by bridge oscillation of magnetic fluid between two permanent magnets subjected to alternating magnetic field

International Nuclear Information System (INIS)

Sudo, Seiichi; Yamamoto, Kazuki; Ishimoto, Yukitaka; Nix, Stephanie

2017-01-01

This paper describes the characteristics of water flow induced by the bridge oscillation of magnetic fluid between two permanent magnets subject to an external alternating magnetic field. The magnetic fluid bridge is formed in the space between a pair of identical coaxial cylindrical permanent magnets submerged in water. The direction of alternating magnetic field is parallel /antiparallel to the magnetic field produced by two permanent magnets. The magnetic fluid bridge responds to the external alternating magnetic field with harmonic oscillation. The oscillation of magnetic fluid bridge generates water flow around the bridge. Water flow is visualized using a thin milk film at the container bottom. Water flows are observed with a high-speed video camera analysis system. The experimental results show that the flow pattern induced by the bridge oscillation depends on the Keulegan–Carpenter number.

Water flow patterns induced by bridge oscillation of magnetic fluid between two permanent magnets subjected to alternating magnetic field

Energy Technology Data Exchange (ETDEWEB)

Sudo, Seiichi, E-mail: sudo@akita-pu.ac.jp [Faculty of Systems Science and Technology, Akita Prefectural University, Ebinokuchi 84-4, Yurihonjo 015-0055 (Japan); Yamamoto, Kazuki [Graduate School of Engineering, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577 (Japan); Ishimoto, Yukitaka; Nix, Stephanie [Faculty of Systems Science and Technology, Akita Prefectural University, Ebinokuchi 84-4, Yurihonjo 015-0055 (Japan)

2017-06-01

This paper describes the characteristics of water flow induced by the bridge oscillation of magnetic fluid between two permanent magnets subject to an external alternating magnetic field. The magnetic fluid bridge is formed in the space between a pair of identical coaxial cylindrical permanent magnets submerged in water. The direction of alternating magnetic field is parallel /antiparallel to the magnetic field produced by two permanent magnets. The magnetic fluid bridge responds to the external alternating magnetic field with harmonic oscillation. The oscillation of magnetic fluid bridge generates water flow around the bridge. Water flow is visualized using a thin milk film at the container bottom. Water flows are observed with a high-speed video camera analysis system. The experimental results show that the flow pattern induced by the bridge oscillation depends on the Keulegan–Carpenter number.

Friedel oscillations in one-dimensional metals: From Luttinger's theorem to the Luttinger liquid

International Nuclear Information System (INIS)

Vieira, Daniel; Freire, Henrique J.P.; Campo, V.L.; Capelle, K.

2008-01-01

Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe-Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations

Some comparison of two fractional oscillators

International Nuclear Information System (INIS)

Kang Yonggang; Zhang Xiu'e

2010-01-01

The other form of fractional oscillator equation comparing to the widely discussed one is ushered in. The properties of vibration of two fractional oscillators are discussed under the influence of different initial conditions. The interpretation of the characteristics of the fractional oscillators using different method is illustrated. Based on two fractional oscillator equations, two linked bodies and the continuous system are studied.

Synchronization effects in two coupled one-dimensional lattices of phase oscillators

International Nuclear Information System (INIS)

Pando L, Carlos L.

2001-03-01

We study synchronization effects in a model consisting of two identical unidirectionally coupled 1-D arrays of phase oscillators. The master array is in the spatio-temporal chaos regime and the coupling across the two arrays is not strong enough in order to reach complete synchronization. The time series of the distance between the arrays is the main object of our study and this shows on-off intermittency. We can approximate the dynamics of the aforementioned time series with that of a first-order Markov process with two symbols. This model can be implemented in arrays of phase-locked loops (PPL) and Josephson junctions. (author)

Transport properties and giant Shubnikov-de Haas oscillations in the first organic conductor with metal complex anion containing selenocyanate ligand, (ET)2TlHg(SeCN)4

International Nuclear Information System (INIS)

Laukhin, V.N.; Audouard, A.; Rakoto, H.; Broto, J.M.; Goze, F.; Coffe, G.; Brossard, L.; Redoules, J.P.; Kartsovnik, M.V.; Kushch, N.D.; Buravov, L.I.; Khomenko, A.G.; Yagubskii, E.B.; Askenazy, S.; Pari, P.

1995-01-01

Temperature dependence of the resistivity in various crystallographic directions and high pulsed field magnetoresistance of organic metal α-(ET) 2 TlHg(SeCN) 4 have been studied at temperatures down to 80 mK. Giant Shubnikov-de Haas oscillations, which are attributed to the two-dimensional nature of the cylindrical Fermi surface with a very small warping along the direction of the lowest conductivity have been observed. Four harmonics of the fast oscillations with fundamental frequency F 0 =653±3 T and slow frequency oscillations with F s =38±5 T have been revealed. (orig.)

Energy spectrum inverse problem of q-deformed harmonic oscillator and entanglement of composite bosons

Science.gov (United States)

Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

2017-06-01

Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.

Approaching Resonant Absorption of Environmental Xenobiotics Harmonic Oscillation by Linear Structures

Directory of Open Access Journals (Sweden)

Cornelia A. Bulucea

2012-03-01

Full Text Available Over the last several decades, it has become increasingly accepted that the term xenobiotic relates to environmental impact, since environmental xenobiotics are understood to be substances foreign to a biological system, which did not exist in nature before their synthesis by humans. In this context, xenobiotics are persistent pollutants such as dioxins and polychlorinated biphenyls, as well as plastics and pesticides. Dangerous and unstable situations can result from the presence of environmental xenobiotics since their harmful effects on humans and ecosystems are often unpredictable. For instance, the immune system is extremely vulnerable and sensitive to modulation by environmental xenobitics. Various experimental assays could be performed to ascertain the immunotoxic potential of environmental xenobiotics, taking into account genetic factors, the route of xenobiotic penetration, and the amount and duration of exposure, as well as the wave shape of the xenobiotic. In this paper, we propose an approach for the analysis of xenobiotic metabolism using mathematical models and corresponding methods. This study focuses on a pattern depicting mathematically modeled processes of resonant absorption of a xenobiotic harmonic oscillation by an organism modulated as an absorbing oscillator structure. We represent the xenobiotic concentration degree through a spatial concentration vector, and we model and simulate the oscillating regime of environmental xenobiotic absorption. It is anticipated that the results could be used to facilitate the assessment of the processes of environmental xenobiotic absorption, distribution, biotransformation and removal within the framework of compartmental analysis, by establishing appropriate mathematical models and simulations.

On bunch lengthening using the fourth harmonic cavity in the NSLS VUV ring

International Nuclear Information System (INIS)

Wachtel, J.M.

1988-02-01

It has been suggested that the phase of the beam excited voltage in the harmonic cavity can be controlled by detuning its resonant frequency from the beam current harmonic. Unfortunately the detuning needed to flatten the acceleration waveform also corresponds to the region of Robinson instability for the harmonic cavity. Therefore, lengthening the bunch may be followed by large amplitude synchrotron oscillation of the bunch center of mass. Bunch lengthening is discussed in this note from several points of view. There follows a simple review of single electron oscillations in a quartic potential. Then equations are developed for the coupled oscillations of a cavity and a rigid bunch as a fully nonlinear, time dependent initial value problem. Next, a computer program that solves these equations for one, two or more cavities, with and without externally driven fields, is described and some simulations of the harmonic cavity interaction are shown. Finally, the fully nonlinear equations are linearized to derive a dispersion relation for the case of beam excitation in the harmonic cavity. 6 refs., 5 figs

Harmonic synchronization in resistively coupled Josephson junctions

International Nuclear Information System (INIS)

Blackburn, J.A.; Gronbech-Jensen, N.; Smith, H.J.T.

1994-01-01

The oscillations of two resistively coupled Josephson junctions biased only by a single dc current source are shown to lock harmonically in a 1:2 mode over a significant range of bias current, even when the junctions are identical. The dependence of this locking on both junction and coupling parameters is examined, and it is found that, for this particular two-junction configuration, 1:1 locking can never occur, and also that a minimum coupling coefficient is needed to support harmonic locking. Some issues related to subharmonic locking are also discussed

Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

Directory of Open Access Journals (Sweden)

Jinghao Zhu

2015-11-01

Full Text Available A quantized impedance is proposed to theoretically establish the relationship between the atomic eigenfrequency and the intrinsic frequency of the one-dimensional oscillator in this paper. The classical oscillator is modified by the idea that the electron transition is treated as a charge-discharge process of a suggested capacitor with the capacitive energy equal to the energy level difference of the jumping electron. The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency. The quantized resistance reflects that the damping coefficient of the oscillator is the mean collision frequency of the transition electron. In addition, the first and third order electric susceptibilities based on the oscillator are accordingly quantized. Our simulation of the hydrogen atom emission spectrum based on the proposed method agrees well with the experimental one. Our results exhibits that the one-dimensional oscillator with the quantized impedance may become useful in the estimations of the refractive index and one- or multi-photon absorption coefficients of some nonmagnetic media composed of hydrogen-like atoms.

High spin rotations of nuclei with the harmonic oscillator potential

International Nuclear Information System (INIS)

Cerkaski, M.; Szymanski, Z.

1978-01-01

Calculations of the nuclear properties at high angular momentum have been performed recently. They are based on the liquid drop model of a nucleus and/or on the assumption of the single particle shell structure of the nucleonic motion. The calculations are usually complicated and involve long computer codes. In this article we shall discuss general trends in fast rotating nuclei in the approximation of the harmonic oscillator potential. We shall see that using the Bohr Mottelson simplified version of the rigorous solution of Valatin one can perform a rather simple analysis of the rotational bands, structure of the yrast line, moments of inertia etc. in the rotating nucleus. While the precision fit to experimental data in actual nuclei is not the purpose of this paper, one can still hope to reach some general understanding within the model of the simple relations resulting in nuclei at high spin. (author)

Tunneling ionization and harmonic generation in two-color fields

International Nuclear Information System (INIS)

Kondo, K.; Kobayashi, Y.; Sagisaka, A.; Nabekawa, Y.; Watanabe, S.

1996-01-01

Tunneling ionization and harmonic generation in two-color fields were studied with a fundamental beam (ω) and its harmonics (2ω,3ω), which were generated by a 100-fs Ti:sapphire laser. Ion yields of atoms and molecules were successfully controlled by means of a change in the relative phase between ω and 3ω pulses. Two-color interference was clearly observed in photoelectron spectra and harmonic spectra. In the ω endash 2ω field even-order harmonics were observed in which the intensity was almost equal to that of the odd harmonics because of an asymmetric optical field. These results were compared with the quasi-static model for ionization and with the quantum theory for harmonic generation. copyright 1996 Optical Society of America

Dynamic hysteresis behaviors for the two-dimensional mixed spin (2, 5/2) ferrimagnetic Ising model in an oscillating magnetic field

Science.gov (United States)

Ertaş, Mehmet

2015-09-01

Keskin and Ertaş (2009) presented a study of the magnetic properties of a mixed spin (2, 5/2) ferrimagnetic Ising model within an oscillating magnetic field. They employed dynamic mean-field calculations to find the dynamic phase transition temperatures, the dynamic compensation points of the model and to present the dynamic phase diagrams. In this work, we extend the study and investigate the dynamic hysteresis behaviors for the two-dimensional (2D) mixed spin (2, 5/2) ferrimagnetic Ising model on a hexagonal lattice in an oscillating magnetic field within the framework of dynamic mean-field calculations. The dynamic hysteresis curves are obtained for both the ferromagnetic and antiferromagnetic interactions and the effects of the Hamiltonian parameters on the dynamic hysteresis behaviors are discussed in detail. The thermal behaviors of the coercivity and remanent magnetizations are also investigated. The results are compared with some theoretical and experimental works and a qualitatively good agreement is found. Finally, the dynamic phase diagrams depending on the frequency of an oscillating magnetic field in the plane of the reduced temperature versus magnetic field amplitude is examined and it is found that the dynamic phase diagrams display richer dynamic critical behavior for higher values of frequency than for lower values.

Benchmark Calculation of Radial Expectation Value for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators

International Nuclear Information System (INIS)

Yu, Rong Mei; Zan, Li Rong; Jiao, Li Guang; Ho, Yew Kam

2017-01-01

Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies. (author)

Classical and multilinear harmonic analysis

CERN Document Server

Muscalu, Camil

2013-01-01

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this vo...

Gradient formula for the four-dimensional hyperspherical harmonics

International Nuclear Information System (INIS)

Santos, M.B.

1975-01-01

The gradient formula for the hyperspherical harmonics in 4 dimensions is derived, a result which is here obtainned in two distinct ways: either by differentiation of a closed expression for the hyperspherical harmonics or by making use of the Wigner-Eckart theorem for the R 4 group. The result is useful for physical applications in view of the significance of the R 4 group in several physical problems [pt

Entanglement entropy in the quantum networks of a coupled quantum harmonic oscillator

International Nuclear Information System (INIS)

Jafarizadeh, M A; Nami, S; Eghbalifam, F

2015-01-01

We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a network are calculated.In partitioning an arbitrary graph into two parts there are some nodes in each part which are not connected to the nodes of the other part. So, these nodes of each part can be in distinct subsets. Therefore, the graph is separated into four subsets. The nodes of the first and last subsets are those which are not connected to the nodes of the other part. In theorem 1, by using the generalized Schur complement method in these four subsets, we prove that all the graphs whose connections between the two alternative subsets are complete, have the same entropy. A large number of graphs satisfy this theorem. Then the entanglement entropy in the limit of the large coupling and large size of the system is investigated in these graphs. Also, the asymptotic behaviors of the Schmidt numbers and entanglement entropy in the limit of infinite coupling are shown.One important quantity about partitioning is the conductance of the graph. The conductance of the graph is considered in various graphs. In these graphs we compare the conductance of the graph and the entanglement entropy. (paper)

Transport properties and giant Shubnikov-de Haas oscillations in the first organic conductor with metal complex anion containing selenocyanate ligand, (ET){sub 2}TlHg(SeCN){sub 4}

Energy Technology Data Exchange (ETDEWEB)

Laukhin, V.N. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France)]|[Institute of Chemical Physics in Chernogolovka, Russian Academy of Sciences, Chernogolovka, MD 142432 (Russian Federation); Audouard, A. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Rakoto, H. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Broto, J.M. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Goze, F. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Coffe, G. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Brossard, L. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Redoules, J.P. [Service National des Champs Magnetiques Pulses du CNRS et Laboratoire de Physique des Solides, URA CNRS 074, Complexe Scientifique de Rangueil, 31077 Toulouse (France); Kartsovnik, M.V. [Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, MD 142432 (Russian Federation); Kushch, N.D. [Institute of Chemical Physics in Chernogolovka, Russian Academy of Sciences, Chernogolovka, MD 142432 (Russian Federation); Buravov, L.I.

1995-05-01

Temperature dependence of the resistivity in various crystallographic directions and high pulsed field magnetoresistance of organic metal {alpha}-(ET){sub 2}TlHg(SeCN){sub 4} have been studied at temperatures down to 80 mK. Giant Shubnikov-de Haas oscillations, which are attributed to the two-dimensional nature of the cylindrical Fermi surface with a very small warping along the direction of the lowest conductivity have been observed. Four harmonics of the fast oscillations with fundamental frequency F{sub 0}=653{+-}3 T and slow frequency oscillations with F{sub s}=38{+-}5 T have been revealed. (orig.).

A position-dependent mass harmonic oscillator and deformed space

Science.gov (United States)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Classical and quantum mechanics of the damped harmonic oscillator

International Nuclear Information System (INIS)

Dekker, H.

1981-01-01

The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of the problem are discussed on the basis of Havas' classical Hamiltonian and the quantum mechanical Suessmann-Hasse-Albrecht models as coined by the Muenchen/Garching nuclear physics group. It is then shown how by imposing a restriction on the classical trajectories in order to connect the Hamiltonian with the energy, the time-independent Bateman-Morse-Feshbach-Bopp Hamiltonian leads to the time-dependent Caldirola-Kanai Hamiltonian. Canonical quantization of either formulation entails a violation of Heisenberg's principle. By means of a unified treatment of both the electrical and mechanical semi-infinite transmission line, this defect is related to the disregard of additional quantum fluctuations that are intrinsically connected with the dissipation. The difficulties of these models are discussed. Then it is proved that the Bateman dual Hamiltonian is connected to a recently developed complex symplectic formulation by a simple canonical transformation. (orig.)

The Tucson-Melbourne Three-Body Force in a Translationally-Invariant Harmonic Oscillator Basis

Science.gov (United States)

Marsden, David; Navratil, Petr; Barrett, Bruce

2000-09-01

A translationally-invariant three-body basis set has been employed in shell model calculations on ^3H and ^3He including the Tucson-Melbourne form of the real nuclear three-body force. The basis consists of harmonic oscillators in Jacobi coordinates, explicitly avoiding the centre of mass drift problem in the calculations. The derivation of the three-body matrix elements and the results of large basis effective interaction shell model calculations will be presented. J. L. Friar, B. F. Gibson, G. L. Payne and S. A. Coon; Few Body Systems 5, 13 (1988) P. Navratil, G.P. Kamuntavicius and B.R. Barrett; Phys. Rev. C. 61, 044001 (2000)

A new look at the quantum mechanics of the harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Kastrup, H.A.

2006-12-15

At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to

An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth

Directory of Open Access Journals (Sweden)

Marcin Salamaga

2013-09-01

Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.

Born-Oppenheimer description of two atoms in a combined oscillator and lattice trap

DEFF Research Database (Denmark)

Sørensen, Ole Søe; Mølmer, Klaus

2012-01-01

We analyze the quantum states of two identical bosons in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest-neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We sho...... that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motions validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motions in molecules....

Two-and-one-half-dimensional magnetohydrodynamic simulations of the plasma sheet in the presence of oxygen ions: The plasma sheet oscillation and compressional Pc 5 waves

International Nuclear Information System (INIS)

Lu Li; Liu Zhenxing; Cao Jinbin

2002-01-01

Two-and-one-half-dimensional magnetohydrodynamic simulations of the multicomponent plasma sheet with the velocity curl term in the magnetic equation are represented. The simulation results can be summarized as follows: (1) There is an oscillation of the plasma sheet with the period on the order of 400 s (Pc 5 range); (2) the magnetic equator is a node of the magnetic field disturbance; (3) the magnetic energy integral varies antiphase with the internal energy integral; (4) disturbed waves have a propagating speed on the order of 10 km/s earthward; (5) the abundance of oxygen ions influences amplitude, period, and dissipation of the plasma sheet oscillation. It is suggested that the compressional Pc 5 waves, which are observed in the plasma sheet close to the magnetic equator, may be caused by the plasma sheet oscillation, or may be generated from the resonance of the plasma sheet oscillation with some Pc 5 perturbation waves coming from the outer magnetosphere

Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA

Science.gov (United States)

Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M.

2016-09-01

Aims: We consider a coronal loop kink oscillation observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics. Methods: We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the displacement is fitted as the sum of two damped sinusoids, having periods P1 and P2, and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs. Results: We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P1 = 5.00±0.62 min, P2 = 2.20±0.23 min, P1/ 2P2 = 1.15±0.22, and τ/P = 3.35 ± 1.45. A movie associated to Fig. 5 is available in electronic form at http://www.aanda.org

Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling

DEFF Research Database (Denmark)

Marchukov, O. V.; Fedorov, D. V.; Jensen, A. S.

2015-01-01

We investigate a two-dimensional system of fermions with two internal (spin) degrees of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body short range repulsion. We obtain self-consistent mean-field $N...

Wake structure and thrust generation of a flapping foil in two-dimensional flow

DEFF Research Database (Denmark)

Andersen, Anders Peter; Bohr, Tomas; Schnipper, Teis

2017-01-01

We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream. We explore pure pitching and pure heaving, and contrast these two generic types of kinematics. We compare...... measurements and simulations when the foil is forced with pitching oscillations, and we find a close correspondence between flow visualisations using thickness variations in the soap film and the numerically determined vortex structures. Numerically, we determine wake maps spanned by oscillation frequency...

Investigation of Student Reasoning about Harmonic Motions

Science.gov (United States)

Tongnopparat, N.; Poonyawatpornkul, J.; Wattanakasiwich, P.

This study aimed to investigate student reasoning about harmonic oscillations. We conducted a semi-structured interview based on three situations of harmonic motions—(1) a mass attaching to spring and horizontally oscillating without damping, (2) the same situation but vertically oscillating and (3) a mass attaching to spring and oscillating in viscous liquid. Forty-five second-year students taking a vibrations and wave course at Chiang Mai University, Thailand participated in a fifteen-minute interview, which was video-recorded. The videos were transcribed and analyzed by three physics instructors. As results, we found that most students had misconceptions about angular frequency and energy mostly in the second and third situations.

The harmonic oscillator in the forceless mechanics of Hertz and in the Riemannian space-time geometry

International Nuclear Information System (INIS)

Fueloep, L.

1987-10-01

The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)

Magnetic anisotropy of two-dimensional nanostructures: Transition-metal triangular stripes

International Nuclear Information System (INIS)

Dorantes-Davila, J.; Villasenor-Gonzalez, P.; Pastor, G.M.

2005-01-01

The magnetic anisotropy energy (MAE) of one-dimensional stripes having infinite length and triangular lateral structure are investigated in the framework of a self-consistent tight-binding method. One observes discontinuous changes in the easy magnetization direction along the crossover from one to two dimensions. The MAE oscillates as a function of stripe width and depends strongly on the considered transition metal (TM). The MAE of the two-leg ladder is strongly reduced as compared to that of the monoatomic chain and the convergence to the two-dimensional limit is rather slow

Relativistic Bosons in Time-Harmonic Electric Fields

Science.gov (United States)

Buhucianu, Ovidiu; Dariescu, Marina-Aura; Dariescu, Ciprian

2012-02-01

In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field and a static magnetic induction, both directed along the normal to the sample's plane. The Klein-Gordon equation describing the relativistic bosons leads to a Mathieu's type equation for the temporal part of the wave functions. It follows that, for the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic stationary amplitude behavior.

High efficiency fourth-harmonic generation from nanosecond fiber master oscillator power amplifier

Science.gov (United States)

Mu, Xiaodong; Steinvurzel, Paul; Rose, Todd S.; Lotshaw, William T.; Beck, Steven M.; Clemmons, James H.

2016-03-01

We demonstrate high power, deep ultraviolet (DUV) conversion to 266 nm through frequency quadrupling of a nanosecond pulse width 1064 nm fiber master oscillator power amplifier (MOPA). The MOPA system uses an Yb-doped double-clad polarization-maintaining large mode area tapered fiber as the final gain stage to generate 0.5-mJ, 10 W, 1.7- ns single mode pulses at a repetition rate of 20 kHz with measured spectral bandwidth of 10.6 GHz (40 pm), and beam qualities of Mx 2=1.07 and My 2=1.03, respectively. Using LBO and BBO crystals for the second-harmonic generation (SHG) and fourth-harmonic generation (FHG), we have achieved 375 μJ (7.5 W) and 92.5 μJ (1.85 W) at wavelengths of 532 nm and 266 nm, respectively. To the best of our knowledge these are the highest narrowband infrared, green and UV pulse energies obtained to date from a fully spliced fiber amplifier. We also demonstrate high efficiency SHG and FHG with walk-off compensated (WOC) crystal pairs and tightly focused pump beam. An SHG efficiency of 75%, FHG efficiency of 47%, and an overall efficiency of 35% from 1064 nm to 266 nm are obtained.

Enhancement of harmonic generation using a two section undulator

International Nuclear Information System (INIS)

Prazeres, R.; Glotin, F.; Jaroszynski, D.A.; Ortega, J.M.; Rippon, C.

1999-01-01

Enhancement of the 2nd and 3rd harmonic of the wavelength of a Free-Electron Laser (FEL) has been measured when a single electron beam is crossing a two-section undulator. To produce the harmonic radiation enhancement, the undulator is arranged so that the resonance wavelength of the 2nd undulator (downstream) matches a harmonic of the 1st undulator (upstream). Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction efficiency, through a hole in one of the cavity mirrors. We present measurements that show that the optical power at the 2nd and 3rd harmonic can be enhanced, by about one order of magnitude, in two configurations: when the resonance wavelength of the 2nd undulator matches the harmonic of 1st one (harmonic configuration), or when the gap of the 2nd undulator is slightly larger than first one (step-tapered configuration). We examine the dependence of the harmonic power on the gap of the 2nd undulator. This fundamental/harmonic mode of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture

Creating tuneable microwave media from a two-dimensional lattice of re-entrant posts

Energy Technology Data Exchange (ETDEWEB)

Goryachev, Maxim; Tobar, Michael E. [ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009 (Australia)

2015-11-28

The potential capabilities of resonators based on two dimensional arrays of re-entrant posts is demonstrated. Such posts may be regarded as magnetically coupled lumped element microwave harmonic oscillators, arranged in a 2D lattices structure, which is enclosed in a 3D cavity. By arranging these elements in certain 2D patterns, we demonstrate how to achieve certain requirements with respect to field localisation and device spectra. Special attention is paid to symmetries of the lattices, mechanical tuning, design of areas of high localisation of magnetic energy; this in turn creates unique discrete mode spectra. We demonstrate analogies between systems designed on the proposed platform and well known physical phenomena such as polarisation, frustration, and Whispering Gallery Modes. The mechanical tunability of the cavity with multiple posts is analysed, and its consequences to optomechanical applications is calculated. One particular application to quantum memory is demonstrated with a cavity design consisting of separate resonators analogous to discrete Fabry–Pérot resonators. Finally, we propose a generalised approach to a microwave system design based on the concept of Programmable Cavity Arrays.

Inverted oscillator

Energy Technology Data Exchange (ETDEWEB)

Yuce, C [Physics Department, Anadolu University, Eskisehir (Turkey); Kilic, A [Physics Department, Anadolu University, Eskisehir (Turkey); Coruh, A [Physics Department, Sakarya University, Sakarya (Turkey)

2006-07-15

The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wavefunction for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete, and the energy is given as a linear function of the quantum number n.

QUANTUM NATURE OF CYCLOTRON HARMONICS IN THERMAL SPECTRA OF NEUTRON STARS

International Nuclear Information System (INIS)

Suleimanov, V. F.; Werner, K.; Pavlov, G. G.

2010-01-01

Some isolated neutron stars (NSs) show harmonically spaced absorption features in their thermal soft X-ray spectra. The interpretation of the features as a cyclotron line and its harmonics has been suggested, but the usual explanation of the harmonics as caused by relativistic effects fails because the relativistic corrections are extremely small in this case. We suggest that the features, known as quantum oscillations, correspond to the peaks in the energy dependence of the free-free opacity in a quantizing magnetic field. The peaks arise when the transitions to new Landau levels become allowed with increasing the photon energy; they are strongly enhanced by the square-root singularities in the phase-space density of quantum states in the case when the free (non-quantized) motion is effectively one dimensional. To explore observable properties of these quantum oscillations, we calculate models of hydrogen NS atmospheres with B ∼ 10 10 -10 11 G (i.e., electron cyclotron energy E c,e ∼ 0.1-1 keV) and T eff = 1-3 MK. Such conditions are thought to be typical for the so-called central compact objects in supernova remnants, such as 1E 1207.4-5209 in PKS 1209-51/52. We show that observable features at the electron cyclotron harmonics form at moderately large values of the quantization parameter, b eff ≡ E c,e /kT eff ≅ 0.5-20. The equivalent widths of the features can reach ∼100-200 eV; they grow with increasing b eff and are lower for higher harmonics.

Theoretical Investigation of Current Instabilities and Terahertz Oscillations in a Two-Dimensional Electron Fluid

National Research Council Canada - National Science Library

Dyakonov, M

1997-01-01

The purpose of this work is to develop further the theory of novel mechanisms for generation and detection of electromagnetic radiation in the terahertz range using the plasma oscillations of the two...

Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein–Gordon lattice

International Nuclear Information System (INIS)

Quan, Xu; Qiang, Tian

2009-01-01

We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein–Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom

Ergodic time-reversible chaos for Gibbs' canonical oscillator

International Nuclear Information System (INIS)

Hoover, William Graham; Sprott, Julien Clinton; Patra, Puneet Kumar

2015-01-01

Nosé's pioneering 1984 work inspired a variety of time-reversible deterministic thermostats. Though several groups have developed successful doubly-thermostated models, single-thermostat models have failed to generate Gibbs' canonical distribution for the one-dimensional harmonic oscillator. A 2001 doubly-thermostated model, claimed to be ergodic, has a singly-thermostated version. Though neither of these models is ergodic this work has suggested a successful route toward singly-thermostated ergodicity. We illustrate both ergodicity and its lack for these models using phase-space cross sections and Lyapunov instability as diagnostic tools. - Highlights: • We develop cross-section and Lyapunov methods for diagnosing ergodicity. • We apply these methods to several thermostatted-oscillator problems. • We demonstrate the nonergodicity of previous work. • We find a novel family of ergodic thermostatted-oscillator problems.

Label-free three-dimensional imaging of cell nucleus using third-harmonic generation microscopy

Energy Technology Data Exchange (ETDEWEB)

Lin, Jian; Zheng, Wei; Wang, Zi; Huang, Zhiwei, E-mail: biehzw@nus.edu.sg [Optical Bioimaging Laboratory, Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore 117576 (Singapore)

2014-09-08

We report the implementation of the combined third-harmonic generation (THG) and two-photon excited fluorescence (TPEF) microscopy for label-free three-dimensional (3-D) imaging of cell nucleus morphological changes in liver tissue. THG imaging shows regular spherical shapes of normal hepatocytes nuclei with inner chromatin structures while revealing the condensation of chromatins and nuclear fragmentations in hepatocytes of diseased liver tissue. Colocalized THG and TPEF imaging provides complementary information of cell nuclei and cytoplasm in tissue. This work suggests that 3-D THG microscopy has the potential for quantitative analysis of nuclear morphology in cells at a submicron-resolution without the need for DNA staining.

Label-free three-dimensional imaging of cell nucleus using third-harmonic generation microscopy

International Nuclear Information System (INIS)

Lin, Jian; Zheng, Wei; Wang, Zi; Huang, Zhiwei

2014-01-01

We report the implementation of the combined third-harmonic generation (THG) and two-photon excited fluorescence (TPEF) microscopy for label-free three-dimensional (3-D) imaging of cell nucleus morphological changes in liver tissue. THG imaging shows regular spherical shapes of normal hepatocytes nuclei with inner chromatin structures while revealing the condensation of chromatins and nuclear fragmentations in hepatocytes of diseased liver tissue. Colocalized THG and TPEF imaging provides complementary information of cell nuclei and cytoplasm in tissue. This work suggests that 3-D THG microscopy has the potential for quantitative analysis of nuclear morphology in cells at a submicron-resolution without the need for DNA staining.

The one-dimensional Gross-Pitaevskii equation and its some excitation states

Energy Technology Data Exchange (ETDEWEB)

Prayitno, T. B., E-mail: trunk-002@yahoo.com [Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jl. Pemuda Rawamangun no. 10, Jakarta, 13220 (Indonesia)

2015-04-16

We have derived some excitation states of the one-dimensional Gross-Pitaevskii equation coupled by the gravitational potential. The methods that we have used here are taken by pursuing the recent work of Kivshar et. al. by considering the equation as a macroscopic quantum oscillator. To obtain the states, we have made the appropriate transformation to reduce the three-dimensional Gross-Pitaevskii equation into the one-dimensional Gross-Pitaevskii equation and applying the time-independent perturbation theory in the general solution of the one-dimensional Gross-Pitaevskii equation as a linear superposition of the normalized eigenfunctions of the Schrödinger equation for the harmonic oscillator potential. Moreover, we also impose the condition by assuming that some terms in the equation should be so small in order to preserve the use of the perturbation method.

Oscillation of two-dimensional linear second-order differential systems

International Nuclear Information System (INIS)

Kwong, M.K.; Kaper, H.G.

1985-01-01

This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references

The structure of the Hamiltonian in a finite-dimensional formalism based on Weyl's quantum mechanics

International Nuclear Information System (INIS)

Santhanam, T.S.; Madivanane, S.

1982-01-01

Any discussion on finite-dimensional formulation of quantum mechanics involves the Sylvester matrix (finite Fourier transform). In the usual formulation, a remarkable relation exists that gives the Fourier transform as the exponential of the Hamiltonian of a simple harmonic oscillator. In this paper, assuming that such a relation holds also in the finite dimensional case, we extract the logarithm of the Sylvester matrix and in some cases this can be interpreted as the Hamiltonian of the truncated oscillator. We calculate the Hamiltonian matrix explicitly for some special cases of n = 3,4. (author)

Series expansion of two-dimensional fields produced by iron-core magnets

International Nuclear Information System (INIS)

Satoh, Kotaro.

1997-02-01

This paper discusses the validity of a series expansion of two-dimensional magnetic fields with harmonic functions, and suggests that the series may not converge outside of the pole gap. It also points out that this difficulty may appear due to a slow convergence of the series near to the pole edge, even within the convergent area. (author)

Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

Energy Technology Data Exchange (ETDEWEB)

Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com [Physics Department, Sebelas Maret University, Jl. Ir. Sutami no 36A Kentingan Surakarta 57126 (Indonesia)

2014-09-30

Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

Nonlinear response of a forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two

International Nuclear Information System (INIS)

Ji, J.C.; Zhang, N.

2009-01-01

Non-resonant bifurcations of codimension two may appear in the controlled van der Pol-Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation.

3D Oscillator and Coulomb Systems reduced from Kahler spaces

OpenAIRE

Nersessian, Armen; Yeranyan, Armen

2003-01-01

We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kahler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid are originated. Then we construct the superintegrable oscillator system on three-dimensional sphere and ...

Kerr-like behaviour of second harmonic generation in the far-off resonant regime

Science.gov (United States)

Peřinová, Vlasta; Lukš, Antonín; Křepelka, Jaromír; Leoński, Wiesław; Peřina, Jan

2018-05-01

We separate the Kerr-like behaviour of the second-harmonic generation in the far-off resonant regime from the oscillations caused by the time-dependence of the interaction energy. To this purpose, we consider the approximation obtained from the exact dynamics by the method of small rotations. The Floquet-type decomposition of the approximate dynamics comprises the Kerr-like dynamics and oscillations of the same order of magnitude as those assumed for the exact dynamics of the second-harmonic generation. We have found that a superposition of two states of concentrated quantum phase arises in the fundamental mode in the second-harmonic generation in the far-off resonant limit at a later time than a superposition of two coherent states in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes. The quantum phase fluctuation is higher for the same initial coherent amplitudes in the fundamental mode in the second-harmonic generation in the far-off resonant limit than in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes.

Analytic energies and wave functions of the two-dimensional Schrodinger equation: ground state of two-dimensional quartic potential and classification of solutions

Czech Academy of Sciences Publication Activity Database

Tichý, V.; Kuběna, Aleš Antonín; Skála, L.

2012-01-01

Roč. 90, č. 6 (2012), s. 503-513 ISSN 0008-4204 Institutional support: RVO:67985556 Keywords : Schroninger equation * partial differential equation * analytic solution * anharmonic oscilator * double-well Subject RIV: BE - Theoretical Physics Impact factor: 0.902, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kubena-analytic energies and wave functions of the two-dimensional schrodinger equation.pdf

New SU(1,1) position-dependent effective mass coherent states for a generalized shifted harmonic oscillator

International Nuclear Information System (INIS)

Yahiaoui, Sid-Ahmed; Bentaiba, Mustapha

2014-01-01

A new SU(1,1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM systems and a new set of operators that close the su(1,1) Lie algebra are constructed, being the PDEM CS of the basis for its unitary irreducible representation. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut–Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. As an illustration of our procedure, we depicted the 2D-probability density in the PDEM CS for SHO with the explicit form of the mass distribution with no singularities. (paper)

Two particle states, lepton mixing and oscillations

CERN Document Server

Kachelriess, M; Schönert, S

2000-01-01

Discussions of lepton mixing and oscillations consider generally only flavor oscillations of neutrinos and neglect the accompanying charged leptons. In cases of experimental interest like pion or nuclear beta decay an oscillation pattern is expected indeed only for neutrinos if only one of the two produced particles is observed. We argue that flavor oscillations of neutrinos without detecting the accompanying lepton is a peculiarity of the two-particle states $|l\

Decay of homogeneous two-dimensional quantum turbulence

Science.gov (United States)

Baggaley, Andrew W.; Barenghi, Carlo F.

2018-03-01

We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile, and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, Nv, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law Nv˜t-1 /3 where t is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.

Muonic molecular ions p p μ and p d μ driven by superintense VUV laser pulses: Postexcitation muonic and nuclear oscillations and high-order harmonic generation

Science.gov (United States)

Paramonov, Guennaddi K.; Saalfrank, Peter

2018-05-01

The non-Born-Oppenheimer quantum dynamics of p p μ and p d μ molecular ions excited by ultrashort, superintense VUV laser pulses polarized along the molecular axis (z ) is studied by the numerical solution of the time-dependent Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance R and muon coordinates z and ρ , a transversal degree of freedom. It is shown that in both p p μ and p d μ , muons approximately follow the applied laser field out of phase. After the end of the laser pulse, expectation values , , and demonstrate "post-laser-pulse" oscillations in both p p μ and p d μ . In the case of p d μ , the post-laser-pulse oscillations of and appear as shaped "echo pulses." Power spectra, which are related to high-order harmonic generation (HHG), generated due to muonic and nuclear motion are calculated in the acceleration form. For p d μ it is found that there exists a unique characteristic frequency ωoscp d μ representing both frequencies of post-laser-pulse muonic oscillations and the frequency of nuclear vibrations, which manifest themselves by very sharp maxima in the corresponding power spectra of p d μ . The homonuclear p p μ ion does not possess such a unique characteristic frequency. The "exact" dynamics and power, and HHG spectra of the 3D model are compared with a Born-Oppenheimer, fixed-nuclei model featuring interesting differences: postpulse oscillations are absent and HHG spectra are affected indirectly or directly by nuclear motion.

Polarization-Resolved Study of High Harmonics from Bulk Semiconductors

Science.gov (United States)

Kaneshima, Keisuke; Shinohara, Yasushi; Takeuchi, Kengo; Ishii, Nobuhisa; Imasaka, Kotaro; Kaji, Tomohiro; Ashihara, Satoshi; Ishikawa, Kenichi L.; Itatani, Jiro

2018-06-01

The polarization property of high harmonics from gallium selenide is investigated using linearly polarized midinfrared laser pulses. With a high electric field, the perpendicular polarization component of the odd harmonics emerges, which is not present with a low electric field and cannot be explained by the perturbative nonlinear optics. A two-dimensional single-band model is developed to show that the anisotropic curvature of an energy band of solids, which is pronounced in an outer part of the Brillouin zone, induces the generation of the perpendicular odd harmonics. This model is validated by three-dimensional quantum mechanical simulations, which reproduce the orientation dependence of the odd-order harmonics. The quantum mechanical simulations also reveal that the odd- and even-order harmonics are produced predominantly by the intraband current and interband polarization, respectively. These experimental and theoretical demonstrations clearly show a strong link between the band structure of a solid and the polarization property of the odd-order harmonics.

Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

DEFF Research Database (Denmark)

V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.

2014-01-01

We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin......-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner...... distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding...

Entanglement of higher-derivative oscillators in holographic systems

Energy Technology Data Exchange (ETDEWEB)

Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)

2017-05-15

We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.

Three-dimensional chimera patterns in networks of spiking neuron oscillators

Science.gov (United States)

Kasimatis, T.; Hizanidis, J.; Provata, A.

2018-05-01

We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.

Harmonic analysis on local fields and adelic spaces. I

International Nuclear Information System (INIS)

Osipov, D V; Parshin, A N

2008-01-01

We develop harmonic analysis on the objects of a category C 2 of infinite-dimensional filtered vector spaces over a finite field. This category includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. As the main result, we construct the theory of the Fourier transform on these objects and obtain two-dimensional Poisson formulae

Two-Dimensional Homogeneous Fermi Gases

Science.gov (United States)

Hueck, Klaus; Luick, Niclas; Sobirey, Lennart; Siegl, Jonas; Lompe, Thomas; Moritz, Henning

2018-02-01

We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.

Synchronization in Coupled Oscillators with Two Coexisting Attractors

International Nuclear Information System (INIS)

Han-Han, Zhu; Jun-Zhong, Yang

2008-01-01

Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Duffing oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions. (general)

The pseudo-harmonics method: an application involving perturbations caused by control rod insertion in PWR reactors

International Nuclear Information System (INIS)

Claro, L.H.; Alvim, A.C.M.; Thome, Z.D.

1988-08-01

The objective of this work is to stydy the effect of intense perturbations, such as control rod insertion in the core of PWR reactors, through a perturbation approach consisting of a modified version of the pseudo-harmonics method. A typical one-dimensional PWR reactor model was used as a reference state, from which two perturbations were imposed, simulation gray and black control rod insertion. In the first case, eigenvalue convergence was achieved with the eighth order of approximation approximation and perturbed fluxes and eigenvalue estimates agreed very well with direct calculation results. The second case tested represents a very intense localized perturbation. Oscillation in keff were observed er of approximation increased and the method failed to converge. Results obtained indicate that the pseudo-harmonics method can be used to compute 2 group fluxes and fundamental eigenvalue of perturbated states resulting from gray control rod insertion in PWR reactors. The method is limited, however, by perturbation intensity, as other perturbation methods are. (author) [pt

Considerations on 'Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring'

International Nuclear Information System (INIS)

Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.

2009-01-01

In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.

An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method

International Nuclear Information System (INIS)

Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.

2009-01-01

The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.

Two-harmonic complex spectral-domain optical coherence tomography using achromatic sinusoidal phase modulation

Science.gov (United States)

Lu, Sheng-Hua; Huang, Siang-Ru; Chou, Che-Chung

2018-03-01

We resolve the complex conjugate ambiguity in spectral-domain optical coherence tomography (SD-OCT) by using achromatic two-harmonic method. Unlike previous researches, the optical phase of the fiber interferometer is modulated by an achromatic phase shifter based on an optical delay line. The achromatic phase modulation leads to a wavelength-independent scaling coefficient for the two harmonics. Dividing the mean absolute value of the first harmonic by that of the second harmonic in a B-scan interferogram directly gives the scaling coefficient. It greatly simplifies the determination of the magnitude ratio between the two harmonics without the need of third harmonic and cumbersome iterative calculations. The inverse fast Fourier transform of the complex-valued interferogram constructed with the scaling coefficient, first and second harmonics yields a full-range OCT image. Experimental results confirm the effectiveness of the proposed achromatic two-harmonic technique for suppressing the mirror artifacts in SD-OCT images.

Experimental studies of stability and amplification in a two-cavity second harmonic gyroklystron

International Nuclear Information System (INIS)

Matthews, H.W.; Lawson, W.; Calame, J.P.; Flaherty, M.K.E.; Hogan, B.; Cheng, J.; Latham, P.E.

1994-01-01

Future electron-positron supercolliders will require efficient RF amplifiers in the 10--20 GHz range with peak powers well above the current state of the art. To close this gap, several approaches have received considerable attention in the past few years. Here, the authors report the operating characteristics of a sequence of two-cavity second harmonic gyroklystrons which are derived in part from a previous fundamental tube and utilize output cavities which resonate at twice the drive frequency. They present results from the design simulations as well as details of the stable range of operating parameters. While the harmonic tube is somewhat more susceptible to spurious oscillations and more sensitive to parameter variations than the fundamental device, there is still considerable parameter space available for amplifier operation. Peak powers above 30 MW are obtained with efficiencies greater than 28% and large signal gains of 27 dB. These results depend critically on the magnetic field profile which has a slight up-taper at the optimum operating point. The nominal beam parameters include a pulse length of 1 μs, a voltage near 450 kV, a current in the range 235--245 A, and a perpendicular to parallel velocity ratio (α = v perpendicular /v z ) near one

Stopping power. Projectile and target modeled as oscillators

International Nuclear Information System (INIS)

Stevanovic, N.; Nikezic, D.

2005-01-01

In this Letter the collision of two quantum harmonic oscillators was considered. The oscillators interact through the Coulomb interaction. Stopping power of projectile was calculated assuming that both, target and projectile may be excited. It has been shown that the frequency of the projectile oscillation, ω p influences on stopping power, particularly in the region of Bragg peak. If, ω p ->0 is substitute in the expression for stopping power derived in this Letter, then it comes to the form when the projectile has been treated as point like charged particle

Influence of disorder and magnetic field on conductance of “sandwich” type two dimensional system

Directory of Open Access Journals (Sweden)

Long LIU

2017-04-01

Full Text Available In order to discuss the transport phenomena and the physical properties of the doping of the disorder system under magnetic field, the electron transport in a two-dimensional system is studied by using Green function and scattering matrix theory. Base on the two-dimensional lattice model, the phenomenon of quantized conductance of the "sandwich" type electronic system is analyzed. The contact between the lead and the scatterer reduce the system's conductance, and whittle down the quantum conductance stair-stepping phenomenon; when an external magnetic field acts on to the system, the conductance presents a periodicity oscillation with the magnetic field. The intensity of this oscillation is related to the energy of the electron;with the increase of the impurity concentration, the conductance decreases.In some special doping concentration, the conductance of the system can reach the ideal step value corresponding to some special electron energy. The result could provide reference for further study of the conductance of the "sandwich" type two dimensional system.

Hidden symmetries in one-dimensional quantum Hamiltonians

International Nuclear Information System (INIS)

Curado, E.M.F.; Rego-Monteiro, M.A.; Nazareno, H.N.

2000-11-01

We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The number-type and ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These physical operators are obtained with the help of variables used in a recently developed non commutative differential calculus. This square-well algebra is an example of an algebra in large class of generalized Heisenberg algebras recently constructed. This class of algebras also contains q-oscillators as a particular case. We also show here how this general algebra can address hidden symmetries present in several quantum systems. (author)

High-Harmonic Generation in Solids with and without Topological Edge States

DEFF Research Database (Denmark)

Bauer, Dieter; Hansen, Kenneth Christian Klochmann

2018-01-01

High-harmonic generation in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ by up...... to 14 orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band (and edge-state) electrons, which strongly depends on whether or not topological edge states are present...

Chimera patterns in two-dimensional networks of coupled neurons

Science.gov (United States)

Schmidt, Alexander; Kasimatis, Theodoros; Hizanidis, Johanne; Provata, Astero; Hövel, Philipp

2017-03-01

We discuss synchronization patterns in networks of FitzHugh-Nagumo and leaky integrate-and-fire oscillators coupled in a two-dimensional toroidal geometry. A common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes, including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observed in the two models follow similar rules. For example, the diameter of the rings grows linearly with the coupling radius.

Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators

International Nuclear Information System (INIS)

Stan, Cristina; Cristescu, C.P.; Agop, M.

2007-01-01

In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie's E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system

Phonon transport in a one-dimensional harmonic chain with long-range interaction and mass disorder

Science.gov (United States)

Zhou, Hangbo; Zhang, Gang; Wang, Jian-Sheng; Zhang, Yong-Wei

2016-11-01

Atomic mass and interatomic interaction are the two key quantities that significantly affect the heat conduction carried by phonons. Here, we study the effects of long-range (LR) interatomic interaction and mass disorder on the phonon transport in a one-dimensional harmonic chain with up to 105 atoms. We find that while LR interaction reduces the transmission of low-frequency phonons, it enhances the transmission of high-frequency phonons by suppressing the localization effects caused by mass disorder. Therefore, LR interaction is able to boost heat conductance in the high-temperature regime or in the large size regime, where the high-frequency modes are important.

Solution of two-dimensional equations of neutron transport in 4P0-approximation of spherical harmonics method

International Nuclear Information System (INIS)

Polivanskij, V.P.

1989-01-01

The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs

Simplest simulation model for three-dimensional xenon oscillations in large PWRs

International Nuclear Information System (INIS)

Shimazu, Yoichiro

2004-01-01

Xenon oscillations in large PWRs are well understood and there have been no operational problems remained. However, in order to suppress the oscillations effectively, optimal control strategy is preferable. Generally speaking in such optimality search based on the modern control theory, a large volume of transient core analyses is required. For example, three dimensional core calculations are inevitable for the analyses of radial oscillations. From this point of view, a very simple 3-D model is proposed, which is based on a reactor model of only four points. As in the actual reactor operation, the magnitude of xenon oscillations should be limited from the view point of safety, the model further assumes that the neutron leakage can be also small or even constant. It can explicitly use reactor parameters such as reactivity coefficients and control rod worth directly. The model is so simplified as described above that it can predict oscillation behavior in a very short calculation time even on a PC. However the prediction result is good. The validity of the model in comparison with measured data and the applications are discussed. (author)

Zero-point oscillations, zero-point fluctuations, and fluctuations of zero-point oscillations

International Nuclear Information System (INIS)

Khalili, Farit Ya

2003-01-01

Several physical effects and methodological issues relating to the ground state of an oscillator are considered. Even in the simplest case of an ideal lossless harmonic oscillator, its ground state exhibits properties that are unusual from the classical point of view. In particular, the mean value of the product of two non-negative observables, kinetic and potential energies, is negative in the ground state. It is shown that semiclassical and rigorous quantum approaches yield substantially different results for the ground state energy fluctuations of an oscillator with finite losses. The dependence of zero-point fluctuations on the boundary conditions is considered. Using this dependence, it is possible to transmit information without emitting electromagnetic quanta. Fluctuations of electromagnetic pressure of zero-point oscillations are analyzed, and the corresponding mechanical friction is considered. This friction can be viewed as the most fundamental mechanism limiting the quality factor of mechanical oscillators. Observation of these effects exceeds the possibilities of contemporary experimental physics but almost undoubtedly will be possible in the near future. (methodological notes)

Dynamics of injection locking in a solid-state laser with intracavity second-harmonic generation

International Nuclear Information System (INIS)

Zolotoverkh, I I; Lariontsev, E G

2000-01-01

The dynamics of oscillation in a solid-state laser with intracavity second-harmonic generation under the influence of an external signal at the second-harmonic frequency injected into its cavity in the presence of feedback at the double frequency is theoretically studied. Boundaries of the regions of injection locking for three stationary laser states differing in the nonlinear phase incursion caused by radiation conversion into the second harmonic are found. Relaxation oscillations in the stationary state of injection locking are studied. It is shown that the second relaxation frequency, which is related to phase perturbations of the second harmonic and perturbations of the phase difference of waves in a nonlinear crystal, is excited in a single-mode solid-state laser in addition to the fundamental frequency of relaxation oscillations. Conditions are found under which relaxation oscillations at the second relaxation frequency are excited. (lasers)

Theory and design of compact hybrid microphone arrays on two-dimensional planes for three-dimensional soundfield analysis.

Science.gov (United States)

Chen, Hanchi; Abhayapala, Thushara D; Zhang, Wen

2015-11-01

Soundfield analysis based on spherical harmonic decomposition has been widely used in various applications; however, a drawback is the three-dimensional geometry of the microphone arrays. In this paper, a method to design two-dimensional planar microphone arrays that are capable of capturing three-dimensional (3D) spatial soundfields is proposed. Through the utilization of both omni-directional and first order microphones, the proposed microphone array is capable of measuring soundfield components that are undetectable to conventional planar omni-directional microphone arrays, thus providing the same functionality as 3D arrays designed for the same purpose. Simulations show that the accuracy of the planar microphone array is comparable to traditional spherical microphone arrays. Due to its compact shape, the proposed microphone array greatly increases the feasibility of 3D soundfield analysis techniques in real-world applications.

Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates

Science.gov (United States)

Morera, I.; Mateo, A. Muñoz; Polls, A.; Juliá-Díaz, B.

2018-04-01

We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g >0 ). By using an adiabatic perturbation theory in the parameter g12/g , we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12>0 . As a result, the relative motion of dark solitons with equal chemical potential μ is well approximated by harmonic oscillations of angular frequency wr=(μ /ℏ ) √{(8 /15 ) g12/g } . We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency Ω ) the solitons are driven by the superposition of two harmonic motions at a frequency given by w2=(Ω/√{2 }) 2+wr2 . When g12<0 , these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.

The directional propagation characteristics of elastic wave in two-dimensional thin plate phononic crystals

International Nuclear Information System (INIS)

Wen Jihong; Yu, Dianlong; Wang Gang; Zhao Honggang; Liu Yaozong; Wen Xisen

2007-01-01

The directional propagation characteristics of elastic wave during pass bands in two-dimensional thin plate phononic crystals are analyzed by using the lumped-mass method to yield the phase constant surface. The directions and regions of wave propagation in phononic crystals for certain frequencies during pass bands are predicted with the iso-frequency contour lines of the phase constant surface, which are then validated with the harmonic responses of a finite two-dimensional thin plate phononic crystals with 16x16 unit cells. These results are useful for controlling the wave propagation in the pass bands of phononic crystals

Discretized representations of harmonic variables by bilateral Jacobi operators

Directory of Open Access Journals (Sweden)

Andreas Ruffing

2000-01-01

Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.

Mechanical analog of the synchrotron, illustrating phase stability and two-dimensional focusing

International Nuclear Information System (INIS)

Alvarez, L.W.; Smits, R.; Senecal, G.

1975-01-01

A steel ball bounces in synchronism with a vertically oscillating piston. The piston surface is a hardened steel disk on which the ball bounces; two-dimensional horizontal focusing is provided by the concavity of the surface. The period of oscillation can be varied over a 3:1 range with the amplitude kept constant. As the period is increased, the ball bounces higher. As the period is decreased, the ball bounces lower, contrary to the intuition of most observers. The model illustrates the important properties of synchrotron accelerators. (3 figures)

Magnetooscillations of the tunneling current between two-dimensional electron systems

International Nuclear Information System (INIS)

Raichev, O.E.; Vasko, F.T.

1995-08-01

We calculate electric current caused by electron tunnelling between two-dimensional layers in the magnetic field applied perpendicular to the layers. An elastic scattering of the electrons is taken into account. Analytical results are obtained for two regimes: i) small magnetic field, when the Landau quantization is suppressed by the scattering and the oscillatory part of the current shows nearly harmonic behaviour; ii) high magnetic field, when the Landau levels are well-defined and the conductivity shows series of sharp peaks corresponding to resonant magnetotunneling. In the last case, we used two alternative approaches: self-consistent Born approximation and path integral method, and compared obtained results. (author). 12 refs, 3 figs

Oscillators from nonlinear realizations

Science.gov (United States)

Kozyrev, N.; Krivonos, S.

2018-02-01

We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.

Reentrant behavior in the superconducting phase-dependent resistance of a disordered two-dimensional electron gas

NARCIS (Netherlands)

den Hartog, S.G.; Wees, B.J.van; Klapwijk, T.M; Nazarov, Y.V.; Borghs, G.

1997-01-01

We have investigated the bias-voltage dependence of the phase-dependent differential resistance of a disordered T-shaped two-dimensional electron gas coupled to two superconducting terminals. The resistance oscillations first increase upon lowering the energy. For bias voltages below the Thouless

A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space

International Nuclear Information System (INIS)

Le, Van-Hoang; Nguyen, Thanh-Son

2011-01-01

We establish an explicit form of a non-Abelian SO(8) monopole in a 9-dimensional space and show that it is indeed a direct generalization of Dirac and Yang monopoles. Using the generalized Hurwitz transformation, we have found a connection between a 16-dimensional harmonic oscillator and a 9-dimensional hydrogenlike atom in the field of the SO(8) monopole (MICZ-Kepler problem). Using the built connection the group of dynamical symmetry of the 9-dimensional MICZ-Kepler problem is found as SO(10, 2).

High-Intensity High-order Harmonics Generated from Low-Density Plasma

International Nuclear Information System (INIS)

Ozaki, T.; Bom, L. B. Elouga; Abdul-Hadi, J.; Ganeev, R. A.; Haessler, S.; Salieres, P.

2009-01-01

We study the generation of high-order harmonics from lowly ionized plasma, using the 10 TW, 10 Hz laser of the Advanced Laser Light Source (ALLS). We perform detailed studies on the enhancement of a single order of the high-order harmonic spectrum generated in plasma using the fundamental and second harmonic of the ALLS beam line. We observe quasi-monochromatic harmonics for various targets, including Mn, Cr, Sn, and In. We identify most of the ionic/neutral transitions responsible for the enhancement, which all have strong oscillator strengths. We demonstrate intensity enhancements of the 13th, 17th, 29th, and 33rd harmonics from these targets using the 800 nm pump laser and varying its chirp. We also characterized the attosecond nature of such plasma harmonics, measuring attosecond pulse trains with 360 as duration for chromium plasma, using the technique of ''Reconstruction of Attosecond Beating by Interference of Two-photon Transitions''(RABBIT). These results show that plasma harmonics are intense source of ultrashort coherent soft x-rays.

Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

Science.gov (United States)

Fernandez, Francisco M.

2010-01-01

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

Matter-wave interference, Josephson oscillation and its disruption in a Bose-Einstein condensate on an optical lattice

International Nuclear Information System (INIS)

Adhikari, Sadhan K.

2004-01-01

Using the axially-symmetric time-dependent mean-field Gross-Pitaevskii equation we study the Josephson oscillation in a repulsive Bose-Einstein condensate trapped by a harmonic plus an one-dimensional optical-lattice potential to describe the experiments by Cataliotti et al. [Science 293 (2001) 843, New J. Phys. 5 (2003) 71.1]. After a study of the formation of matter-wave interference upon releasing the condensate from the optical trap, we directly investigate the alternating atomic superfluid Josephson current upon displacing the harmonic trap along the optical axis. The Josephson current is found to be disrupted upon displacing the harmonic trap through a distance greater than a critical distance signaling a superfluid to a classical insulator transition in the condensate

Two port network analysis for three impedance based oscillators

KAUST Repository

Said, Lobna A.

2011-12-01

Two-port network representations are applied to analyze complex networks which can be dissolved into sub-networks connected in series, parallel or cascade. In this paper, the concept of two-port network has been studied for oscillators. Three impedance oscillator based on two port concept has been analyzed using different impedance structures. The effect of each structure on the oscillation condition and the frequency of oscillation have been introduced. Two different implementations using MOS and BJT have been introduced. © 2011 IEEE.

Probing two-centre interference in molecular high harmonic generation

International Nuclear Information System (INIS)

Vozzi, C; Calegari, F; Benedetti, E; Berlasso, R; Sansone, G; Stagira, S; Nisoli, M; Altucci, C; Velotta, R; Torres, R; Heesel, E; Kajumba, N; Marangos, J P

2006-01-01

Two-centre interference in the recombination step of molecular high harmonic generation (HHG) has been probed in CO 2 and O 2 . We report the order dependence of characteristic enhancements or suppressions of high harmonic production in aligned samples of both molecules. In CO 2 , a robust destructive interference was seen consistent with the known separation of the oxygen atoms that are active in HHG. In O 2 , a harmonic enhancement was found indicating constructive interference. A good agreement was found with a simple two-centre interference model that includes the angular distribution function of the sample. The effective momentum of the electron wave was determined from the spectral position of these interferences. Ellipticity-dependent studies in CO 2 clearly show how the destructive interference can be 'switched off' by increasing the degree of ellipticity and thus shifting the effective resonance condition

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

International Nuclear Information System (INIS)

Anteneodo, C; Vallejos, R O

2010-01-01

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ* respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ* in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ* by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

Three-dimensional ray tracing of electrostatic cyclotron harmonic waves and Z mode electromagnetic waves in the magnetosphere

International Nuclear Information System (INIS)

Hashimoto, K.; Yamaashi, K.; Kimura, I.; Kyoto Univ., Japan)

1987-01-01

Three-dimensional ray tracing is performed for electrostatic electron cyclotron harmonic waves and Z mode electromagnetic waves in the earth's magnetosphere using the hot dispersion relation. Propagation characteristics of cyclotron harmonic waves under the electrostatic approximation are considered, and it is noted that waves starting near the equator can propagate over a long distance without damping. Ray tracing without the electrostatic approximation confirms mode conversion from cyclotron harmonic waves to Z mode electromagnetic waves, and the conditions for the conversion are clarified. It is suggested that further conversion to the L-O mode continuum radiation is possible under strict constraints. The present results are not inconsistent with the conversion mechanism for the generation of escaping continuum radiation in the magnetosphere. 20 references

Excitation transfer in two two-level systems coupled to an oscillator

International Nuclear Information System (INIS)

Hagelstein, P L; Chaudhary, I U

2008-01-01

We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated with energy exchange between a two-level system and the oscillator, the level splitting is about the same as would be obtained in the spin-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian

Multidimensional high harmonic spectroscopy

International Nuclear Information System (INIS)

Bruner, Barry D; Soifer, Hadas; Shafir, Dror; Dudovich, Nirit; Serbinenko, Valeria; Smirnova, Olga

2015-01-01

High harmonic generation (HHG) has opened up a new frontier in ultrafast science where attosecond time resolution and Angstrom spatial resolution are accessible in a single measurement. However, reconstructing the dynamics under study is limited by the multiple degrees of freedom involved in strong field interactions. In this paper we describe a new class of measurement schemes for resolving attosecond dynamics, integrating perturbative nonlinear optics with strong-field physics. These approaches serve as a basis for multidimensional high harmonic spectroscopy. Specifically, we show that multidimensional high harmonic spectroscopy can measure tunnel ionization dynamics with high precision, and resolves the interference between multiple ionization channels. In addition, we show how multidimensional HHG can function as a type of lock-in amplifier measurement. Similar to multi-dimensional approaches in nonlinear optical spectroscopy that have resolved correlated femtosecond dynamics, multi-dimensional high harmonic spectroscopy reveals the underlying complex dynamics behind attosecond scale phenomena. (paper)

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

Energy Technology Data Exchange (ETDEWEB)

Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)

2016-03-15

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

International Nuclear Information System (INIS)

Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban

2016-01-01

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.

Phase-matched third harmonic generation in a plasma

International Nuclear Information System (INIS)

Rax, J.M.; Fisch, N.J.

1993-01-01

Relativistic third harmonic generation in a plasma is investigated. The growth of a third harmonic wave is limited by the difference between the phase velocity of the pump and driven waves. This phase velocity mismatch results in a third harmonic amplitude saturation and oscillation. In order to overcome this saturation, the authors describe a phase-matching scheme based on a resonant density modulation. The limitations of this scheme are analyzed

Spontaneous creation of nonzero-angular-momentum modes in tunnel-coupled two-dimensional degenerate Bose gases

International Nuclear Information System (INIS)

Montgomery, T. W. A.; Scott, R. G.; Lesanovsky, I.; Fromhold, T. M.

2010-01-01

We investigate the dynamics of two tunnel-coupled two-dimensional degenerate Bose gases. The reduced dimensionality of the clouds enables us to excite specific angular momentum modes by tuning the coupling strength, thereby creating striking patterns in the atom density profile. The extreme sensitivity of the system to the coupling and initial phase difference results in a rich variety of subsequent dynamics, including vortex production, complex oscillations in relative atom number, and chiral symmetry breaking due to counter-rotation of the two clouds.

Phase-matching-free parametric oscillators based on two dimensional semiconductors

OpenAIRE

Ciattoni, A.; Marini, A.; Rizza, C.; Conti, C.

2017-01-01

Optical parametric oscillators are widely-used pulsed and continuous-wave tunable sources for innumerable applications, as in quantum technologies, imaging and biophysics. A key drawback is material dispersion imposing the phase-matching condition that generally entails a complex setup design, thus hindering tunability and miniaturization. Here we show that the burden of phase-matching is surprisingly absent in parametric micro-resonators adopting monolayer transition-metal dichalcogenides as...

Quantum damped oscillator I: Dissipation and resonances

International Nuclear Information System (INIS)

Chruscinski, Dariusz; Jurkowski, Jacek

2006-01-01

Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator

Understanding fifth-harmonic generation in CLBO

Science.gov (United States)

Patankar, S.; Yang, S. T.; Moody, J. D.; Bayramian, A. J.; Swadling, G. F.; Barker, D.; Datte, P.; Mennerat, G.; Norton, M.; Carr, C. W.; Begishev, I. A.; Bromage, J.; Ross, J. S.

2018-02-01

We report on results of fifth harmonic generation in Cesium Lithium Borate (CLBO) using a three-crystal cascaded frequency conversion scheme designed to study the energy balance of the final sum frequency generation stage. The experimental setup independently combines the first and fourth harmonic of a Nd:Glass laser in a 5mm thick CLBO crystal. Energy balance between the incoming and output energy is close to unity when the CLBO is out of phase matching and approximately 80% when the crystal is in phase matching. A detailed analysis of the residual fundamental and fourth harmonic energy indicates 5th harmonic light is being generated but only 26% is unaccounted for. We attribute the missing light to linear transmission loss in the CLBO oven. The ratio of the output to input energy is unity when the missing 5th harmonic is incorporated into the calculations. Two-dimensional plane wave mixing simulations show agreement with the results at lower intensities.

Quantum entanglement and phase transition in a two-dimensional photon-photon pair model

International Nuclear Information System (INIS)

Zhang Jianjun; Yuan Jianhui; Zhang Junpei; Cheng Ze

2013-01-01

We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as enhanced second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.

Coupled oscillators with parity-time symmetry

Energy Technology Data Exchange (ETDEWEB)

Tsoy, Eduard N., E-mail: etsoy@uzsci.net

2017-02-05

Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed. - Highlights: • A generalization of a Hamiltonian system of linear coupled oscillators with the parity-time (PT) symmetry is suggested. • It is found that an increase of the gain-loss parameter can stabilize the system. • A family of Hamiltonian functions for two coupled nonlinear oscillators with PT-symmetry is obtained.

Location identification of closed crack based on Duffing oscillator transient transition

Science.gov (United States)

Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Deng, Mingxi; Hu, Ning

2018-02-01

The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.

Design of 12-phase, 2-stage Harmonic Rejection Mixer for TV Tuners

Directory of Open Access Journals (Sweden)

D. Lee

2016-06-01

Full Text Available A two-stage 12-phase harmonic rejection mixer (HRM for TV tuners is proposed in order to reject the local oscillator (LO harmonics up to the ninth order. The proposed weighing scheme for 12-phase, 2-stage harmonic mixing can reduce the harmonic rejection (HR sensitivity to the amplitude error caused by irrational numbers such as . To verify this HR, the 2-stage HR circuit is designed with baseband gm weighting in order to save power and improve the HR ratios without calibration. The proposed HRM achieves the third to ninth worst HR ratios, more than 55 dB, according to Monte Carlo simulations. It consumes 6.5 mA under a 2.5 V supply voltage.

Almost-sure identifiability of multidimensional harmonic retrieval

NARCIS (Netherlands)

Jiang, T; Sidiropoulos, ND; ten Berge, JMF

Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the

Evidence for new resonances in the K-barN system: A prima facie case for the even-wave harmonic-oscillator model

International Nuclear Information System (INIS)

Kamath, S.G.

1978-01-01

Arguments are presented to show that the new resonance parameters obtained by Alston-Garnjost et al. in a recent analysis of the K-barN system from 365 to 1320 MeV/c provide a prima facie case for the even-wave harmonic-oscillator theory of baryonic states in the framework of SU(6)/sub W/ x O(3). A new quantum classification of the Λ states belonging to the (70,1 - ) is also proposed

Special values of the spectral zeta function of the non-commutative harmonic oscillator and confluent Heun equations

CERN Document Server

Ichinose, T

2004-01-01

We study the special values at $s=2$ and $3$ of the spectral zeta function $\\zeta_Q(s)$ of the non-commutative harmonic oscillator $Q(x,D_x)$ introduced in \\cite{PW1, 2}. It is shown that the series defining $\\zeta_Q(s)$ converges absolutely for Re $s>1$ and further the respective values $\\zeta_Q(2)$ and $\\zeta_Q(3)$ are represented essentially by contour integrals of the solutions, respectively, of a singly confluent Heun's ordinary differential equation and of exactly the same but an inhomogeneous equation. As a by-product of these results, we obtain integral representations of the solutions of these equations by rational functions. \\par\

Recurrence relations between transformation coefficients of hyperspherical harmonics and their application to Moshinsky coefficients

International Nuclear Information System (INIS)

Raynal, J.

1976-01-01

Closed formulae and recurrence relations for the transformation of a two-body harmonic oscillator wave function to the hyperspherical formalism are given. With them Moshinsky or Smirnov coefficients are obtained from the transformation coefficients of hyperspheric harmonics. For these coefficients the diagonalization method of Talman and Lande reduces to simple recurrence relations which can be used directly to compute them. New closed formulae for these coefficients are also derived: they are needed to compute the two simplest coefficients which determine the sign for the recurrence relation. (Auth.)

Dynamics of two-dimensional solitary vortices in a low-β plasma with convective motion

International Nuclear Information System (INIS)

Makino, Mitsuhiro; Kamimura, Tetsuo; Taniuti, Tosiya.

1980-12-01

Numerical studies of the Hasegawa-Mima equation, derived in the context of drift waves but equivalent to the quasigeostrophic vortex potential equation for Rossby waves, show the stable properties of solitary vortices which are two dimensional, localized, steady and translating solutions of this same equation. A solitary vortex can propagate only in the direction (x-direction) perpendicular to the density gradient. When this solitary vortex solution is inclined at some angle with respect to the x-axis, its propagation direction oscillates in the x and y plane. In two dimensional collisions, i.e. head-on collision and overtaking, solitary vortices interact two-dimensionally and recover their initial shapes at the end of both types of collisions. (author)

Photoinduced High-Frequency Charge Oscillations in Dimerized Systems

Science.gov (United States)

Yonemitsu, Kenji

2018-04-01

Photoinduced charge dynamics in dimerized systems is studied on the basis of the exact diagonalization method and the time-dependent Schrödinger equation for a one-dimensional spinless-fermion model at half filling and a two-dimensional model for κ-(bis[ethylenedithio]tetrathiafulvalene)2X [κ-(BEDT-TTF)2X] at three-quarter filling. After the application of a one-cycle pulse of a specifically polarized electric field, the charge densities at half of the sites of the system oscillate in the same phase and those at the other half oscillate in the opposite phase. For weak fields, the Fourier transform of the time profile of the charge density at any site after photoexcitation has peaks for finite-sized systems that correspond to those of the steady-state optical conductivity spectrum. For strong fields, these peaks are suppressed and a new peak appears on the high-energy side, that is, the charge densities mainly oscillate with a single frequency, although the oscillation is eventually damped. In the two-dimensional case without intersite repulsion and in the one-dimensional case, this frequency corresponds to charge-transfer processes by which all the bonds connecting the two classes of sites are exploited. Thus, this oscillation behaves as an electronic breathing mode. The relevance of the new peak to a recently found reflectivity peak in κ-(BEDT-TTF)2X after photoexcitation is discussed.

Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains

International Nuclear Information System (INIS)

Nkemzi, Boniface

2003-01-01

We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)

Wigner distribution function for an oscillator

International Nuclear Information System (INIS)

Davies, R.W.; Davies, K.T.R.

1975-01-01

We present two new derivations of the Wigner distribution function for a simple harmonic oscillator Hamiltonian. Both methods are facilitated using a formula which expresses the Wigner function as a simple trace. The first method of derivation utilizes a modification of a theorem due to Messiah. An alternative procedure makes use of the coherent state representation of an oscillator. The Wigner distribution function gives a semiclassical joint probability for finding the system with given coordinates and momenta, and the joint probability is factorable for the special case of an oscillator. An important application of this result occurs in the theory of nuclear fission for calculating the probability distributions for the masses, kinetic energies, and vibrational energies of the fission fragments at infinite separation. (U.S.)

Topological phase in two flavor neutrino oscillations

International Nuclear Information System (INIS)

Mehta, Poonam

2009-01-01

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.

Superintegrability in two-dimensional Euclidean space and associated polynomial solutions

International Nuclear Information System (INIS)

Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.

1996-01-01

In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab

Modeling A.C. Electronic Transport through a Two-Dimensional Quantum Point Contact

International Nuclear Information System (INIS)

Aronov, I.E.; Beletskii, N.N.; Berman, G.P.; Campbell, D.K.; Doolen, G.D.; Dudiy, S.V.

1998-01-01

We present the results on the a.c. transport of electrons moving through a two-dimensional (2D) semiconductor quantum point contact (QPC). We concentrate our attention on the characteristic properties of the high frequency admittance (ωapproximately0 - 50 GHz), and on the oscillations of the admittance in the vicinity of the separatrix (when a channel opens or closes), in presence of the relaxation effects. The experimental verification of such oscillations in the admittance would be a strong confirmation of the semi-classical approach to the a.c. transport in a QPC, in the separatrix region

Damped driven coupled oscillators: entanglement, decoherence and the classical limit

Energy Technology Data Exchange (ETDEWEB)

Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co

2009-03-13

We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.

Damped driven coupled oscillators: entanglement, decoherence and the classical limit

International Nuclear Information System (INIS)

Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M

2009-01-01

We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model

Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

International Nuclear Information System (INIS)

Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

2008-08-01

The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities

Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

Energy Technology Data Exchange (ETDEWEB)

Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

2008-08-15

The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities.

High-harmonic generation in a dense medium

International Nuclear Information System (INIS)

Strelkov, V.V.; Platonenko, V.T.; Becker, A.