One dimension harmonic oscillator
International Nuclear Information System (INIS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.
1977-01-01
The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr
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 ...
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 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.)
Introduction to classical and quantum harmonic oscillators
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
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.
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.
'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 ...
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.
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 ...
Laguerre polynomials by a harmonic oscillator
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.
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)
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
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)
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.)
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....
Generating transverse response explicitly from harmonic oscillators
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.
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)
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
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 ...
A Look at Damped Harmonic Oscillators through the Phase Plane
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…
Harmonic and Anharmonic Behaviour of a Simple Oscillator
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…
Coupled harmonic oscillators and their quantum entanglement
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.
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
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)
A harmonic oscillator having “volleyball damping”
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.
Two-dimensional generalized harmonic oscillators and their Darboux partners
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2011-01-01
We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (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.
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 ...
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.
Fundamental and Harmonic Oscillations in Neighboring Coronal Loops
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.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
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.
QUANTUM THEORY OF DAMPED HARMONIC OSCILLATOR
African Journals Online (AJOL)
DJFLEX
However, the problem of quantum oscillator with time-varying frequency had been solved (Um et al,. 1987). The Hamiltonian of this model is usually quadratic in co-ordinates and momentum operators (Ikot et al, 2008). The quantum calculation is applied because it will give the information about the particle at intermediate ...
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
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.
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 ...
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 ...
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.
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 ...
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-.
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
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
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...
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)
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
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…
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)
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.
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 ...
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
Controllability in tunable chains of coupled harmonic oscillators
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....
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....
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
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.
Predicting chaos in memristive oscillator via harmonic balance method.
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.
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)
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
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)
An analogue of the Berry phase for simple harmonic oscillators
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.
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,0
oscillator.
Spontaneous decoherence of coupled harmonic oscillators confined in a ring
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.
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
Optimal control of a harmonic oscillator: Economic interpretations
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.
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
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
Elementary derivation of the quantum propagator for the harmonic oscillator
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.
A method of solving simple harmonic oscillator Schroedinger equation
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.
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
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...
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.
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.
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.
Non-unique monopole oscillations of harmonically confined Yukawa systems
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)
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
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)
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)
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
Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator
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.
Modeling stock return distributions with a quantum harmonic oscillator
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.
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
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
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…
Exact solution of a quantum forced time-dependent harmonic oscillator
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.
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
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)
Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces
International Nuclear Information System (INIS)
Oyewumi, K.A.; Bangudu, E.A.
2003-01-01
Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)
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)
A position-dependent mass harmonic oscillator and deformed space
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.
West Coast Swing Dancing as a Driven Harmonic Oscillator Model
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.
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.)
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
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)
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
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)
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)
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Tepper G, T.
2002-01-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
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
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
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)
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
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.
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
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 SchrÃ¶dinger 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 canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
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
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.)
Information measures of a deformed harmonic oscillator in a static electric field
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.
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
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
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.
Classical and quantum position-dependent mass harmonic oscillators
International Nuclear Information System (INIS)
Cruz y Cruz, S.; Negro, J.; Nieto, L.M.
2007-01-01
The position-dependent mass oscillator is studied from both, classical and quantum mechanical points of view, in order to discuss the ambiguity on the operator ordering of the kinetic term in the quantum framework. The results are illustrated by some examples of specific mass functions
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.
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
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
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
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
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
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
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 ...
Microbubble generator excited by fluidic oscillator's third harmonic frequency
Czech Academy of Sciences Publication Activity Database
Tesař, Václav
2014-01-01
Roč. 92, č. 9 (2014), s. 1603-1615 ISSN 0263-8762 R&D Projects: GA ČR GA13-23046S Institutional support: RVO:61388998 Keywords : fluidic oscillator * microbubble generation * fluidic feedback loop Subject RIV: BK - Fluid Dynamics Impact factor: 2.348, year: 2014 http://dx.doi.org/10.1016/j.cherd.2013.12.004
Rigorous quantum limits on monitoring free masses and harmonic oscillators
Roy, S. M.
2018-03-01
There are heuristic arguments proposing that the accuracy of monitoring position of a free mass m is limited by the standard quantum limit (SQL): σ2( X (t ) ) ≥σ2( X (0 ) ) +(t2/m2) σ2( P (0 ) ) ≥ℏ t /m , where σ2( X (t ) ) and σ2( P (t ) ) denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983), 10.1103/PhysRevLett.51.719] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on σ2( X (t ) ) in terms of σ2( X (0 ) ) and σ2( P (0 ) ) , given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.
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.
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.
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.
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.
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.
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.
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
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.
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)
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Szebehely, V; Bond, V
1983-05-01
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations. 11 references.
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
Zeta functions for the spectrum of the non-commutative harmonic oscillators
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.
Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry
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).
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)
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
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....
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
Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams
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.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
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.
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
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
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
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.
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.
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.
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
International Nuclear Information System (INIS)
Lo, C.F.
2009-01-01
By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)
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
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...... transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration....
Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems
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.
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
(1 + 1) Newton-Hooke group for the simple and damped harmonic oscillator
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.
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
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung
2009-01-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
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.
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.
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
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
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
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
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
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
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.
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.
International Nuclear Information System (INIS)
Xu Hao; Shi Tianjun
2011-01-01
In this article,the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one-dimensional infinite potential well and one-dimensional harmonic oscillator, and then the particular Wigner function of one-dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which,simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one-dimensional infinite potential well and one-dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. (authors)
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
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.
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
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.
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 Tucson-Melbourne Three-Body Force in a Translationally-Invariant Harmonic Oscillator Basis
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)
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
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.
Directory of Open Access Journals (Sweden)
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
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
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)
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.
High efficiency fourth-harmonic generation from nanosecond fiber master oscillator power amplifier
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.
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
Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator
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.
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...
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.
Li, Xiaoli; Li, Duan; Voss, Logan J; Sleigh, Jamie W
2009-11-15
Brain functions are related to neuronal networks of different sizes and distribution, and neuronal networks of different sizes oscillate at different frequencies. Thus the synchronization of neuronal networks is often reflected by cross-frequency interaction. The description of this cross-frequency interaction is therefore a crucial issue in understanding the modulation mechanisms between neuronal populations. A number of different kinds of interaction between frequencies have been reported. In this paper, we develop a general harmonic wavelet transform based bicoherence using a phase randomization method. This allows us to measure the comodulation of oscillations between different frequency bands in neuronal populations. The performance of the method is evaluated by a simulation study. The results show that the improved wavelet bicoherence method can detect a reliable phase coupling value, and also identify zero bicoherence for waves that are not phase-coupled. Spurious bicoherences can be effectively eliminated through the phase randomization method. Finally, this method is applied to electrocorticogram data recorded from rats during transitions between slow-wave sleep, rapid-eye movement sleep and waking. The phase coupling in rapid-eye movement sleep is statistically lower than that during slow-wave sleep, and slightly less than those in the wakeful state. The degree of phase coupling in rapid-eye movement sleep after slow-wave sleep is greater than in rapid-eye movement sleep prior to waking. This method could be applied to investigate the cross-frequency interactions in other physiological signals.
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
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.
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.
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.
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)
International Nuclear Information System (INIS)
Zeng Bei; Zeng Jinyan
2002-01-01
It is shown that for any central potential V(r) there exist a series of conserved aphelion and perihelion vectors R-tilde=pxL-g(r)r, g(r)=rV ' (r). However, if and only if V(r) is a pure or screened Coulomb potential, R-tilde and L constitute an SO 4 algebra in the subspace spanned by the degenerate states with a given energy eigenvalue E ' . While dR/dt=0 always holds, dR ' /dt=0 holds only at the aphelia and perihelia. Moreover, the space spanning the SO 4 algebra for a screened Coulomb potential is smaller than that for a pure Coulomb potential. The relation of closed orbits for a screened Coulomb potential with that for a pure Coulomb potential is clarified. The ratio of the radial frequency ω r and angular frequency ω φ , ω r /ω φ =κ=1 for a pure Coulomb potential irrespective of the angular momentum L and energy E(<0). For a screened Coulomb potential κ is determined by the angular momentum L, and when κ is any rational number (κ<1), the orbit is closed. The situation for a pure or screened isotropic harmonic oscillator is similar
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
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
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.)
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
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.
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.
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
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.
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...
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.
International Nuclear Information System (INIS)
Demiralp, Metin
2010-01-01
This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.
A model of the two-dimensional quantum harmonic oscillator in an AdS{sub 3} background
Energy Technology Data Exchange (ETDEWEB)
Frick, R. [Universitaet zu Koeln, Institut fuer Theoretische Physik, Cologne (Germany)
2016-10-15
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schroedinger picture in which the analogs of the Schroedinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the AdS{sub 3} spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations. (orig.)
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)
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 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.
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.))
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.
International Nuclear Information System (INIS)
Cari, C; Suparmi, A
2013-01-01
The energy eigenvalues and eigenfunctions of Schrodinger equation for three dimensional harmonic oscillator potential plus Rosen-Morse non-central potential are investigated using NU method and Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding radial wave functions are expressed in associated Laguerre polynomials while angular eigen functions are given in terms of Romanovski polynomials. The Rosen-Morse potential is considered to be a perturbation factor to the three dimensional harmonic oscillator potential that causes the increase of radial wave function amplitude and decrease of angular momentum length. Keywords: Schrodinger Equation, Three dimensional Harmonic Oscillator potential, Rosen-morse non-central potential, NU method, Romanovski Polynomials
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....
Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid
Jan Novaes Recica; Luiz Antonio Alcântara Pereira; Miguel Hiroo Hirata
2008-01-01
The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determin...
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.
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.
Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid
Directory of Open Access Journals (Sweden)
Jan Novaes Recica
2008-01-01
Full Text Available The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determined such as to satisfy the no-slip boundary condition.
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\
International Nuclear Information System (INIS)
Kobe, D.H.
1989-01-01
The Berry phase is derived in a manifestly gauge-invariant way, without adiabatic or cyclic requirements. It is invariant under unitary transformations, contrary to recent assertions. A time-dependent generalized harmonic oscillator is taken as an example. The energy of the system is not in general the Hamiltonian. An energy, the time derivative of which is the power, is obtained from the equation of motion. When the system is quantized, the Berry phase is zero, and is invariant under unitary transformations. If the energy is chosen incorrectly to be the Hamiltonian, a nonzero Berry phase is obtained. In this case the total phase, the sun of the dynamical and Berry phases, is equal to the correct total phase through first order in perturbation theory. (author)
International Nuclear Information System (INIS)
Mshelia, E.D.
1994-07-01
The method of normal coordinates of the theory of vibrations is used in decoupling the motion of n oscillators (1 ≤ n ≤4) representing intrinsic degrees of freedom coupled to collective motion in a quantum mechanical model that allows the determination of the probability for energy transfer from collective to intrinsic excitations in a dissipative system. (author). 21 refs
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Ghesquière, Anne, E-mail: Anne.Ghesquiere@nithep.ac.za; Sinayskiy, Ilya, E-mail: sinayskiy@ukzn.ac.za; Petruccione, Francesco, E-mail: petruccione@ukzn.ac.za
2013-10-15
A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.
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.
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)
Rectification of harmonically oscillating magnetic fields in quarter circular Josephson junctions
International Nuclear Information System (INIS)
Shaju, P.D.; Kuriakose, V.C.
2003-01-01
A novel method for rectifying harmonically varying magnetic fields is demonstrated using fluxons in quarter circular Josephson junctions (JJs). A JJ with a quarter circular geometry terminated with a load resistor at one end is found to be capable of rectifying alternating fields when biased with a constant dc current. An external magnetic field applied parallel to the dielectric barrier of the junction interacts with the edges of the junction and make asymmetric boundary conditions. These asymmetric boundary conditions facilitate fluxon penetration under a dc bias from one end of the junction in alternate half cycles of the applied field. Thus effective rectification of the field can be achieved using quarter circular JJs. This unique phenomenon is specific to this geometry and can be exploited for making superconducting magnetic field rectifiers. This proposed device is expected to have important applications in millimeter and sub-millimeter radio wave astronomy
Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
International Nuclear Information System (INIS)
Luo, Albert C.J.; Chen Lidi
2005-01-01
In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems
Low-noise sub-harmonic injection locked multiloop ring oscillator
Weilin, Xu; Di, Wu; Xueming, Wei; Baolin, Wei; Jihai, Duan; Fadi, Gui
2016-09-01
A three-stage differential voltage-controlled ring oscillator is presented for wide-tuning and low-phase noise requirement of clock and data recovery circuit in ultra wideband (UWB) wireless body area network. To improve the performance of phase noise of delay cell with coarse and fine frequency tuning, injection locked technology together with pseudo differential architecture are adopted. In addition, a multiloop is employed for frequency boosting. Two RVCOs, the standard RVCO without the IL block and the proposed IL RVCO, were fabricated in SMIC 0.18 μm 1P6M Salicide CMOS process. The proposed IL RVCO exhibits a measured phase noise of -112.37 dBc/Hz at 1 MHz offset from the center frequency of 1 GHz, while dissipating a current of 8 mA excluding the buffer from a 1.8-V supply voltage. It shows a 16.07 dB phase noise improvement at 1 MHz offset compared to the standard topology. Project supported by the National Natural Science Foundation of China (No. 61264001), the Guangxi Natural Science Foundation (Nos. 2013GXNSFAA019333, 2015GXNSFAA139301, 2014GXNSFAA118386), the Graduate Education Innovation Program of GUET (No. GDYCSZ201457), the Project of Guangxi Education Department (No. LD14066B) and the High-Level-Innovation Team and Outstanding Scholar Project of Guangxi Higher Education Institutes.
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-06
We theoretically and experimentally evaluate the propagation, generation and amplification of signal, harmonic and intermodulation distortion terms inside a Semiconductor Optical Amplifier (SOA) under Coherent Population Oscillation (CPO) regime. For that purpose, we present a general optical field model, valid for any arbitrarily-spaced radiofrequency tones, which is necessary to correctly describe the operation of CPO based slow light Microwave Photonic phase shifters which comprise an electrooptic modulator and a SOA followed by an optical filter and supplements another recently published for true time delay operation based on the propagation of optical intensities. The phase shifter performance has been evaluated in terms of the nonlinear distortion up to 3rd order, for a modulating signal constituted of two tones, in function of the electrooptic modulator input RF power and the SOA input optical power, obtaining a very good agreement between theoretical and experimental results. A complete theoretical spectral analysis is also presented which shows that under small signal operation conditions, the 3rd order intermodulation products at 2Ω1 + Ω2 and 2Ω2 + Ω1 experience a power dip/phase transition characteristic of the fundamental tones phase shifting operation.
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
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.
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.
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.
International Nuclear Information System (INIS)
Wang, Chen-Wen; Zhu, Chaoyuan; Lin, Sheng-Hsien; Yang, Ling; Yu, Jian-Guo
2014-01-01
Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X 1 A g ↔ A 1 B 1u absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v 10 is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases
International Nuclear Information System (INIS)
Sarkar, P.; Bhattacharyya, S.P.
1995-01-01
The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab
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.
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
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.
International Nuclear Information System (INIS)
Mikkelsen, H.H.; Flyvbjerg, H.
1991-05-01
The time-dependent Schroedinger equation for a Coulomb collision between a heavy point charge and a harmonically bound electron is solved exactly numerically. The energy transferred to the electron is studied as a function of impact parameter and projectile charge. Special attention is given to the Barkas effect, and the transition from light ion to heavy ion stopping. All results are compared with classical and recent approximate results, whose precision and ranges of validity are discussed. (orig.)
International Nuclear Information System (INIS)
Santos Coelho, Leandro dos; Mariani, Viviana Cocco
2008-01-01
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature
Energy Technology Data Exchange (ETDEWEB)
dos Santos Coelho, Leandro [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil); Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Santos Coelho, Leandro dos [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: leandro.coelho@pucpr.br; Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: viviana.mariani@pucpr.br
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.
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.
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.
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.
Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude
2006-03-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.
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
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
Directory of Open Access Journals (Sweden)
Halimatus Sa’diyah
2017-12-01
Full Text Available The purpose of this research is to analyze of students' difficulties on the material elasticity and harmonic oscillation in the inquiry-based physics learning. It has eight stages. They are the orientation, the problem formulation, the formulation of hypotheses, the data obtaining, the testing hypotheses, conclusions, the implementation of the conclusions and generalizations, and the reflection stage. This research determines the student's learning difficulties on the each stage. The subject of this research is all of the students in X IPA 4 SMA N Sambungmacan Sragen. The amount of this research subject is thirty students. The method used in this research is descriptive qualitative. The data acquired with the learning process observation, the student's response questionnaire, and the student's cognitive tests. The results show that the student has difficulty in analyzing the elasticity and the force of deviation, speed, and acceleration concept, illustrates hooke law, and the matter's modulus elasticity. The difficult stages of the inquiry-based physics learning are the problem formulation, the formulation of hypotheses, the data obtaining, the testing hypotheses, conclusions, the implementation of the conclusions and generalizations, and the reflection stage.
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2016-05-15
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
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)
Gluck, P.; Krakower, Zeev
2010-01-01
We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)
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
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
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2017-05-15
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
Huang, Yongjun; Flores, Jaime Gonzalo Flor; Cai, Ziqiang; Yu, Mingbin; Kwong, Dim-Lee; Wen, Guangjun; Churchill, Layne; Wong, Chee Wei
2017-06-29
For the sensitive high-resolution force- and field-sensing applications, the large-mass microelectromechanical system (MEMS) and optomechanical cavity have been proposed to realize the sub-aN/Hz 1/2 resolution levels. In view of the optomechanical cavity-based force- and field-sensors, the optomechanical coupling is the key parameter for achieving high sensitivity and resolution. Here we demonstrate a chip-scale optomechanical cavity with large mass which operates at ≈77.7 kHz fundamental mode and intrinsically exhibiting large optomechanical coupling of 44 GHz/nm or more, for both optical resonance modes. The mechanical stiffening range of ≈58 kHz and a more than 100 th -order harmonics are obtained, with which the free-running frequency instability is lower than 10 -6 at 100 ms integration time. Such results can be applied to further improve the sensing performance of the optomechanical inspired chip-scale sensors.
Oscillators from nonlinear realizations
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.
International Nuclear Information System (INIS)
Schunck, N.; Dobaczewski, J.
2017-01-01
Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
International Nuclear Information System (INIS)
Schunck, Nicolas F.; McDonnell, J.; Sheikh, J.A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.
The variational spiked oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Ullah, N.
1992-08-01
A variational analysis of the spiked harmonic oscillator Hamiltonian -d 2 / d x 2 + x 2 + δ/ x 5/2 , δ > 0, is reported in this work. A trial function satisfying Dirichlet boundary conditions is suggested. The results are excellent for a large range of values of the coupling parameter. (author)
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
This paper completes a descrption of the quantization procedure in the harmonic superspace approach. The Feynman rules for N=2 matter and Yang-Mills theories are derived and the various examples of harmonic supergraph calculations are given. Calculations appear to be not more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any troubles, a non-locality in these disappears on-shell. The important property is that the quantum corrections are always writen as integrals over the full harmonic superspace even though the initial action is an integral over the analytic subspace. As a by-product our results imply a very simple proof of finiteness of a wide class of the N=4, d=2 non-linear Σ-models. The most general self-couplings of hypermultiplets including those with broken SU(2) are considered.The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
are carried out in HO basis, this study ought to pro- vide an insight into ... coupling are presented in Section 2 and the con- truction of VOHB is ..... quantum numbers of the target state. After initializing .... Computational facilities pro- vided by the ...
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
We consider the second-order differential operator. H = − + |x|2, x ∈ Rd. (1) ... In other words, the range of the Hermite fractional integral. 337 ... convergence of the solution of the Schrödinger equation (42) to the initial data. Our work was ... Given a multi-index α = (αj )d j=1 ∈ Nd ..... For the second term of (24), we have. ∫.
Investigation of Student Reasoning about Harmonic Motions
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.
Brownian parametric oscillators
Zerbe, Christine; Jung, Peter; Hänggi, Peter
1994-05-01
We discuss the stochastic dynamics of dissipative, white-noise-driven Floquet oscillators, characterized by a time-periodic stiffness. Thus far, little attention has been paid to these exactly solvable nonstationary systems, although they carry a rich potential for several experimental applications. Here, we calculate and discuss the mean values and variances, as well as the correlation functions and the Floquet spectrum. As one main result, we find for certain parameter values that the fluctuations of the position coordinate are suppressed as compared to the equilibrium value of a harmonic oscillator (parametric squeezing).
Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.
2017-11-01
We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton
Helson, Henry
2010-01-01
This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.
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
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
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
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.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Directory of Open Access Journals (Sweden)
Piotr FOLĘGA
2014-03-01
Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.
Analysing harmonic motions with an iPhone’s magnetometer
Yavuz, Ahmet; Kağan Temiz, Burak
2016-05-01
In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.
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
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
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
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.
Nonlinear (Anharmonic Casimir Oscillator
Directory of Open Access Journals (Sweden)
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
Nonlinearity induced synchronization enhancement in mechanical oscillators
Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.; Antonio, Dario; Arroyo, Sebastian I.; Zanette, Damian H.
2018-05-08
An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.
Harmonics and energy management
International Nuclear Information System (INIS)
Andresen, M.
1993-01-01
To summarize what this paper has presented: Voltage and current non-sinusoidal wave shapes exist in our power system. These harmonics result from the prolific use of non-linear loads. The use of these types of loads is increasing dramatically, partly due to the push to implement energy management techniques involving harmonic generating equipment. Harmonic analysis can identify specific harmonics, their frequency, magnitude, and phase shift referenced to the fundamental. Harmonic distortion forces the use of true RMS multimeters for measurement accuracy. High levels of neutral current and N-G voltages are now possible. Transformers may overheat and fail even though they are below rated capacity. Low power factors due to harmonics cannot be corrected by the installation of capacitors, and knowledge of the fundamental VARs or the displacement power factor is needed to use capacitors alone for power factor correction. The harmonic related problems presented are by no means an exhaustive list. Many other concerns arise when harmonics are involved in the power system. The critical issue behind these problems is that many of the devices being recommended from an energy management point of view are contributing to the harmonic levels, and thus to the potential for harmonic problems. We can no longer live in the sinusoidal mentality if we are to be effective in saving energy and reducing costs
Oscillations of rigid bar in the special relativity
International Nuclear Information System (INIS)
Paiva, F.M.; Teixeira, A.F.F.
2011-12-01
In the special relativity, a rigid bar slides on herself, with a extreme oscillating harmonically. We have discovered at the movement amplitude and in the bar length, indispensable for the elimination of non physical solutions
International Nuclear Information System (INIS)
McNeill, G.A.
1981-01-01
Present high-speed data acquisition systems in nuclear diagnostics use high-frequency oscillators to provide timing references for signals recorded on fast, traveling-wave oscilloscopes. An oscillator's sinusoidal wave shape is superimposed on the recorded signal with each cycle representing a fixed time increment. During data analysis the sinusoid is stripped from the signal, leaving a clean signal shape with known timing. Since all signal/time relationships are totally dependant upon working oscillators, these critical devices must have remote verification of proper operation. This manual presents the newly-developed oscillator monitor which will provide the required verification
The electronic system for mechanical oscillation parameters registration
Directory of Open Access Journals (Sweden)
Bulavin L. A.
2008-08-01
Full Text Available On the basis of the 8-bit microcontroller Microchip PIC16F630 the digital electronic device for harmonic oscillation parameters registration was developed. The device features are simple electric circuit and high operating speed (response time is less than 10 microseconds. The relevant software for the computer-controlled recording of harmonic oscillation parameters was designed. The device can be used as a part of the experimental setup for consistent fluids rheological parameters measurements.
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.
Tuset-Sanchis, Luis; Castro-Palacio, Juan C.; Gómez-Tejedor, José A.; Manjón, Francisco J.; Monsoriu, Juan A.
2015-01-01
A smartphone acceleration sensor is used to study two-dimensional harmonic oscillations. The data recorded by the free android application, Accelerometer Toy, is used to determine the periods of oscillation by graphical analysis. Different patterns of the Lissajous curves resulting from the superposition of harmonic motions are illustrated for…
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.
Lites, B.W.; Rutten, R.J.; Thomas, J.H.
1995-01-01
We show results from SO/Sacramento Peak data to discuss three issues: (i)--the spatial occurrence of chromospheric 3--min oscillations; (ii)--the validity of Ca II H&K line-center Doppler Shift measurements; (iii)--the signi ?cance of oscillation power and phase at frequencies above 10 mHz.
Symmetry properties of second harmonics generated by antisymmetric Lamb waves
Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen
2018-03-01
Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.
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)
Electromagnetic cyclotron harmonic waves
International Nuclear Information System (INIS)
Ohnuma, T.; Watanabe, T.; Hamamatsu, K.
1981-09-01
Electromagnetic electron cyclotron harmonic waves just below the electron cyclotron harmonics are investigated numerically and experimentally. Backward waves which are observed to propagate nearly perpendicular to the magnetic field just below the electron cyclotron frequency in a high density magnetoplasma are confirmed to be in accord with the theoretical electromagnetic cyclotron waves. (author)
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
Indian Academy of Sciences (India)
IMTECH),. Chandigarh. Praveen Kumar is pursuing his PhD in chemical dynamics at. Panjab University,. Chandigarh. Keywords. Chemical oscillations, autoca-. talYSis, Lotka-Volterra model, bistability, hysteresis, Briggs-. Rauscher reaction.
Indian Academy of Sciences (India)
the law of mass-action that every simple reaction approaches ... from thermodynamic equilibrium. Such oscillating systems cor- respond to thermodynamically open systems. .... experimentally observable, and the third is always unstable.
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.
International Nuclear Information System (INIS)
Lin, Qui-xun; Van Wechel, T.D.
1987-01-01
A single gap harmonic buncher has been constructed as a pretandem buncher. Over 85% of a proton dc beam has been bunched into pulses. The width (fwhm) of the pulses is 0.7 ns. The buncher is based on that built at Argonne. Changes were made to the buncher's configuration so that the buncher could be tuned to the desired four harmonic frequencies. A method of calibrating and setting the relative phases and amplitudes of the four harmonic frequencies has been used to obtain an optimum sawtooth-like bunching waveform
Harmonic supergraphs. Green functions
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Gievetsky, V.; Sokatchev, E.
1985-01-01
The quantization procedure in the harmonic superspace approach is worked out. Harmonic distributions are introduced and are used to construct the analytic superspace delta-functions and the Green functions for the hypermultiplet and the N=2 Yang-Mills superfields. The gauge fixing is described and the relevant Faddeev-Popov ghosts are defined. The corresponding BRST transformations are found. The harmonic superspace quantization of the N=2 gauge theory turns out to be rather simple and has many parallels with that for the standard (N=0) Yang-Mills theory. In particular, no ghosts-forghosts are needed
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.
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.
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.
Superstrings and harmonic superspace
International Nuclear Information System (INIS)
Kallosh, R.E.; AN SSSR, Moscow. Fizicheskij Inst.)
1987-01-01
The paper on superstrings and harmonic superspace is a contribution to the book dedicated to E.S. Fradkin on his sixtieth birthday. The purpose of the paper is to propose a description of N = 2,3 superspace which could be used for the investigation of the effective d = 10 harmonic superspace corresponding to the heterotic superstring. A description is given of the structure of semi-simple Lie algebras in the Cartan-Weyl basis, as well as the general properties of the even, compact part of harmonic superspace. The main properties of the four-dimensional N = 2 SYM theory are discussed, along with the N = 3, d = 4 super Yang-Mills theory. Finally the relation between the harmonic superspace and the heterotic E 8 x E 8 superstring is examined. (U.K.)
Harmonic excitations in quasicrystals
International Nuclear Information System (INIS)
Luck, J.M.
1986-03-01
The harmonic excitations (phonons) of quasicrystals are studied in a simple one-dimensional model. The spectrum is a Cantor set, which exhibits selfsimilarity properties. The eigenstates are generically ''critical'', i.e. neither extended nor localized
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)
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Energy Technology Data Exchange (ETDEWEB)
Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae
2015-02-15
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
International Nuclear Information System (INIS)
Ganeev, R. A.; Bom, L. B. Elouga; Kieffer, J.-C.; Ozaki, T.
2007-01-01
We demonstrate the intensity enhancement of single harmonics in high-order harmonic generation from laser plasma. We identified several targets (In, Sn, Sb, Cr, and Mn) that demonstrate resonance-induced enhancement of single harmonic, that are spectrally close to ionic transitions with strong oscillator strengths. We optimized and obtained enhancements of the 13th, 17th, 21st, 29th, and 33rd harmonics from the above targets, by varying the chirp of the 800 nm wavelength femtosecond laser. We also observe harmonic enhancement by using frequency-doubled pump laser (400 nm wavelength). For Mn plasma pumped by the 400 nm wavelength laser, the maximum order of the enhanced harmonic observed was the 17th order (λ=23.5 nm), which corresponds to the highest photon energy (52.9 eV) reported for an enhanced single harmonic
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.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian; Ashwin, Peter; Rodrigues, Ana [Centre for Systems, Dynamics and Control and Department of Mathematics, University of Exeter, Exeter EX4 4QF (United Kingdom)
2016-09-15
The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions.
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016-09-01
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling-including three and four-way interactions of the oscillator phases-that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
Harmonization versus Mutual Recognition
DEFF Research Database (Denmark)
Jørgensen, Jan Guldager; Schröder, Philipp
The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired with the oppor......The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired...... countries and three firms, where firms first lobby for the policy coordination regime (harmonization versus mutual recognition), and subsequently, in case of harmonization, the global standard is auctioned among the firms. We discuss welfare effects and conclude with policy implications. In particular......, harmonized standards may fail to harvest the full pro-competitive effects from trade liberalization compared to mutual recognition; moreover, the issue is most pronounced in markets featuring price competition....
Second harmonic generation imaging
2013-01-01
Second-harmonic generation (SHG) microscopy has shown great promise for imaging live cells and tissues, with applications in basic science, medical research, and tissue engineering. Second Harmonic Generation Imaging offers a complete guide to this optical modality, from basic principles, instrumentation, methods, and image analysis to biomedical applications. The book features contributions by experts in second-harmonic imaging, including many pioneering researchers in the field. Written for researchers at all levels, it takes an in-depth look at the current state of the art and possibilities of SHG microscopy. Organized into three sections, the book: Provides an introduction to the physics of the process, step-by-step instructions on how to build an SHG microscope, and comparisons with related imaging techniques Gives an overview of the capabilities of SHG microscopy for imaging tissues and cells—including cell membranes, muscle, collagen in tissues, and microtubules in live cells—by summarizing experi...
International Nuclear Information System (INIS)
Au, R.; Fowler, M.; Hanawa, H.; Riedel, J.; Qua, Z.G.
1984-01-01
In early 1983 it was decided to mount coils on arms separated by 120 degrees and buck them out so that the third harmonic dphi/dt component would be cancelled and thus the first and second field harmonics could be very accurately measured. The original intention was to do as others had done, namely, use fast ADC's to read the voltages, and computer process the result to get the Fourier components. However, because of the 100 to 1 dynamic range of the fast ADC's and the likelihood that noise would be a problem, the authors decided to do things differently. Using a fast Fourier transform analyzer was considered, but this instrument is very expensive, so they decided to use a completely electronic analog approach: The authors decided to use active bandpass filters to render the harmonic components
Harmonic arbitrary waveform generator
Roberts, Brock Franklin
2017-11-28
High frequency arbitrary waveforms have applications in radar, communications, medical imaging, therapy, electronic warfare, and charged particle acceleration and control. State of the art arbitrary waveform generators are limited in the frequency they can operate by the speed of the Digital to Analog converters that directly create their arbitrary waveforms. The architecture of the Harmonic Arbitrary Waveform Generator allows the phase and amplitude of the high frequency content of waveforms to be controlled without taxing the Digital to Analog converters that control them. The Harmonic Arbitrary Waveform Generator converts a high frequency input, into a precision, adjustable, high frequency arbitrary waveform.
General Criterion for Harmonicity
Proesmans, Karel; Vandebroek, Hans; Van den Broeck, Christian
2017-10-01
Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring," namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.
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.
Comparing Harmonic Similarity Measures
de Haas, W.B.; Robine, M.; Hanna, P.; Veltkamp, R.C.; Wiering, F.
2010-01-01
We present an overview of the most recent developments in polyphonic music retrieval and an experiment in which we compare two harmonic similarity measures. In contrast to earlier work, in this paper we specifically focus on the symbolic chord description as the primary musical representation and
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom
2017-01-01
-robust to noise, or very computationally inten- sive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the liter- ature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also...
Pruitt, Kathryn Ringler
2012-01-01
This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the "best" metrical foot is chosen…
Young children's harmonic perception.
Costa-Giomi, Eugenia
2003-11-01
Harmony and tonality are two of the most difficult elements for young children to perceive and manipulate and are seldom taught in the schools until the end of early childhood. Children's gradual harmonic and tonal development has been attributed to their cumulative exposure to Western tonal music and their increasing experiential knowledge of its rules and principles. Two questions that are relevant to this problem are: (1) Can focused and systematic teaching accelerate the learning of the harmonic/tonal principles that seem to occur in an implicit way throughout childhood? (2) Are there cognitive constraints that make it difficult for young children to perceive and/or manipulate certain harmonic and tonal principles? A series of studies specifically addressed the first question and suggested some possible answers to the second one. Results showed that harmonic instruction has limited effects on children's perception of harmony and indicated that the drastic improvement in the perception of implied harmony noted approximately at age 9 is due to development rather than instruction. I propose that young children's difficulty in perceiving implied harmony stems from their attention behaviors. Older children have less memory constraints and more strategies to direct their attention to the relevant cues of the stimulus. Younger children focus their attention on the melody, if present in the stimulus, and specifically on its concrete elements such as rhythm, pitch, and contour rather than its abstract elements such as harmony and key. The inference of the abstract harmonic organization of a melody required in the perception of implied harmony is thus an elusive task for the young child.
Symmetries in physics and harmonics
International Nuclear Information System (INIS)
Kolk, D.
2006-01-01
In this book the symmetries of elementary particles are described in relation to the rules of harmonics in music. The selection rules are described in connections with harmonic intervals. Also symmetry breaking is considered in this framework. (HSI)
Harmonic Patterns in Forex Trading
Nemček, Sebastian
2013-01-01
This diploma thesis is committed to examination of validity of Harmonic Patterns in Forex trading. Scott Carney described existing and introduced new Harmonic Patterns in 1999 in his book Harmonic Trader. These patterns use the Fibonacci principle to analyze price action and to provide both bullish and bearish trading signals. The goal of this thesis is to find out whether harmonic trading strategy on selected pairs is profitable in FX market, which patterns are the most profitable and what i...
Atto second high harmonic sources
International Nuclear Information System (INIS)
Nam, Chang Hee
2008-01-01
High harmonic generation is a powerful method to produce attosecond pulses. The high harmonics, emitted from atoms driven by intense femtosecond laser pulses, can from an attosecond pulse train with equally spaced harmonic spectrum or an isolated single attosecond pulse with broad continuum spectrum. Using high power femtosecond laser technology developed at CXRC, we have investigated the spectral and temporal characteristics of high harmonics obtained from gaseous atoms. The spectral structure of harmonics could be manipulated by controlling laser chirp, and continuous tuning of harmonic wavelengths was achieved. For rigorous temporal characterization of attosecond harmonic pulses a cross correlation technique was applied to the photoionization process by harmonic and IR femtosecond pulses and achieved the complete temporal reconstruction of attosecond pulse trains, revealing the detailed temporal structure of the attosecond chirp by material dispersion. The duration of attosecond high harmonic pulses is usually much longer than that of transform limited pulses due to the inherent chirp originating from the harmonic generation process. The attosecond chirp compensation in the harmonic generation medium itself was demonstrated, thereby realizing the generation of near transform limited attosecond pulses. The interference of attosecond electron wave packets, generated from an atom by attosecond harmonic pulses, will be also presented
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
Diatomic Molecules Effective Potential for an Harmonic Oscillator ...
African Journals Online (AJOL)
A model anharmonic potential was considered and was used in the Schrödinger time independent wave equation to describe a carbon monoxide molecule. Central difference scheme was used in approximating the derivative term in the Schrödinger equation leading to a tri-diagonal band system of equation. The method of ...
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...
Fourier transformations for difference analogs of the harmonic oscillator
International Nuclear Information System (INIS)
Askey, R.; Atakishiyev, N.M.
1995-01-01
The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs
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.
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
- out direct ... concepts, exact knowledge of the spectrum is not enough for the reconstruction of ..... As the superpotential is related to the ground-state wave function, we demand ..... q-hypergeometric function multiplied by some weight factor.
Laser cooling of a harmonic oscillator's bath with optomechanics
Xu, Xunnong; Taylor, Jacob
Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
ω = 8.5 · 10−4 (continuous line), and for normal q(t) (dashed line). Figure 2. Plot for the two branches of Snyder p(t) with l = 10−5 and ω = 8.5 · 10−4 (continuous line), and for normal p(t) (dashed line). where d is a suitable constant in order to achieve the initial condition q(t = 0) = 1, and p can be expressed in terms of q:.
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
Second harmonic inversion for ultrasound contrast harmonic imaging
Energy Technology Data Exchange (ETDEWEB)
Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico [THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam (Netherlands); Cachard, Christian; Basset, Olivier, E-mail: mirza.pasovic@creatis.insa-lyon.fr [CREATIS-LRMN, Universite de Lyon, INSA-Lyon, Universite Lyon 1, Inserm U630, CNRS UMR 5220 (France)
2011-06-07
Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f{sub 0} and the same amplitude P{sub 0} to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.
Second harmonic inversion for ultrasound contrast harmonic imaging
International Nuclear Information System (INIS)
Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico; Cachard, Christian; Basset, Olivier
2011-01-01
Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f 0 and the same amplitude P 0 to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.
Graf, Rudolf F
1996-01-01
This series of circuits provides designers with a quick source for oscillator circuits. Why waste time paging through huge encyclopedias when you can choose the topic you need and select any of the specialized circuits sorted by application?This book in the series has 250-300 practical, ready-to-use circuit designs, with schematics and brief explanations of circuit operation. The original source for each circuit is listed in an appendix, making it easy to obtain additional information.Ready-to-use circuits.Grouped by application for easy look-up.Circuit source listing
Relativistic harmonic content of nonlinear electromagnetic waves in underdense plasmas
International Nuclear Information System (INIS)
Mori, W.B.; Decker, C.D.; Leemans, W.P.
1993-01-01
The relativistic harmonic content of large amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w p /w o ) much-lt 1 and critical density (w p /w o ) ≅ 1 limits. For weak nonlinearities, eE o /mcw o p /w o . Arguments are given for extending these results for arbitrary wave amplitudes. The authors also show that the use of the variable x-ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results
Wolff, Thomas H; Shubin, Carol
2003-01-01
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for fu...
The Harmonization of Accounting
Directory of Open Access Journals (Sweden)
Hajnal Noémi
2017-11-01
Full Text Available The development and configuration of the regulatory framework of the accounting systems in Romania and Hungary took place in different ways. Among the reasons for the diversities in these countries’ accounting systems, the following can be certainly mentioned: different purposes of taxation, legal structure, the accountancy’s connection with the corporate law and family law, diversification on corporate financing policy, and cultural heterogeneity. Both countries quickly caught up with the international accounting harmonization standards. The adaptation of the international accounting standards has many advantages and disadvantages; these have been discussed in several previous researches. This paper aims at comparing the Romanian and Hungarian states’ accounting regulations from the early 1990s, which were implemented in order to harmonize the states’ accountancy regulations with the international standards, and their impact on the economy, based on secondary analysis.
Analysis of graphic representation ability in oscillation phenomena
Dewi, A. R. C.; Putra, N. M. D.; Susilo
2018-03-01
This study aims to investigates how the ability of students to representation graphs of linear function and harmonic function in understanding of oscillation phenomena. Method of this research used mix methods with concurrent embedded design. The subjects were 35 students of class X MIA 3 SMA 1 Bae Kudus. Data collection through giving essays and interviews that lead to the ability to read and draw graphs in material of Hooke's law and oscillation characteristics. The results of study showed that most of the students had difficulty in drawing graph of linear function and harmonic function of deviation with time. Students’ difficulties in drawing the graph of linear function is the difficulty of analyzing the variable data needed in graph making, confusing the placement of variable data on the coordinate axis, the difficulty of determining the scale interval on each coordinate, and the variation of how to connect the dots forming the graph. Students’ difficulties in representing the graph of harmonic function is to determine the time interval of sine harmonic function, the difficulty to determine the initial deviation point of the drawing, the difficulty of finding the deviation equation of the case of oscillation characteristics and the confusion to different among the maximum deviation (amplitude) with the length of the spring caused the load.Complexity of the characteristic attributes of the oscillation phenomena graphs, students tend to show less well the ability of graphical representation of harmonic functions than the performance of the graphical representation of linear functions.
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 harmonics generation in relativistic electron beam with virtual cathode
Energy Technology Data Exchange (ETDEWEB)
Kurkin, S. A., E-mail: KurkinSA@gmail.com; Badarin, A. A.; Koronovskii, A. A.; Hramov, A. E. [Saratov State Technical University, Politechnicheskaja 77, Saratov 410028, Russia and Saratov State University, Astrakhanskaja 83, Saratov 410012 (Russian Federation)
2014-09-15
The study of the microwave generation regimes with intense higher harmonics taking place in a high-power vircator consisting of a relativistic electron beam with a virtual cathode has been made. The characteristics of these regimes, in particular, the typical spectra and their variations with the change of the system parameters (beam current, the induction of external magnetic field) as well as physical processes occurring in the system have been analyzed by means of 3D electromagnetic simulation. It has been shown that the system under study demonstrates the tendency to the sufficient growth of the amplitudes of higher harmonics in the spectrum of current oscillations in the VC region with the increase of beam current. The obtained results allow us to consider virtual cathode oscillators as promising high power mmw-to-THz sources.
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
[Harmonization of TSH Measurements.
Takeoka, Keiko; Hidaka, Yoh; Hishinuma, Akira; Ikeda, Katsuyoshi; Okubo, Shigeo; Tsuchiya, Tatsuyuki; Hashiguchi, Teruto; Furuta, Koh; Hotta, Taeko; Matsushita, Kazuyuki; Matsumoto, Hiroyuki; Murakami, Masami; Maekawa, Masato
2016-05-01
The measured concentration of thyroid stimulating hormone (TSH) differs depending on the reagents used. Harmonization of TSH is crucial because the decision limits are described in current clinical practice guide- lines as absolute values, e.g. 2.5 mIU/L in early pregnancy. In this study, we tried to harmonize the report- ed concentrations of TSH using the all-procedure trimmed mean. TSH was measured in 146 serum samples, with values ranging from 0.01 to 18.8 mIU/L, using 4 immunoassays. The concentration of TSH was highest with E test TOSOH and lowest with LUMIPULSE. The concentrations with each reagent were recalculated with the following formulas: E test TOSOH 0.855x-0.014; ECLusys 0.993x+0.079; ARCHITECT 1.041x- 0.010; and LUMIPULSE 1.096x-0.015. Recalculation eliminated the between-assay discrepancy. These formulas may be used until harmonization of TSH is achieved by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC).
Freely floating structures trapping time-harmonic water waves (revisited)
Kuznetsov, Nikolay; Motygin, Oleg
2014-01-01
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of ...
Harmonic Instability Source Identification in Large Wind Farms
DEFF Research Database (Denmark)
Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei
2017-01-01
A large-scale power electronics based power system like a wind farm introduces the passive and active impedances. The interactions between the active and passive impedances can lead to harmonic-frequency oscillations above the fundamental frequency, which can be called harmonic instability....... This paper presents an approach to identify which wind turbine and which bus has more contribution to the harmonic instability problems. In the approach, a wind farm is modeled as a Multi-Input Multi-Output (MIMO) dynamic system. The poles of the MIMO transfer matrix are used to predict the system...... instability and the eigenvalues sensitivity analysis in respect to the elements of the MIMO matrix locates the most influencing buses of the wind farm. Time-domain simulations in PSCAD software environment for a 400-MW wind farm validate that the presented approach is an effective tool to determine the main...
Gliding and Quasi-harmonic Tremor Behaviour of Raung Volcano: November 2014 Crisis Period Case Study
Directory of Open Access Journals (Sweden)
Vico Luthfi Ipmawan
2018-01-01
Full Text Available DOI: 10.17014/ijog.5.1.13-21The seismic activity of Raung Volcano was raised on 11 November 2014. As many as 1709 tremors were recorded followed by continuous tremors appearing in late November 2014. Quasi-harmonic and gliding tremors appeared in a spectrogram on 12 November 2014. The quasi-harmonic tremors refer to tremors that have no fully harmonic form in spectrum. The gliding harmonic tremors refer to harmonic tremors that have frequency jumps with either positive or negative increment. After signal restitution processing, the Maximum Entropy Spectral Analysis (MESA method was applied in Raung recordings resulting the spectrum and the spectrogram of tremors. The quasi-harmonic tremors have the monotonic spectrum in its head and centre segment, and the harmonic one in its tails. There are twenty-four spectrums that show frequency changes between the monotonic and harmonic. The similarity between the fundamental frequency range of the monotonic and harmonic ones suggests that both signals are excited from a common resonator. The alternating of monotonic and harmonic respectively over this period is qualitatively similar with Julian’s synthetic time series about the nonlinear oscillator model. It is suggested that Raung Volcano magma pressure is sizeable to make a chaotic vibration. A pressure increasing in Raung magmatic conduit causes the increasing of P-wave velocity and makes a positive gliding frequency.
Power oscillation damping controller
DEFF Research Database (Denmark)
2012-01-01
A power oscillation damping controller is provided for a power generation device such as a wind turbine device. The power oscillation damping controller receives an oscillation indicating signal indicative of a power oscillation in an electricity network and provides an oscillation damping control...
International Nuclear Information System (INIS)
Akhiezer, A.I.; Davydov, L.N.; Spol'nik, Z.A.
1976-01-01
Oscillations of a nonideal crystal are studied, in which macroscopic defects (pores) form a hyperlattice. It is shown that alongside with acoustic and optical phonons (relative to the hyperlattice), in such a crystal oscillations of the third type are possible which are a hydridization of sound oscillations of atoms and surface oscillations of a pore. Oscillation spectra of all three types were obtained
Correlator of the reactor oscillator; Korelator reaktorskog oscilatora
Energy Technology Data Exchange (ETDEWEB)
Petrovic, M; Markovic, V; Velickovic, Lj [The Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)
1965-07-01
Reactor oscillator is used for materials testing. Mechanical oscillations of the samples in the core cause perturbations of the power distribution. The perturbation amplitude, i.e. phase angle between the perturbation and the mechanical movement of the sample is proportional to the properties of the tested material. Since the perturbation of the power is not a simple periodic function it is necessary to distinguish the principal harmonic. The size of amplitude gives information about the properties of the sample.
The Two-Beam Free Electron Laser Oscillator
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.
Oscillators - a simple introduction
DEFF Research Database (Denmark)
Lindberg, Erik
2013-01-01
Oscillators are kernel components of electrical and electronic circuits. Discussion of history, mechanisms and design based on Barkhausens observation. Discussion of a Wien Bridge oscillator based on the question: Why does this circuit oscillate ?......Oscillators are kernel components of electrical and electronic circuits. Discussion of history, mechanisms and design based on Barkhausens observation. Discussion of a Wien Bridge oscillator based on the question: Why does this circuit oscillate ?...
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....
Next generation data harmonization
Armstrong, Chandler; Brown, Ryan M.; Chaves, Jillian; Czerniejewski, Adam; Del Vecchio, Justin; Perkins, Timothy K.; Rudnicki, Ron; Tauer, Greg
2015-05-01
Analysts are presented with a never ending stream of data sources. Often, subsets of data sources to solve problems are easily identified but the process to align data sets is time consuming. However, many semantic technologies do allow for fast harmonization of data to overcome these problems. These include ontologies that serve as alignment targets, visual tools and natural language processing that generate semantic graphs in terms of the ontologies, and analytics that leverage these graphs. This research reviews a developed prototype that employs all these approaches to perform analysis across disparate data sources documenting violent, extremist events.
Boltzmann map for quantum oscillators
International Nuclear Information System (INIS)
Streater, R.F.
1987-01-01
The authors define a map tau on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points of tau. The map tau is the composition of a double stochastic map T*, and the quasifree reduction Q. Under mixing conditions on T, iterates of tau take any initial state to the Gibbs states, provided that the oscillator frequencies are mutually rational. They give an example of a system with three degrees of freedom with energies omega 1 , omega 2 , and omega 3 mutually irrational, but obeying a relation n 1 omega 1 + n 2 omega 2 = n 3 omega 3 , n/sub i/epsilon Z. The iterated Boltzmann map converges from an initial state rho to independent Gibbs states of the three oscillators at betas (inverse temperatures) β 1 , β 2 , β 3 obeying the equation n 1 omega 1 β 1 + n 2 omega 3 β 1 number. The equilibrium state can be rewritten as a grand canonical state. They show that for two, three, or four fermions we can get the usual rate equations as a special case
Harmonic states for the free particle
International Nuclear Information System (INIS)
Guerrero, J; López-Ruiz, F F; Aldaya, V; Cossío, F
2011-01-01
Different families of states, which are solutions of the time-dependent free Schrödinger equation, are imported from the harmonic oscillator using the quantum Arnold transformation introduced in Aldaya et al (2011 J. Phys. A: Math. Theor.44 065302). Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite–Gauss and Laguerre–Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined. (paper)
Tissue Harmonic Synthetic Aperture Imaging
DEFF Research Database (Denmark)
Rasmussen, Joachim
The main purpose of this PhD project is to develop an ultrasonic method for tissue harmonic synthetic aperture imaging. The motivation is to advance the field of synthetic aperture imaging in ultrasound, which has shown great potentials in the clinic. Suggestions for synthetic aperture tissue...... system complexity compared to conventional synthetic aperture techniques. In this project, SASB is sought combined with a pulse inversion technique for 2nd harmonic tissue harmonic imaging. The advantages in tissue harmonic imaging (THI) are expected to further improve the image quality of SASB...
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.
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.)
On a generalized oscillator system: interbasis expansions
Energy Technology Data Exchange (ETDEWEB)
Kibler, M [Lyon-1 Univ., 69 - Villeurbanne (France). Inst. de Physique Nucleaire; Mardoyan, L G; Pogosyan, G S [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics
1997-12-31
This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The Schroedinger equation for this generalized oscillator system is separable in spherical, cylindrical, and spheroidal (prolate and oblate) coordinates. The quantum mechanical spectrum of this system is worked out in some details. The problem of interbasis expansions of the wave functions is completely solved. The coefficients for the expansion of the cylindrical basis in terms of the spherical basis, and vice-versa, are found to be analytic continuations (to real values of their arguments) of Clebsch-Gordan coefficients for the group SU(2). The interbasis expansion coefficients for the prolate and oblate spheroidal bases in terms of the spherical or the cylindrical bases are shown to satisfy three-term recursion relations. Finally, a connection between the generalized oscillator system (projected on the z-line) and the Morse system (in one dimension) are discussed. 41 refs.,.
On a generalized oscillator system: interbasis expansions
International Nuclear Information System (INIS)
Kibler, M.; Mardoyan, L.G.; Pogosyan, G.S.
1996-01-01
This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The Schroedinger equation for this generalized oscillator system is separable in spherical, cylindrical, and spheroidal (prolate and oblate) coordinates. The quantum mechanical spectrum of this system is worked out in some details. The problem of interbasis expansions of the wave functions is completely solved. The coefficients for the expansion of the cylindrical basis in terms of the spherical basis, and vice-versa, are found to be analytic continuations (to real values of their arguments) of Clebsch-Gordan coefficients for the group SU(2). The interbasis expansion coefficients for the prolate and oblate spheroidal bases in terms of the spherical or the cylindrical bases are shown to satisfy three-term recursion relations. Finally, a connection between the generalized oscillator system (projected on the z-line) and the Morse system (in one dimension) are discussed. 41 refs.,
Harmonic Quantum Coherence of Multiple Excitons in PbS/CdS Core-Shell Nanocrystals
Tahara, Hirokazu; Sakamoto, Masanori; Teranishi, Toshiharu; Kanemitsu, Yoshihiko
2017-12-01
The generation and recombination dynamics of multiple excitons in nanocrystals (NCs) have attracted much attention from the viewpoints of fundamental physics and device applications. However, the quantum coherence of multiple exciton states in NCs still remains unclear due to a lack of experimental support. Here, we report the first observation of harmonic dipole oscillations in PbS/CdS core-shell NCs using a phase-locked interference detection method for transient absorption. From the ultrafast coherent dynamics and excitation-photon-fluence dependence of the oscillations, we found that multiple excitons cause the harmonic dipole oscillations with ω , 2 ω , and 3 ω oscillations, even though the excitation pulse energy is set to the exciton resonance frequency, ω . This observation is closely related to the quantum coherence of multiple exciton states in NCs, providing important insights into multiple exciton generation mechanisms.
Inducing and destruction of chimeras and chimera-like states by an external harmonic force
Shepelev, I. A.; Vadivasova, T. E.
2018-03-01
We study the phenomena of chimera destruction and inducing of chimera-like states in an ensemble of nonlocally coupled chaotic Rössler oscillators under an external harmonic force. The localized harmonic influence can lead to both destruction and changing of the spatial topology of chimeras. At the same time this influence can cause the emergence of stable chimera-like states (induced chimeras) for the regime of partial coherent chaos. Induced chimeras are also observed for the global influence. We show the possibility of controlling the chimera-like state topology by varying the parameters of localized external harmonic influence.
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.)
Transient regime in second harmonic generation
Szeftel, Jacob; Sandeau, Laure; Sandeau, Nicolas; Delezoide, Camille; Khater, Antoine
2013-09-01
The time growth of the electromagnetic field at the fundamental and double frequencies is studied from the very onset of the second harmonic generation (SHG) process for a set of dipoles lacking a symmetry centre and exhibiting a nonresonant coupling with a classical electromagnetic field. This approach consists first of solving the Schrödinger equation by applying a generalised Rabi rotation to the Hamiltonian describing the light-dipole interaction. This rotation has been devised for the resulting Hamiltonian to show up time-independent for both components of the electromagnetic field at the fundamental frequency and the second harmonic one. Then an energy conservation argument, derived from the Poynting theorem, is introduced to work out an additional relationship between the electromagnetic field and its associated electric polarisation. Finally this analysis yields the full time behaviour of all physical quantities of interest. The calculated results reproduce accurately both the observed spatial oscillations of the SHG intensity (Maker's fringes) and its power law dependence on the intensity of the incoming light at the fundamental frequency.
The Feynman integral for time-dependent anharmonic oscillators
International Nuclear Information System (INIS)
Grothaus, M.; Khandekar, D.C.; da Silva, J.L.; Streit, L.
1997-01-01
We review some basic notions and results of white noise analysis that are used in the construction of the Feynman integrand as a generalized white noise functional. We show that the Feynman integrand for the time-dependent harmonic oscillator in an external potential is a Hida distribution. copyright 1997 American Institute of Physics
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
Location identification of closed crack based on Duffing oscillator transient transition
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.
Second harmonic generation microscopy
DEFF Research Database (Denmark)
Brüggemann, Dagmar Adeline; Brewer, Jonathan R.; Risbo, Jens
2010-01-01
Myofibers and collagen show non-linear optical properties enabling imaging using second harmonic generation (SHG) microscopy. The technique is evaluated for use as a tool for real-time studies of thermally induced changes in thin samples of unfixed and unstained pork. The forward and the backward...... scattered SHG light reveal complementary features of the structures of myofibers and collagen fibers. Upon heating the myofibers show no structural changes before reaching a temperature of 53 °C. At this temperature the SHG signal becomes extinct. The extinction of the SHG at 53 °C coincides with a low......-temperature endotherm peak observable in the differential scanning calorimetry (DSC) thermograms. DSC analysis of epimysium, the connective tissue layer that enfold skeletal muscles, produces one large endotherm starting at 57 °C and peaking at 59.5 °C. SHG microscopy of collagen fibers reveals a variability of thermal...
Azimuthal anisotropy: The higher harmonics
International Nuclear Information System (INIS)
Poskanzer, Arthur M.; STAR Collaboration
2004-01-01
We report the first observations of the fourth harmonic (v 4 ) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v 4 is about a factor of 10 smaller than v 2 . For the sixth (v 6 ) and eighth (v 8 ) harmonics upper limits on the magnitudes are reported
Harmonic Series Meets Fibonacci Sequence
Chen, Hongwei; Kennedy, Chris
2012-01-01
The terms of a conditionally convergent series may be rearranged to converge to any prescribed real value. What if the harmonic series is grouped into Fibonacci length blocks? Or the harmonic series is arranged in alternating Fibonacci length blocks? Or rearranged and alternated into separate blocks of even and odd terms of Fibonacci length?
Tuvan Throat Singing and Harmonics
Ruiz, Michael J.; Wilken, David
2018-01-01
Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the…
Harmonics in transmission power systems
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz
. The comparison shows that results obtained used both types of the cores are the same, so it is concluded that both cores can be used for harmonic measurements. Low-inductance resistors are introduced in the secondary circuits, in series with the metering and protective relaying. On those resistors, the harmonic......Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need...... end only so the ground is not used as a return path. A way to reduce the capacitive coupling is to provide shielding. Harmonic currents are measured using the conventional inductive voltage transformers. Both protective and metering cores were compared if they could be used for harmonic measurements...
Tuvan throat singing and harmonics
Ruiz, Michael J.; Wilken, David
2018-05-01
Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the listener hears two pitches simultaneously. Harmonics such as H8, H9, H10, and H12 form part of a pentatonic scale and are commonly selected for melody tones by Tuvan singers. A real-time spectrogram is provided in a video (Ruiz M J 2018 Video: Tuvan Throat Singing and Harmonics http://mjtruiz.com/ped/tuva/) so that Tuvan harmonics can be visualized as they are heard.
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
Hybrid Reactor Simulation and 3-D Information Display of BWR Out-of-Phase Oscillation
International Nuclear Information System (INIS)
Edwards, Robert; Huang, Zhengyu
2001-01-01
The real-time hybrid reactor simulation (HRS) capability of the Penn State TRIGA reactor has been expanded for boiling water reactor (BWR) out-of-phase behavior. During BWR out-of-phase oscillation half of the core can significantly oscillate out of phase with the other half, while the average power reported by the neutronic instrumentation may show a much lower amplitude for the oscillations. A description of the new HRS is given; three computers are employed to handle all the computations required, including real-time data processing and graph generation. BWR out-of-phase oscillation was successfully simulated. By adjusting the reactivity feedback gains from boiling channels to the TRIGA reactor and to the first harmonic mode power simulation, limit cycle can be generated with both reactor power and the simulated first harmonic power. A 3-D display of spatial power distributions of fundamental mode, first harmonic, and total powers over the reactor cross section is shown
Chimera states in nonlocally coupled phase oscillators with biharmonic interaction
Cheng, Hongyan; Dai, Qionglin; Wu, Nianping; Feng, Yuee; Li, Haihong; Yang, Junzhong
2018-03-01
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example, sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction. We find novel chimera states with features such as that oscillators in the same coherent cluster may split into two groups with a phase difference around π/2 and that oscillators in adjacent coherent clusters may have a phase difference close to π/2. The different impacts of the coupling ranges in the first and the second harmonic interactions on chimera dynamics are investigated based on the synchronous dynamics in globally coupled phase oscillators. Our study suggests a new direction in the field of chimera dynamics.
Forced oscillations of cracked beam under the stochastic cyclic loading
Matsko, I.; Javors'kyj, I.; Yuzefovych, R.; Zakrzewski, Z.
2018-05-01
An analysis of forced oscillations of cracked beam using statistical methods for periodically correlated random processes is presented. The oscillation realizations are obtained on the basis of numerical solutions of differential equations of the second order, for the case when applied force is described by a sum of harmonic and stationary random process. It is established that due to crack appearance forced oscillations acquire properties of second-order periodical non-stationarity. It is shown that in a super-resonance regime covariance and spectral characteristics, which describe non-stationary structure of forced oscillations, are more sensitive to crack growth than the characteristics of the oscillation's deterministic part. Using diagnostic indicators formed on their basis allows the detection of small cracks.
Energy Technology Data Exchange (ETDEWEB)
Graham, Peter W.; /Stanford U., ITP; Horn, Bart; Kachru, Shamit; /Stanford U., ITP /SLAC; Rajendran, Surjeet; /Johns Hopkins U. /Stanford U., ITP; Torroba, Gonzalo; /Stanford U., ITP /SLAC
2011-12-14
We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k = +1, and are supported by a negative cosmological term and matter with -1 < w < -1 = 3. In the case of moderate bounces (where the ratio of the maximal scale factor a{sub +} to the minimal scale factor a{sub -} is {Omicron}(1)), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a{sub +} = a{sub -}, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.
Harmonic operation of high gain harmonic generation free electron laser
International Nuclear Information System (INIS)
Deng Haixiao; Chinese Academy of Sciences, Beijing; Dai Zhimin
2008-01-01
In high gain harmonic generation (HGHG) free electron laser (FEL), with the right choice of parameters of the modulator undulator, the dispersive section and the seed laser, one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation, instead of the fundamental frequency of the radiator radiation in conventional HGHG, thus the radiator undulator is in harmonic operation (HO) mode. In this paper, we investigate HO of HGHG FEL. Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given. It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level. Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy. (authors)
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
Power quality issues current harmonics
Mikkili, Suresh
2015-01-01
Power Quality Issues: Current Harmonics provides solutions for the mitigation of power quality problems related to harmonics. Focusing on active power filters (APFs) due to their excellent harmonic and reactive power compensation in two-wire (single phase), three-wire (three-phase without neutral), and four-wire (three-phase with neutral) AC power networks with nonlinear loads, the text:Introduces the APF technology, describing various APF configurations and offering guidelines for the selection of APFs for specific application considerationsCompares shunt active filter (SHAF) control strategi
DEFF Research Database (Denmark)
Bache, Morten; Lodahl, Peter; Mamaev, Alexander V.
2002-01-01
We predict and experimentally observe temporal self-pulsing in singly resonant intracavity second-harmonic generation under conditions of simultaneous parametric oscillation. The threshold for self-pulsing as a function of cavity tuning and phase mismatch are found from analysis of a three...
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
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
Mapping Electrostatic Forces Using Higher Harmonics Tapping Mode Atomic Force Microscopy in Liquid
van Noort, S.J.T.; Willemsen, O.H.; van der Werf, Kees; de Grooth, B.G.; Greve, Jan
1999-01-01
A simple model of a damped, harmonic oscillator is used to describe the motion of an atomic force microscope cantilever tapping in fluid. By use of experimentally obtained parameters, excellent agreement is found between theory and experimental results. From the model we estimate that the force
Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics
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…
Generation of even harmonics in a relativistic laser plasma of atomic clusters
International Nuclear Information System (INIS)
Krainov, V.P.; Rastunkov, V.S.
2004-01-01
It is shown that the irradiation of atomic clusters by a superintense femtosecond laser pulse gives rise to various harmonics of the laser field. They arise as a result of elastic collisions of free electrons with atomic ions inside the clusters in the presence of the laser filed. The yield of even harmonics whose electromagnetic field is transverse is attributed to the relativism of the motion of electrons and the consideration of their drift velocity associated with the internal ionization of atoms and atomic ions of a cluster. These harmonics are emitted in the same direction as odd harmonics. The conductivities and electromagnetic fields of the harmonics are calculated. The generation efficiency of the harmonics slowly decreases as the harmonic number increases. The generation of even harmonics ceases when the drift velocity of electrons becomes equal to zero and only the oscillation velocity of electrons is nonzero. The results can also be applied to the irradiation of solid-state targets inside a skin layer
International Nuclear Information System (INIS)
Faghihi-Nik, M.; Ghorbanalilu, M.; Shokri, B.
2010-01-01
Complete text of publication follows. Generation of harmonic radiation is an important subject of laser plasma interaction and attracts great attention due to a wide range of applications. It has been seen that intense electromagnetic and quasi-static transverse magnetic fields are generated in laser plasma interaction. An extremely intense magnetic field (up to hundreds of MG) has been observed by experimental measurements in interaction of short laser pulses with plasma. These self-generated or applied magnetic fields affect the propagation of the laser pulses. In most laser interactions with homogeneous plasma, odd harmonics of laser frequency are generated. In this paper, we point out the possibility of even harmonics generation when a linearly polarized laser beam propagates in homogeneous plasma in the presence of a transverse magnetic field. It is shown that applying external field induces a transverse current density oscillating twice of the laser field which leds to generation of second harmonic radiation. This current density is derived using the perturbation method, and the steady state amplitude of the second harmonic obtained by solution of the wave equation. By the same procedure the current density and then the steady state amplitude of higher order harmonics are calculated. The efficiency of harmonic generation (the ratio of harmonic power to incident power) is a drastically function of the strength of external magnetic field. It is found that the efficiency of even harmonics is zero in the absence of magnetic field and increases as the magnetic field is increased. For odd harmonics, applying the external magnetic field enhances the generated harmonics as well. The conversion efficiency also increases with increase in plasma density and intensity of the laser beam.
Classical and multilinear harmonic analysis
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...
Explaining the harmonic sequence paradox.
Schmidt, Ulrich; Zimper, Alexander
2012-05-01
According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced. ©2011 The British Psychological Society.
Introduction to abstract harmonic analysis
Loomis, Lynn H
2011-01-01
Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Cohabiting with the harmonic pollution
International Nuclear Information System (INIS)
Garcia C, Antonio A
1999-01-01
The Norm IEEE 519 tries of the permissible limits of harmonic distortion in the point of common joining between the energy supplier company and the industry. However fulfilling these limits of distortion doesn't guarantee that the problem for the company has finished, on the contrary will have to counteract the effects created by the harmonic distortion toward the interior of its electric system and to cohabit with this distortion
Ma, Hongbin
2015-01-01
This book presents the fundamental fluid flow and heat transfer principles occurring in oscillating heat pipes and also provides updated developments and recent innovations in research and applications of heat pipes. Starting with fundamental presentation of heat pipes, the focus is on oscillating motions and its heat transfer enhancement in a two-phase heat transfer system. The book covers thermodynamic analysis, interfacial phenomenon, thin film evaporation, theoretical models of oscillating motion and heat transfer of single phase and two-phase flows, primary factors affecting oscillating motions and heat transfer, neutron imaging study of oscillating motions in an oscillating heat pipes, and nanofluid’s effect on the heat transfer performance in oscillating heat pipes. The importance of thermally-excited oscillating motion combined with phase change heat transfer to a wide variety of applications is emphasized. This book is an essential resource and learning tool for senior undergraduate, gradua...
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
Modeling and Identification of Harmonic Instability Problems In Wind Farms
DEFF Research Database (Denmark)
Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei
2016-01-01
In power electronics based power systems like wind farms, the interactions between the inner control systems of the power converters and the passive components may lead to high frequency oscillations, which can be called harmonic instability. In this paper, a simple methodology is presented...... to identify harmonic instability problems in wind farms, where many wind turbines, cables, transformers, capacitor banks, shunt reactors, etc, typically are located. This methodology introduces the wind farm as a Multi-Input Multi-Outpur (MIMO) control system, where the linearized models of fast inner control....../EMTDC software environment for a 400-MW wind farm. The proposed analytical analysis method and time-domain simulation results show that both dynamics of the power electronic converter and the parameters of the passive component can effect on the wind farm stability....
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
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.
Coherent harmonics generated by a super-short electron pulse
International Nuclear Information System (INIS)
Ding Wu
1996-01-01
A novel mechanism generating superradiance harmonics is found. In this superradiance harmonics, the temporal width of harmonics is extremely short, the ratio of high harmonic fundamental wave is much higher than the known superradiance harmonics
General Lp-harmonic Blaschke bodies
Indian Academy of Sciences (India)
Abstract. Lutwak introduced the harmonic Blaschke combination and the harmonic. Blaschke body of a star body. Further, Feng and Wang introduced the concept of the L p- harmonic Blaschke body of a star body. In this paper, we define the notion of general. L p-harmonic Blaschke bodies and establish some of its ...
General Lp-harmonic Blaschke bodies
Indian Academy of Sciences (India)
Lutwak introduced the harmonic Blaschke combination and the harmonic Blaschke body of a star body. Further, Feng and Wang introduced the concept of the -harmonic Blaschke body of a star body. In this paper, we define the notion of general -harmonic Blaschke bodies and establish some of its properties.
Audibility of harmonics in 'periodic white noise'
Duifhuis, H.; Tomesen, H.H.
1970-01-01
In a previous article (Duifhuis, 1970) results' concerning the audibility of harmonics in a periodic pulse have been presented. Each of the lower harmonics could be perceived separately, whereas the high harmonics were heard together as one complex signal. High harmonics, however, appeared to be
1981-03-01
Final Report: February 1978 ZAUTOMATIC OSCILLATING TURRET SYSTEM September 1980 * 6. PERFORMING 01G. REPORT NUMBER .J7. AUTHOR(S) S. CONTRACT OR GRANT...o....e.... *24 APPENDIX P-4 OSCILLATING BUMPER TURRET ...................... 25 A. DESCRIPTION 1. Turret Controls ...Other criteria requirements were: 1. Turret controls inside cab. 2. Automatic oscillation with fixed elevation to range from 20* below the horizontal to
Neutrino oscillations in matter
International Nuclear Information System (INIS)
Mikheyev, S.P.; Smirnov, A.Yu.
1986-01-01
In this paper we describe united formalism of ν-oscillations for different regimes, which is immediate generalization of vacuum oscillations theory. Adequate graphical representation of this formalism is given. We summarize main properties of ν-oscillations for different density distributions. (orig./BBOE)
The colpitts oscillator family
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
A tutorial study of the Colpitts oscillator family defined as all oscillators based on a nonlinear amplifier and a three- terminal linear resonance circuit with one coil and two capacitors. The original patents are investigated. The eigenvalues of the linearized Jacobian for oscillators based...
Oscillators in resonance p:q:r
International Nuclear Information System (INIS)
Arribas, M.; Elipe, A.; Floria, L.; Riaguas, A.
2006-01-01
A canonical transformation is proposed to handle Hamiltonian systems made of the addition or subtraction of three harmonic oscillators in p:q:r resonance. This transformation is an extension of the classical Lissajous transformation for the 1:1 resonance. Our extended Lissajous variables consist of three pairs of action-angle variables, which makes possible the application of perturbation theories without encountering small divisors. A set of functions, related with the Lissajous variables, are found, and are used to describe the phase flow of reduced space after normalization
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
Collapse of simple harmonic universe
International Nuclear Information System (INIS)
Mithani, Audrey T.; Vilenkin, Alexander
2012-01-01
In a recent paper Graham et al constructed oscillating and static universe models which are stable with respect to all classical perturbations. Here we show that such universes are quantum-mechanically unstable and can collapse by quantum tunneling to zero radius. We also present instantons describing nucleation of oscillating and static universes from nothing
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.
Relativistic Bosons in Time-Harmonic Electric Fields
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.
Noncommuting limits of oscillator wave functions
International Nuclear Information System (INIS)
Daboul, J.; Pogosyan, G. S.; Wolf, K. B.
2007-01-01
Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite-Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry
Nature's Autonomous Oscillators
Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.
2012-01-01
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
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.
Golden quantum oscillator and Binet–Fibonacci calculus
International Nuclear Information System (INIS)
Pashaev, Oktay K; Nalci, Sengul
2012-01-01
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = −1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)
Solution Hamilton-Jacobi equation for oscillator Caldirola-Kanai
Directory of Open Access Journals (Sweden)
LEONARDO PASTRANA ARTEAGA
2016-12-01
Full Text Available The method allows Hamilton-Jacobi explicitly determine the generating function from which is possible to derive a transformation that makes soluble Hamilton's equations. Using the separation of variables the partial differential equation of the first order called Hamilton-Jacobi equation is solved; as a particular case consider the oscillator Caldirola-Kanai (CK, which is characterized in that the mass presents a temporal evolution exponentially . We demonstrate that the oscillator CK position presents an exponential decay in time similar to that obtained in the damped sub-critical oscillator, which reflects the dissipation of total mechanical energy. We found that in the limit that the damping factor is small, the behavior is the same as an oscillator with simple harmonic motion, where the effects of energy dissipation is negligible.
Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation
Kondratov, D. V.; Mogilevich, L. I.; Popov, V. S.; Popova, A. A.
2018-01-01
The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well.
Golden quantum oscillator and Binet-Fibonacci calculus
Energy Technology Data Exchange (ETDEWEB)
Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)
2012-01-13
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)
HARMONIZED EUROPE OR EUROPEAN HARMONY?
Directory of Open Access Journals (Sweden)
Cosmin Marinescu
2007-07-01
Full Text Available Recent evolutions in Europe raise questions on the viability of the present economic and social model that defines the European construction project. In this paper, the author will try to explain the viability of institutional European model that sticks between free market mechanisms and protectionism. The main challenge for the EU is about the possibility to bring together the institutional convergence and the welfare for all Europeans. This is the result of the view, still dominant, of European politics elite, according to which institutional harmonization is the solution of a more dynamic and prosper Europe. But, economic realities convince us that, more and more, a harmonized, standardized Europe is not necessarily identical with a Europe of harmony and social cooperation. If „development through integration” seems to be harmonization through „institutional transplant”, how could then be the European model one sufficiently wide open to market, which creates the prosperity so long waited for by new member countries?
Harmonic superspaces of extended supersymmetry
International Nuclear Information System (INIS)
Ivanov, E.; Kalitzin, S.; Nguyen Ai Viet; Ogievetsky, V.
1984-01-01
The main technical apparatus of the harmonic superspace approach to extended SUSY, the calculus of harmonic variables on homogeneous spaces of the SUSY automorphism groups, is presented in detail for N=2, 3, 4. The basic harmonics for the coset manifolds G/H with G=SU(2), H=U(1); G=SU(3), H=SU(2)xU(1) and H=U(1)xU(1); G=SU(4), H=SU(3)xU(1), H=SU(2)xSU(2)xU(1), H=SU(2)xU(1)xU(1) and H=U(1)xU(1)xU(1); G=USp(2), H=SU(2)xSU(2), H=SU(2)xU(1) and H=U(1)xU(1) are tabulated a number of useful relations among them
A memristor-based third-order oscillator: beyond oscillation
Talukdar, Abdul Hafiz Ibne
2012-10-06
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
A memristor-based third-order oscillator: beyond oscillation
Talukdar, Abdul Hafiz Ibne; Radwan, Ahmed G.; Salama, Khaled N.
2012-01-01
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
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)
International Nuclear Information System (INIS)
Taneichi, T.; Kobayashi, T.
2007-01-01
Discussion on wavelength dependent 'anharmonic' effects in a pump-probe signal for a system of wavepacket on one- and two-dimensional harmonic potentials was given. The Fourier power spectrum of the signal, calculated for a model composed of a three-state electronic system coupled to a set of displaced harmonic oscillators, depends on the pulse duration. Condition under which the wavepacket motion in the harmonic potential substantially deviates from that of the classical point mass is derived. The Fourier power spectrum has enhanced components with frequencies of harmonics even in a system composed of ideally harmonic potentials. Utility of the Fourier analysis of the spectrum for clarification of the squeezed molecular vibrational state is discussed. Calculated oscillatory behavior in phase of a pump-probe signal, as a function of probe frequency, was discussed in terms of a two-dimensional effect on a pump-probe signal
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1987-01-01
In the present paper we show how the N = 2 superconformal group is realised in harmonic superspace and examine conformal invariance of N = 2 off-shell theories. We believe that the example of N = O self-dual Yang-Mills equations can serve as an instructive introduction to the subject of harmonic superspace and this is examined. The rigid N = 2 conformal supersymmetry and its local version, i.e. N = 2 conformal supergravity is also discussed. The paper is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. (author)
Elements of abstract harmonic analysis
Bachman, George
2013-01-01
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give
Harmonic modeling of induction motors
Energy Technology Data Exchange (ETDEWEB)
Pedra, J.; Sainz, L.; Corcoles, F. [Department of Electrical Engineering, ETSEIB-UPC, Av. Diagonal 647, 08028 Barcelona (Spain)
2006-07-15
The paper proposes an induction motor model for the study of harmonic load flow in balanced and unbalanced conditions. The parameters of this model are obtained from motor manufacturer data and the positive- and negative-sequence equivalent circuits of the single- and double-cage models. An approximate harmonic model based on motor manufacturer data only is also proposed. In addition, the paper includes manufacturer data and the calculated parameters of 36 induction motors of different rated powers. This database is used to analyze the proposed models. (author)
Optimal Selective Harmonic Control for Power Harmonics Mitigation
DEFF Research Database (Denmark)
Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede
2015-01-01
of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...
Probabilistic Harmonic Modeling of Wind Power Plants
DEFF Research Database (Denmark)
Guest, Emerson; Jensen, Kim H.; Rasmussen, Tonny Wederberg
2017-01-01
A probabilistic sequence domain (SD) harmonic model of a grid-connected voltage-source converter is used to estimate harmonic emissions in a wind power plant (WPP) comprised of Type-IV wind turbines. The SD representation naturally partitioned converter generated voltage harmonics into those...... with deterministic phase and those with probabilistic phase. A case study performed on a string of ten 3MW, Type-IV wind turbines implemented in PSCAD was used to verify the probabilistic SD harmonic model. The probabilistic SD harmonic model can be employed in the planning phase of WPP projects to assess harmonic...
Low-order-mode harmonic multiplying gyrotron traveling-wave amplifier in W band
International Nuclear Information System (INIS)
Yeh, Y. S.; Chen, C. H.; Yang, S. J.; Lai, C. H.; Lin, T. Y.; Lo, Y. C.; Hong, J. W.; Hung, C. L.; Chang, T. H.
2012-01-01
Harmonic multiplying gyrotron traveling-wave amplifiers (gyro-TWAs) allow for magnetic field reduction and frequency multiplication. To avoid absolute instabilities, this work proposes a W-band harmonic multiplying gyro-TWA operating at low-order modes. By amplifying a fundamental harmonic TE 11 drive wave, the second harmonic component of the beam current initiates a TE 21 wave to be amplified. Absolute instabilities in the gyro-TWA are suppressed by shortening the interaction circuit and increasing wall losses. Simulation results reveal that compared with Ka-band gyro-TWTs, the lower wall losses effectively suppress absolute instabilities in the W-band gyro-TWA. However, a global reflective oscillation occurs as the wall losses decrease. Increasing the length or resistivity of the lossy section can reduce the feedback of the oscillation to stabilize the amplifier. The W-band harmonic multiplying gyro-TWA is predicted to yield a peak output power of 111 kW at 98 GHz with an efficiency of 25%, a saturated gain of 26 dB, and a bandwidth of 1.6 GHz for a 60 kV, 7.5 A electron beam with an axial velocity spread of 8%.
Deep saturated Free Electron Laser oscillators and frozen spikes
Energy Technology Data Exchange (ETDEWEB)
Ottaviani, P.L. [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Pagnutti, S., E-mail: simonetta.pagnutti@enea.it [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Dattoli, G., E-mail: giuseppe.dattoli@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Sabia, E., E-mail: elio.sabia@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Petrillo, V., E-mail: vittoria.petrillo@mi.infn.it [Universita' degli Studi di Milano, via Celoria 16, IT 20133, Milano (Italy); INFN - Mi, via Celoria 16, IT 20133, Milano (Italy); Slot, P.J.M. van der, E-mail: p.j.m.vanderslot@utwente.nl [Mesa+ Institute for Nanotechnology, University of Twente, P.O.Box 217, 7500 AE, Enschede (Netherlands); Biedron, S., E-mail: sandra.biedron@colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States); Milton, S., E-mail: milton@engr.colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States)
2016-10-21
We analyze the behavior of Free Electron Laser (FEL) oscillators operating in the deep saturated regime and point out the formation of sub-peaks of the optical pulse. These are very stable configurations and the sub-peaks are found to have a duration corresponding to the coherence length. We speculate on the physical mechanisms underlying their growth and attempt an identification with natural mode-locked structures in FEL oscillators. Their impact on the intra-cavity nonlinear harmonic generation is also discussed along with the possibility of exploiting them as cavity out-coupler.
Vertical vibration and shape oscillation of acoustically levitated water drops
International Nuclear Information System (INIS)
Geng, D. L.; Xie, W. J.; Yan, N.; Wei, B.
2014-01-01
We present the vertical harmonic vibration of levitated water drops within ultrasound field. The restoring force to maintain such a vibration mode is provided by the resultant force of acoustic radiation force and drop gravity. Experiments reveal that the vibration frequency increases with the aspect ratio for drops with the same volume, which agrees with the theoretical prediction for those cases of nearly equiaxed drops. During the vertical vibration, the floating drops undergo the second order shape oscillation. The shape oscillation frequency is determined to be twice the vibration frequency.
Vertical vibration and shape oscillation of acoustically levitated water drops
Energy Technology Data Exchange (ETDEWEB)
Geng, D. L.; Xie, W. J.; Yan, N.; Wei, B., E-mail: bbwei@nwpu.edu.cn [Department of Applied Physics, Northwestern Polytechnical University, Xi' an 710072 (China)
2014-09-08
We present the vertical harmonic vibration of levitated water drops within ultrasound field. The restoring force to maintain such a vibration mode is provided by the resultant force of acoustic radiation force and drop gravity. Experiments reveal that the vibration frequency increases with the aspect ratio for drops with the same volume, which agrees with the theoretical prediction for those cases of nearly equiaxed drops. During the vertical vibration, the floating drops undergo the second order shape oscillation. The shape oscillation frequency is determined to be twice the vibration frequency.
On a generalized oscillator: invariance algebra and interbasis expansions
International Nuclear Information System (INIS)
Hakopyan, E.M.; Pogosyan, G.S.; Sisakyan, A.N.; Kibler, M.
1998-01-01
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the super integrable character for the generalized oscillator system is investigated from the point of view of a quadratic invariance algebra
Discrete oscillator design linear, nonlinear, transient, and noise domains
Rhea, Randall W
2014-01-01
Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and today's engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of os
Kato, Shoji
2016-01-01
This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...
Modeling Bloch oscillations in nanoscale Josephson junctions
Vora, Heli; Kautz, R. L.; Nam, S. W.; Aumentado, J.
2018-01-01
Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage-current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I = (n/m)2ef induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic (m = 1) steps. We also demonstrate that the GS model allows a detailed semiquantitative fit to experimental voltage-current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations. PMID:29577106
Oscillations in stellar atmospheres
International Nuclear Information System (INIS)
Costa, A.; Ringuelet, A.E.; Fontenla, J.M.
1989-01-01
Atmospheric excitation and propagation of oscillations are analyzed for typical pulsating stars. The linear, plane-parallel approach for the pulsating atmosphere gives a local description of the phenomenon. From the local analysis of oscillations, the minimum frequencies are obtained for radially propagating waves. The comparison of the minimum frequencies obtained for a variety of stellar types is in good agreement with the observed periods of the oscillations. The role of the atmosphere in the globar stellar pulsations is thus emphasized. 7 refs
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
A flight investigation of oscillating air forces: Equipment and technique
Reed, W. H., III
1975-01-01
The equipment and techniques are described which are to be used in a project aimed at measuring oscillating air forces and dynamic aeroelastic response of a swept wing airplane at high subsonic speeds. Electro-hydraulic inertia type shakers installed in the wing tips will excite various elastic airplane modes while the related oscillating chordwise pressures at two spanwise wing stations and the wing mode shapes are recorded on magnetic tape. The data reduction technique, following the principle of a wattmeter harmonic analyzer employed by Bratt, Wight, and Tilly, utilizes magnetic tape and high speed electronic multipliers to record directly the real and imaginary components of oscillatory data signals relative to a simple harmonic reference signal. Through an extension of this technique an automatic flight-flutter-test data analyzer is suggested in which vector plots of mechanical admittance or impedance would be plotted during the flight test.
Entanglement in the harmonic chain and quantum fields
International Nuclear Information System (INIS)
Kofler, J.; Vedral, V.; Brukner, C.
2005-01-01
Full text: Relativistic field theory is a natural basis for the theoretical investigation of quantum entanglement, since the concept of locality and causality is inherently included. Vacuum entanglement of relativistic fields manifests itself in Hawking radiation and the Unruh effect. But it also is encountered in the linear harmonic chain, which - in the continuum limit and if generalized to three spatial dimensions - becomes the real scalar Klein-Gordon field. One can define average position and momentum operators for two separated blocks of oscillators in the harmonic chain and investigate the entanglement - by means of a separability criterion - between these blocks as a function of their distance and the coupling between the oscillators. This motivated us to rewrite the general separability conditions for continuous variables into the language of quantum field theory, where the position and momentum operator become integrals of the Klein-Gordon field and the conjugate momentum field, respectively. The role of the modes (or particles) is then merely played by the space(-time) regions over which the integration takes (author)
Harmonic structures and intrinsic torsion
DEFF Research Database (Denmark)
Conti, Diego; Madsen, Thomas Bruun
We discuss the construction of 8-manifolds with harmonic Sp(2)Sp(1)-structures. In particular, we find 10 new examples of nilmanifolds that admit a closed 4-form Omega whose stabiliser is Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough...
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
N=2 conformal supersymmetry is realized in harmonic superspace, its peculiarities are analyzed. The coordinate group and analytical prepotentials for N=2 conformal supergravity are found. A new version of the N=2 Einstein supergravity with infinite number of auxiliary fields is suggested. A hypermultiplet without central charges and constraints is used as a compensator
Sums of Generalized Harmonic Series
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 9. Sums of Generalized Harmonic Series: For Kids from Five to Fifteen. Zurab Silagadze. General Article Volume 20 Issue 9 September 2015 pp 822-843. Fulltext. Click here to view fulltext PDF. Permanent link:
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.)
Design and Characterization of 1.8-3.2 THz Schottky-based Harmonic Mixers
Bulcha, BT; Hesler, JL; Drakinskiy, V; Stake, J; Valavanis, A; Dean, P; Li, LH; Barker, NS
2016-01-01
A room-temperature Schottky diode-based WM-86 (WR-0.34) harmonic mixer was developed to build high-resolution spectrometers, and multi-pixel receivers in the THz region for applications such as radio astronomy, plasma diagnostics, and remote sensing. The mixer consists of a quartz-based Local Oscillator (LO), Intermediate-Frequency (IF) circuits, and a GaAs-based beam-lead THz circuit with an integrated diode. Measurements of the harmonic mixer were performed using a 2 THz solid-state source ...
Laser dynamics of asynchronous rational harmonic mode-locked fiber soliton lasers
International Nuclear Information System (INIS)
Jyu, Siao-Shan; Jiang, Guo-Hao; Lai, Yinchieh
2013-01-01
Laser dynamics of asynchronous rational harmonic mode-locked (ARHM) fiber soliton lasers are investigated in detail. In particular, based on the unique laser dynamics of asynchronous mode-locking, we have developed a new method for determining the effective active modulation strength in situ for ARHM lasers. By measuring the magnitudes of the slowly oscillating pulse timing position and central frequency, the effective phase modulation strength at the multiplication frequency of rational harmonic mode-locking can be accurately inferred. The method can be a very useful tool for developing ARHM fiber lasers. (paper)
Oyster Creek fuel thermal margin during core thermal-hydraulic oscillations
International Nuclear Information System (INIS)
Dougher, J.D.
1990-01-01
The Oyster Creek nuclear facility, a boiling water reactor (BWR)-2 plant type, has never experienced core thermal-hydraulic instability. Power oscillations, however, have been observed in other BWR cores both domestically and internationally. Two modes of oscillations have been observed, core wide and regional half-core. During core wide oscillations, the neutron flux in the core oscillates in the radial fundamental mode. During regional half-core oscillations, higher order harmonics in the radial plane result in out-of-phase oscillations with the neutron flux in one half of the core oscillating 180 deg out-of-phase with the neutron flux in the other half of the core. General Design Criteria 12 requires either prevention or detection and suppression of power oscillations which could result in violations of fuel design limits. Analyses performed by General Electric have demonstrated that for large-magnitude oscillations the potential exists for violation of the safety limit minimum critical power ratio (MCPR). However, for plants with a flow-biased neutron flux scram automatic mitigation of oscillations may be provided at an oscillation magnitude below that at which the safety limit is challenged. Plant-specific analysis for Oyster Creek demonstrates that the existing average power range monitor (APRM) system will sense and suppress power oscillations prior to violation of any safety limits
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
Lenore White Harmon: One Woman's Career Development.
Fouad, Nadya A.
1997-01-01
Presents biographical information on Lenore White Harmon, noted professor, counselor, and researcher. In a question-and-answer section, Harmon describes her early career decisions, work history, research efforts, professional contributions, important influences and reflections on her career development. (KW)
Tides and tidal harmonics at Umbharat, Gujarat
Digital Repository Service at National Institute of Oceanography (India)
Suryanarayana, A.; Swamy, G.N.
A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...
Higher order harmonics of reactor neutron equation
International Nuclear Information System (INIS)
Li Fu; Hu Yongming; Luo Zhengpei
1996-01-01
The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out
The Oscillator Principle of Nature
DEFF Research Database (Denmark)
Lindberg, Erik
2012-01-01
Oscillators are found on all levels in Nature. The general oscillator concept is defined and investigated. Oscillators may synchronize into fractal patterns. Apparently oscillators are the basic principle in Nature. The concepts of zero and infinite are discussed. Electronic manmade oscillators...
Harmonic disturbance location by applying Bayesian inference
Ye, G.; Xiang, Y.; Cuk, V.; Cobben, J.F.G.
2016-01-01
Harmonic pollution is one of the most important power quality issues in electric power systems. Correct location of the main harmonic disturbance source is a key step to solve the problem. This paper presents a method to detect the location of harmonic disturbance source in low voltage network
Detection of Harmonic Occurring using Kalman Filtering
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Shoro, Ghulam Mustafa; Imran, Raja Muhammed
2014-01-01
/current characteristic. These harmonics are not to be allowed to grow beyond a certain limit to avoid any grave consequence to the customer’s main supply. Filters can be implemented at the power source or utility location to eliminate these harmonics. In this paper we detect the instance at which these harmonics occur...
Third Harmonic Imaging using a Pulse Inversion
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
The pulse inversion (PI) technique can be utilized to separate and enhance harmonic components of a waveform for tissue harmonic imaging. While most ultrasound systems can perform pulse inversion, only few image the 3rd harmonic component. PI pulse subtraction can isolate and enhance the 3rd...
International Nuclear Information System (INIS)
Rodrigues, R. de Lima
2007-01-01
In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra C 7. The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic limit. (author)
DEFF Research Database (Denmark)
Hjorth, Poul G.
2008-01-01
We discuss nonlinear mechanical systems containing several oscillators whose frequecies are all much higher than frequencies associated with the remaining degrees of freedom. In this situation a near constant of the motion, an adiabatic invariant, exists which is the sum of all the oscillator...... actions. The phenomenon is illustrated, and calculations of the small change of the adiabatic invariant is outlined....
Synchronization of hyperchaotic oscillators
DEFF Research Database (Denmark)
Tamasevicius, A.; Cenys, A.; Mykolaitis, G.
1997-01-01
Synchronization of chaotic oscillators is believed to have promising applications in secure communications. Hyperchaotic systems with multiple positive Lyapunov exponents (LEs) have an advantage over common chaotic systems with only one positive LE. Three different types of hyperchaotic electronic...... oscillators are investigated demonstrating synchronization by means of only one properly selected variable....
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Gordon, Christopher R.
2013-01-01
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier
International Nuclear Information System (INIS)
Chruscinski, Dariusz
2006-01-01
We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba
A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate
Lin, Ruixing; Xu, Lin; Zheng, Xian
2018-03-01
Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.
Oscillations of a spring-magnet system damped by a conductive plate
Ladera, C. L.; Donoso, G.
2013-09-01
We study the motion of a spring-magnet system that oscillates with very low frequencies above a circular horizontal non-magnetizable conductive plate. The magnet oscillations couple with the plate via the Foucault currents induced therein. We develop a simple theoretical model for this magneto-mechanical oscillator, a model that leads to the equation of a damped harmonic oscillator, whose weak attenuation constant depends upon the system parameters, e.g. the electrical conductivity of the constituent material of the plate and its thickness. We present a set of validating experiments, the results of which are predicted with good accuracy by our analytical model. Additional experiments can be performed with this oscillating system or its variants. This oscillator is simple and low-cost, easy to assemble, and can be used in experiments or project works in physics teaching laboratories at the undergraduate level.
Oscillations of a spring–magnet system damped by a conductive plate
International Nuclear Information System (INIS)
Ladera, C L; Donoso, G
2013-01-01
We study the motion of a spring–magnet system that oscillates with very low frequencies above a circular horizontal non-magnetizable conductive plate. The magnet oscillations couple with the plate via the Foucault currents induced therein. We develop a simple theoretical model for this magneto-mechanical oscillator, a model that leads to the equation of a damped harmonic oscillator, whose weak attenuation constant depends upon the system parameters, e.g. the electrical conductivity of the constituent material of the plate and its thickness. We present a set of validating experiments, the results of which are predicted with good accuracy by our analytical model. Additional experiments can be performed with this oscillating system or its variants. This oscillator is simple and low-cost, easy to assemble, and can be used in experiments or project works in physics teaching laboratories at the undergraduate level. (paper)
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
First operation of a harmonic lasing self-seeded free electron laser
International Nuclear Information System (INIS)
Schneidmiller, E.A.; Faatz, B.; Kuhlmann, M.; Roensch-Schulenburg, J.; Schreiber, S.; Tischer, M.; Yurkov, M.V.
2016-12-01
Harmonic lasing is a perspective mode of operation of X-ray FEL user facilities that allows to provide brilliant beams of higher energy photons for user experiments. Another useful application of harmonic lasing is so called Harmonic Lasing Self-Seeded Free Electron Laser (HLSS FEL) that allows to improve spectral brightness of these facilities. In the past, harmonic lasing has been demonstrated in the FEL oscillators in infrared and visible wavelength ranges, but not in high-gain FELs and not at short wavelengths. In this paper we report on the first evidence of the harmonic lasing and the first operation of the HLSS FEL at the soft X-ray FEL user facility FLASH in the wavelength range between 4.5 nm and 15 nm. Spectral brightness was improved in comparison with Self-Amplified Spontaneous emission (SASE) FEL by a factor of six in the exponential gain regime. A better performance of HLSS FEL with respect to SASE FEL in the post-saturation regime with a tapered undulator was observed as well. The first demonstration of harmonic lasing in a high-gain FEL and at short wavelengths paves the way for a variety of applications of this new operation mode in X-ray FELs.
The Spectrum of Particles with Short-Ranged Interactions in a Harmonic Trap
Directory of Open Access Journals (Sweden)
Metsch B. Ch.
2010-04-01
Full Text Available The possibility to control short-ranged interactions of cold gases in optical traps by Feshbachresonances makes these systems ideal candidates to study universal scaling properties and Eﬁmov physics. The spectrum of particles in a trap, idealised by a harmonic oscillator potential, in the zero range limit with 2- and 3-particle contact interactions is studied numerically. The Hamiltonian is regularised by restricting the oscillator basis and the coupling constants are tuned such that the ground state energies of the 2- and 3-particle sector are reproduced [1],[2]. Results for 2-, 3-, and 4 particle systems are presented and compared to exact results [3],[4].
Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.
Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene
2017-08-01
Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.
Harmonic Detection at Initialization With Kalman Filter
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Imran, Raja Muhammad; Shoro, Ghulam Mustafa
2014-01-01
Most power electronic equipment these days generate harmonic disturbances, these devices hold nonlinear voltage/current characteristic. The harmonics generated can potentially be harmful to the consumer supply. Typically, filters are integrated at the power source or utility location to filter out...... the affect of harmonics on the supply. For the detection of these harmonics various techniques are available and one of that technique is the Kalman filter. In this paper we investigate that what are the consequences when harmonic detection system based on Kalman Filtering is initialized...
Waveguide harmonic damper for klystron amplifier
International Nuclear Information System (INIS)
Kang, Y.
1998-01-01
A waveguide harmonic damper was designed for removing the harmonic frequency power from the klystron amplifiers of the APS linac. Straight coaxial probe antennas are used in a rectangular waveguide to form a damper. A linear array of the probe antennas is used on a narrow wall of the rectangular waveguide for damping klystron harmonics while decoupling the fundamental frequency in dominent TE 01 mode. The klystron harmonics can exist in the waveguide as waveguide higher-order modes above cutoff. Computer simulations are made to investigate the waveguide harmonic damping characteristics of the damper
Harmonic space and quaternionic manifolds
International Nuclear Information System (INIS)
Galperin, A.; Ogievetsky, O.; Ivanov, E.
1992-10-01
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs
Data harmonization and model performance
The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.
Study of Pressure Oscillations in Supersonic Parachute
Dahal, Nimesh; Fukiba, Katsuyoshi; Mizuta, Kazuki; Maru, Yusuke
2018-04-01
Supersonic parachutes are a critical element of planetary mission whose simple structure, light-weight characteristics together with high ratio of aerodynamic drag makes them the most suitable aerodynamic decelerators. The use of parachute in supersonic flow produces complex shock/shock and wake/shock interaction giving rise to dynamic pressure oscillations. The study of supersonic parachute is difficult, because parachute has very flexible structure which makes obtaining experimental pressure data difficult. In this study, a supersonic wind tunnel test using two rigid bodies is done. The wind tunnel test was done at Mach number 3 by varying the distance between the front and rear objects, and the distance of a bundle point which divides suspension lines and a riser. The analysis of Schlieren movies revealed shock wave oscillation which was repetitive and had large pressure variation. The pressure variation differed in each case of change in distance between the front and rear objects, and the change in distance between riser and the rear object. The causes of pressure oscillation are: interaction of wake caused by front object with the shock wave, fundamental harmonic vibration of suspension lines, interference between shock waves, and the boundary layer of suspension lines.
Coupled oscillators and Feynman's three papers
International Nuclear Information System (INIS)
Kim, Y S
2007-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the 'rest of the universe' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators
Harmonic ratcheting for fast acceleration
Cook, N.; Brennan, J. M.; Peggs, S.
2014-04-01
A major challenge in the design of rf cavities for the acceleration of medium-energy charged ions is the need to rapidly sweep the radio frequency over a large range. From low-power medical synchrotrons to high-power accelerator driven subcritical reactor systems, and from fixed focus alternating gradient accelerators to rapid cycling synchrotrons, there is a strong need for more efficient, and faster, acceleration of protons and light ions in the semirelativistic range of hundreds of MeV/u. A conventional way to achieve a large, rapid frequency sweep (perhaps over a range of a factor of 6) is to use custom-designed ferrite-loaded cavities. Ferrite rings enable the precise tuning of the resonant frequency of a cavity, through the control of the incremental permeability that is possible by introducing a pseudoconstant azimuthal magnetic field. However, rapid changes over large permeability ranges incur anomalous behavior such as the "Q-loss" and "f-dot" loss phenomena that limit performance while requiring high bias currents. Notwithstanding the incomplete understanding of these phenomena, they can be ameliorated by introducing a "harmonic ratcheting" acceleration scheme in which two or more rf cavities take turns accelerating the beam—one turns on when the other turns off, at different harmonics—so that the radio frequency can be constrained to remain in a smaller range. Harmonic ratcheting also has straightforward performance advantages, depending on the particular parameter set at hand. In some typical cases it is possible to halve the length of the cavities, or to double the effective gap voltage, or to double the repetition rate. This paper discusses and quantifies the advantages of harmonic ratcheting in general. Simulation results for the particular case of a rapid cycling medical synchrotron ratcheting from harmonic number 9 to 2 show that stability and performance criteria are met even when realistic engineering details are taken into consideration.
Harmonic Lattice Dynamics of Germanium
Energy Technology Data Exchange (ETDEWEB)
Nelin, G
1974-07-01
The phonon dispersion relations of the DELTA-, LAMBDA-, and SIGMA-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field.
Harmonic Lattice Dynamics of Germanium
International Nuclear Information System (INIS)
Nelin, G.
1974-01-01
The phonon dispersion relations of the Δ-, Λ-, and Σ-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
Expansion into lattice harmonics in cubic symmetries
Kontrym-Sznajd, G.
2018-05-01
On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.
Complex harmonic modal analysis of rotor systems
International Nuclear Information System (INIS)
Han, Dong Ju
2015-01-01
Complex harmonic analysis for rotor systems has been proposed from the strict complex modal analysis based upon Floquet theory. In this process the harmonic balance method is adopted, effectively associated with conventional eigenvalue analysis. Also, the harmonic coefficients equivalent to dFRFs in harmonic mode has been derived in practice. The modes are classified from identifying the modal characteristics, and the adaptation of harmonic balance method has been proven by comparing the results of the stability analyses from Floque theory and the eigen analysis. The modal features of each critical speed are depicted in quantitatively and qualitatively by showing that the strengths of each component of the harmonic coefficients are estimated from the order of magnitude analysis according to their harmonic patterns. This effectiveness has been verified by comparing with the numerical solutions
Observation of Quasichanneling Oscillations
International Nuclear Information System (INIS)
Wistisen, T. N.; Mikkelsen, R. E.; Uggerhoj, University I.; Wienands, University; Markiewicz, T. W.
2017-01-01
Here, we report on the first experimental observations of quasichanneling oscillations, recently seen in simulations and described theoretically. Although above-barrier particles penetrating a single crystal are generally seen as behaving almost as in an amorphous substance, distinct oscillation peaks nevertheless appear for particles in that category. The quasichanneling oscillations were observed at SLAC National Accelerator Laboratory by aiming 20.35 GeV positrons and electrons at a thin silicon crystal bent to a radius of R = 0.15 m, exploiting the quasimosaic effect. For electrons, two relatively faint quasichanneling peaks were observed, while for positrons, seven quasichanneling peaks were clearly identified.
LSND neutrino oscillation results
International Nuclear Information System (INIS)
Louis, W.C.
1996-01-01
In the past several years, a number of experiments have searched for neutrino oscillations, where a neutrino of one type (say bar ν μ ) spontaneously transforms into a neutrino of another type (say bar ν e ). For this phenomenon to occur, neutrinos must be massive and the apparent conservation law of lepton families must be violated. In 1995 the LSND experiment published data showing candidate events that are consistent with bar ν μ oscillations. Additional data are reported here which provide stronger evidence for neutrino oscillations
International Nuclear Information System (INIS)
Kayser, Boris
2014-01-01
To complement the neutrino-physics lectures given at the 2011 International School on Astro Particle Physics devoted to Neutrino Physics and Astrophysics (ISAPP 2011; Varenna, Italy), at the 2011 European School of High Energy Physics (ESHEP 2011; Cheila Gradistei, Romania), and, in modified form, at other summer schools, we present here a written description of the physics of neutrino oscillation. This description is centered on a new way of deriving the oscillation probability. We also provide a brief guide to references relevant to topics other than neutrino oscillation that were covered in the lectures
Energy Technology Data Exchange (ETDEWEB)
Kayser, Boris [Fermilab (United States)
2014-07-01
To complement the neutrino-physics lectures given at the 2011 International School on Astro Particle Physics devoted to Neutrino Physics and Astrophysics (ISAPP 2011; Varenna, Italy), at the 2011 European School of High Energy Physics (ESHEP 2011; Cheila Gradistei, Romania), and, in modified form, at other summer schools, we present here a written description of the physics of neutrino oscillation. This description is centered on a new way of deriving the oscillation probability. We also provide a brief guide to references relevant to topics other than neutrino oscillation that were covered in the lectures.
International Nuclear Information System (INIS)
Agaisse, R.; Leguen, R.; Ombredane, D.
1960-01-01
The authors present a mechanical device and an electronic control circuit which have been designed to sinusoidally modulate the reactivity of the Proserpine atomic pile. The mechanical device comprises an oscillator and a mechanism assembly. The oscillator is made of cadmium blades which generate the reactivity oscillation. The mechanism assembly comprises a pulse generator for cycle splitting, a gearbox and an engine. The electronic device comprises or performs pulse detection, an on-off device, cycle pulse shaping, phase separation, a dephasing amplifier, electronic switches, counting scales, and control devices. All these elements are briefly presented
An Enhanced GINGER Simulation Code with Harmonic Emission and HDF5 IO Capabilities
International Nuclear Information System (INIS)
Fawley, William M.
2006-01-01
GINGER [1] is an axisymmetric, polychromatic (r-z-t) FEL simulation code originally developed in the mid-1980's to model the performance of single-pass amplifiers. Over the past 15 years GINGER's capabilities have been extended to include more complicated configurations such as undulators with drift spaces, dispersive sections, and vacuum chamber wakefield effects; multi-pass oscillators; and multi-stage harmonic cascades. Its coding base has been tuned to permit running effectively on platforms ranging from desktop PC's to massively parallel processors such as the IBM-SP. Recently, we have made significant changes to GINGER by replacing the original predictor-corrector field solver with a new direct implicit algorithm, adding harmonic emission capability, and switching to the HDF5 IO library [2] for output diagnostics. In this paper, we discuss some details regarding these changes and also present simulation results for LCLS SASE emission at λ = 0.15 nm and higher harmonics
QED effects induced harmonics generation in extreme intense laser foil interaction
Yu, J. Y.; Yuan, T.; Liu, W. Y.; Chen, M.; Luo, W.; Weng, S. M.; Sheng, Z. M.
2018-04-01
A new mechanism of harmonics generation (HG) induced by quantum electrodynamics (QED) effects in extreme intense laser foil interaction is found and investigated by particle-in-cell (PIC) simulations. When two laser pulses with identical intensities of 1.6× {10}24 {{W}} {{{cm}}}-2 are counter-incident on a thin foil target, harmonics emission is observed in their reflected electromagnetic waves. Such harmonics radiation is excited due to transversely oscillating electric currents coming from the vibration of QED effect generated {e}-{e}+ pairs. The effects of laser intensity and polarization were studied. By distinguishing the cascade depth of generated photons and pairs, the influence of QED cascades on HG was analyzed. Although the current HG is not an efficient way for radiation source applications, it may provide a unique way to detect the QED processes in the near future ultra-relativistic laser solid interactions.
Diagonal ordering operation technique applied to Morse oscillator
Energy Technology Data Exchange (ETDEWEB)
Popov, Dušan, E-mail: dusan_popov@yahoo.co.uk [Politehnica University Timisoara, Department of Physical Foundations of Engineering, Bd. V. Parvan No. 2, 300223 Timisoara (Romania); Dong, Shi-Hai [CIDETEC, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Mexico D.F. 07700 (Mexico); Popov, Miodrag [Politehnica University Timisoara, Department of Steel Structures and Building Mechanics, Traian Lalescu Street, No. 2/A, 300223 Timisoara (Romania)
2015-11-15
We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the last section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.
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.
Finite-element time evolution operator for the anharmonic oscillator
Milton, Kimball A.
1995-01-01
The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.
Data-adaptive harmonic analysis and prediction of sea level change in North Atlantic region
Kondrashov, D. A.; Chekroun, M.
2017-12-01
This study aims to characterize North Atlantic sea level variability across the temporal and spatial scales. We apply recently developed data-adaptive Harmonic Decomposition (DAH) and Multilayer Stuart-Landau Models (MSLM) stochastic modeling techniques [Chekroun and Kondrashov, 2017] to monthly 1993-2017 dataset of Combined TOPEX/Poseidon, Jason-1 and Jason-2/OSTM altimetry fields over North Atlantic region. The key numerical feature of the DAH relies on the eigendecomposition of a matrix constructed from time-lagged spatial cross-correlations. In particular, eigenmodes form an orthogonal set of oscillating data-adaptive harmonic modes (DAHMs) that come in pairs and in exact phase quadrature for a given temporal frequency. Furthermore, the pairs of data-adaptive harmonic coefficients (DAHCs), obtained by projecting the dataset onto associated DAHMs, can be very efficiently modeled by a universal parametric family of simple nonlinear stochastic models - coupled Stuart-Landau oscillators stacked per frequency, and synchronized across different frequencies by the stochastic forcing. Despite the short record of altimetry dataset, developed DAH-MSLM model provides for skillful prediction of key dynamical and statistical features of sea level variability. References M. D. Chekroun and D. Kondrashov, Data-adaptive harmonic spectra and multilayer Stuart-Landau models. HAL preprint, 2017, https://hal.archives-ouvertes.fr/hal-01537797
Quantitative modeling of the third harmonic emission spectrum of plasmonic nanoantennas.
Hentschel, Mario; Utikal, Tobias; Giessen, Harald; Lippitz, Markus
2012-07-11
Plasmonic dimer nanoantennas are characterized by a strong enhancement of the optical field, leading to large nonlinear effects. The third harmonic emission spectrum thus depends strongly on the antenna shape and size as well as on its gap size. Despite the complex shape of the nanostructure, we find that for a large range of different geometries the nonlinear spectral properties are fully determined by the linear response of the antenna. We find excellent agreement between the measured spectra and predictions from a simple nonlinear oscillator model. We extract the oscillator parameters from the linear spectrum and use the amplitude of the nonlinear perturbation only as scaling parameter of the third harmonic spectra. Deviations from the model only occur for gap sizes below 20 nm, indicating that only for these small distances the antenna hot spot contributes noticeable to the third harmonic generation. Because of its simplicity and intuitiveness, our model allows for the rational design of efficient plasmonic nonlinear light sources and is thus crucial for the design of future plasmonic devices that give substantial enhancement of nonlinear processes such as higher harmonics generation as well as difference frequency mixing for plasmonically enhanced terahertz generation.
The Influence of Second Harmonic Phase and Amplitude Variation in Cyclically Pitching Wings
Culler, Ethan; Farnsworth, John
2017-11-01
From wind tunnel testing of a cyber-physical wing model, it has been found that the pitch trajectory for stall flutter is described by an array of higher harmonic frequencies with decaying energy content. These frequencies distort the stall flutter motion from that of a pure sinusoidal oscillation in pitch and can have a significant effect on the resulting force production. In order to understand how these higher harmonic frequencies contribute to the overall pitching moment characteristics of a wing in stall flutter, a rigid finite span wing model, with aspect ratio four, was pitched in the wind tunnel. The prescribed motion of the pitch cycle was varied by changing the amplitude ratio and phase of the second harmonic of the oscillation frequency. The second harmonic represents the second highest energy mode in the pitching cycle spectra. Pitching moment and planar particle image velocimetry data was collected. From these pitching trajectories, a significant dependence of pitching moment on both the phase and amplitude of the prescribed waveforms was found. Specifically, for the same amplitude ratio, variations in the phase produced changes of approximately 30 percent in the phase averaged pitching moment.
Kerr-like behaviour of second harmonic generation in the far-off resonant regime
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.
OSCILLATING FILAMENTS. I. OSCILLATION AND GEOMETRICAL FRAGMENTATION
Energy Technology Data Exchange (ETDEWEB)
Gritschneder, Matthias; Heigl, Stefan; Burkert, Andreas, E-mail: gritschm@usm.uni-muenchen.de [University Observatory Munich, LMU Munich, Scheinerstrasse 1, D-81679 Munich (Germany)
2017-01-10
We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid-based AMR code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if the cylinder is bent, such as with a slight sinusoidal perturbation, an otherwise stable configuration starts to oscillate, is triggered into fragmentation, and collapses. This previously unstudied behavior allows a filament to fragment at any given scale, as long as it has slight bends. We call this process “geometrical fragmentation.” In our realization, the spacing between the cores matches the wavelength of the sinusoidal perturbation, whereas up to now, filaments were thought to be only fragmenting on the characteristic scale set by the mass-to-line ratio. Using first principles, we derive the oscillation period as well as the collapse timescale analytically. To enable a direct comparison with observations, we study the line-of-sight velocity for different inclinations. We show that the overall oscillation pattern can hide the infall signature of cores.
Second harmonic generation in a bounded magnetoplasma
International Nuclear Information System (INIS)
Thomas, D.G.
1975-01-01
An experimental study of second harmonic generation in a magnetized plasma contained in a cylindrical cavity resonator shows how the harmonic power varies with fundamental power, background gas pressure, and magnetization. Two cavities were designed. For each the TM010 resonance was in the S-band and the TM011 resonance in the C-band. Both frequencies were harmonically related when the d.c. discharge sustaining the plasma was adjusted to give plasma frequencies of approximately 0.7 GHz and 1.53 GHz. The experimental results show the harmonic power approximately proportional to the square of the fundamental power from 5 to 100 mw, and a decreasing function of pressure from 10 to 150 millitorr. Experiments at constant plasma frequency and varying magnetic field from 0 to 3000 Gauss show a sharp drop in harmonic power to undetectable levels when the electron cyclotron frequency approximates either the fundamental or second harmonic frequencies. These effects are attributed, respectively, to the coupling of fundamental power to other modes and to cavity detuning away from the harmonic. With the plasma frequency adjusted to maintain simultaneous resonance of fundamental and harmonic, a harmonic signal maximum occurred when the upper hybrid frequency approximated the harmonic frequency. Several anomalies, apparently related to the magnetization, background gas, and electron density distribution were observed. Otherwise, the results are qualitatively consistent with the first order theory for a cold, collisional plasma
Again on neutrino oscillations
International Nuclear Information System (INIS)
Bilenky, S.M.; Pontecorvo, B.
1976-01-01
The general case is treated of a weak interaction theory in which a term violating lepton charges is present. In such a scheme the particles with definite masses are Majorana neutrinos (2N if in the weak interaction participate N four-component neutrinos). Neutrino oscillations are discussed and it is shown that the minimum average intensity at the earth of solar neutrinos is 1/2N of the intensity expected when oscillations are absent
International Nuclear Information System (INIS)
Belblidia, L.A.; Bratianu, C.
1979-01-01
Boiling flow in a steam generator, a water-cooled reactor, and other multiphase processes can be subject to instabilities. It appears that the most predominant instabilities are the so-called density-wave oscillations. They can cause difficulties for three main reasons; they may induce burnout; they may cause mechanical vibrations of components; and they create system control problems. A comprehensive review is presented of experimental and theoretical studies concerning density-wave oscillations. (author)
Oscillators and operational amplifiers
Lindberg, Erik
2005-01-01
A generalized approach to the design of oscillators using operational amplifiers as active elements is presented. A piecewise-linear model of the amplifier is used so that it make sense to investigate the eigenvalues of the Jacobian of the differential equations. The characteristic equation of the general circuit is derived. The dynamic nonlinear transfer characteristic of the amplifier is investigated. Examples of negative resistance oscillators are discussed.
Energy Technology Data Exchange (ETDEWEB)
Blacher, S; Perdang, J [Institut d' Astrophysique, B-4200 Cointe-Ougree (Belgium)
1981-09-01
A numerical experiment on Hamiltonian oscillations demonstrates the existence of chaotic motions which satisfy the property of phase coherence. It is observed that the low-frequency end of the power spectrum of such motions is remarkably similar in structure to the low-frequency SCLERA spectra. Since the smallness of the observed solar amplitudes is not a sufficient mathematical ground for inefficiency of non-linear effects the possibility of chaos among solar oscillations cannot be discarded a priori.