Covariant harmonic oscillators and coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, D. (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)
1993-01-01
Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics.
Second harmonic FEL oscillation
NASA Astrophysics Data System (ADS)
Neil, George R.; Benson, S. V.; Biallas, G.; Freund, H. P.; Gubeli, J.; Jordan, K.; Myers, S.; Shinn, M. D.
2002-05-01
We have produced and measured for the first time second harmonic oscillation in the infrared region by the high-average-power Jefferson Lab Infrared Free Electron Laser. The finite geometry and beam emittance allows sufficient gain for lasing to occur. We were able to lase at pulse rates up to 74.85 MHz and could produce over 4.5 W average and 40 kW peak of IR power in a 40 nm FWHM bandwidth at 2925 nm. In agreement with predictions, the source preferentially lased in a TEM 01 mode. We present results of initial source performance measurements and comparisons with theory and simulation.
Second Harmonic FEL Oscillation
NASA Astrophysics Data System (ADS)
Neil, George R.; Benson, S. V.; Biallas, G.; Gubeli, J.; Jordan, K.; Myers, S.; Shinn, M. D.
2001-08-01
We have produced and measured for the first time second harmonic oscillation in the infrared region by a free electron laser. Although such lasing is ideally forbidden, since the gain of a plane wave is zero on axis for an electron beam perfectly aligned with a wiggler, a transverse mode antisymmetry allows sufficient gain in this experiment for lasing to occur. We lased at pulse rates up to 74.85 MHz and could produce over 4.5 W average and 40 kW peak of IR power in a 40 nm FWHM bandwidth at 2925 nm. In agreement with predictions, the source preferentially lased in a TEM01 mode.
Relativistic harmonic oscillator revisited
Bars, Itzhak
2009-02-15
The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Galilean covariant harmonic oscillator
NASA Technical Reports Server (NTRS)
Horzela, Andrzej; Kapuscik, Edward
1993-01-01
A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier
Chruscinski, Dariusz . E-mail: darch@phys.uni.torun.pl
2006-04-15
We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.
Making space for harmonic oscillators
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Quantum wormholes and harmonic oscillators
NASA Technical Reports Server (NTRS)
Garay, Luis J.
1993-01-01
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Harmonic oscillator states in aberration optics
NASA Technical Reports Server (NTRS)
Wolf, Kurt Bernardo
1993-01-01
The states of the three-dimensional quantum harmonic oscillator classify optical aberrations of axis-symmetric systems due to the isomorphism between the two mathematical structures. Cartesian quanta and angular momentum classifications have their corresponding aberration classifications. The operation of concatenation of optical elements introduces a new operation between harmonic oscillator states.
Quantum phases for a generalized harmonic oscillator
NASA Astrophysics Data System (ADS)
Bracken, Paul
2008-03-01
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.
Squeezing in a 2-D generalized oscillator
NASA Technical Reports Server (NTRS)
Castanos, Octavio; Lopez-Pena, Ramon; Manko, Vladimir I.
1994-01-01
A two-dimensional generalized oscillator with time-dependent parameters is considered to study the two-mode squeezing phenomena. Specific choices of the parameters are used to determine the dispersion matrix and analytic expressions, in terms of standard hermite polynomials, of the wavefunctions and photon distributions.
Harmonic Oscillators as Bridges between Theories
NASA Astrophysics Data System (ADS)
Kim, Y. S.; Noz, Marilyn E.
2005-03-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
2D magnetic nanoparticle imaging using magnetization response second harmonic
NASA Astrophysics Data System (ADS)
Tanaka, Saburo; Murata, Hayaki; Oishi, Tomoya; Suzuki, Toshifumi; Zhang, Yi
2015-06-01
A detection method and an imaging technique for magnetic nanoparticles (MNPs) have been investigated. In MNP detection and in magnetic particle imaging (MPI), the most commonly employed method is the detection of the odd harmonics of the magnetization response. We examined the advantage of using the second harmonic response when applying an AC magnetic modulation field and a DC bias field. If the magnetization response is detected by a Cu-wound-coil detection system, the output voltage from the coil is proportional to the change in the flux, dϕ/dt. Thus, the dependence of the derivative of the magnetization, M, on an AC magnetic modulation field and a DC bias field were calculated and investigated. The calculations were in good agreement with the experimental results. We demonstrated that the use of the second harmonic response for the detection of MNPs has an advantage compared with the usage of the third harmonic response, when the Cu-wound-coil detection system is employed and the amplitude of the ratio of the AC modulation field and a knee field Hac/Hk is less than 2. We also constructed a 2D MPI scanner using a pair of permanent ring magnets with a bore of ϕ80 mm separated by 90 mm. The magnets generated a gradient of Gz=3.17 T/m transverse to the imaging bore and Gx=1.33 T/m along the longitudinal axis. An original concentrated 10 μl Resovist solution in a ϕ2×3 mm2 vessel was used as a sample, and it was imaged by the scanner. As a result, a 2D contour map image could be successfully generated using the method with a lock-in amplifier.
The harmonic oscillator and nuclear physics
NASA Technical Reports Server (NTRS)
Rowe, D. J.
1993-01-01
The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.
Second International Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo (Editor); Wolf, Kurt Bernardo (Editor)
1995-01-01
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
Quantum harmonic oscillator with superoscillating initial datum
Buniy, R. V.; Struppa, D. C.; Colombo, F.; Sabadini, I.
2014-11-15
In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
Quantum nondemolition measurements of harmonic oscillators
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Caves, C. M.; Zimmermann, M.; Sandberg, V. D.; Drever, R. W. P.
1978-01-01
Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.
Quantum harmonic oscillator in a thermal bath
NASA Technical Reports Server (NTRS)
Zhang, Yuhong
1993-01-01
The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
Factorization method for the truncated harmonic oscillator
NASA Astrophysics Data System (ADS)
Fernández C, D. J.; Morales-Salgado, V. S.
2015-04-01
Factorization procedures of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. Certain systems obtained in a straightforward way through said method possess differential ladder operators of both types, third and fourth order. Since systems with this kind of operators are linked with the Painlevé IV and V equations respectively, several solutions of these non-linear second-order differential equations will be simply found.
Fisher information of quantum damped harmonic oscillators
NASA Astrophysics Data System (ADS)
Aguiar, V.; Guedes, I.
2015-04-01
We calculate the time-dependent Fisher information in position ({{F}x}) and momentum ({{F}p}) for the lowest lying state ≤ft( n=0 \\right) of two classes of quantum damped (Lane-Emden (LE) and Caldirola-Kanai (CK)) harmonic oscillators. The expressions of {{F}x} and {{F}p} are written in terms of ρ , a c-number quantity satisfying a nonlinear differential equation. Analytical solutions of ρ were obtained. For the LE and CK oscillators, we observe that {{F}x} increases while {{F}p} decreases with increasing time. The product {{F}x}{{F}p} increases and tends to a constant value in the limit t\\to ∞ for the LE oscillator, while it is time-independent for the CK oscillator. Moreover, for the CK oscillator the product {{F}x}{{F}p} decreases as the damping ≤ft( γ \\right) increases. Relations among the Fisher information, Leipnik and Shannon entropies, and the Stam and Cramer-Rao inequalities are given. A discussion on the squeezing phenomenon in position for the oscillators is presented.
Harmonic oscillator interaction with squeezed radiation
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Nikonov, D. E.
1993-01-01
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
Joint entropy of quantum damped harmonic oscillators
NASA Astrophysics Data System (ADS)
Aguiar, V.; Guedes, I.
2014-05-01
We use the dynamical invariant method and a unitary transformation to obtain the exact Schrödinger wave function, ψn(x,t), and calculate for n=0 the time-dependent joint entropy (Leipnik’s entropy) for two classes of quantum damped harmonic oscillators. We observe that the joint entropy does not vary in time for the Caldirola-Kanai oscillator, while it decreases and tends to a constant value (ln({e}/{2})) for asymptotic times for the Lane-Emden ones. This is due to the fact that for the latter, the damping factor decreases as time increases. The results show that the time dependence of the joint entropy is quite complex and does not obey a general trend of monotonously increase with time.
The Coupled Harmonic Oscillator: Not Just for Seniors Anymore.
ERIC Educational Resources Information Center
Preyer, Norris W.
1996-01-01
Presents experiments that use Microcomputer Based Laboratory (MBL) techniques to enable freshmen physics students to investigate complex systems, such as nonlinear oscillators or coupled harmonic oscillators, at a level appropriate for an independent project. (JRH)
Coherent states for the relativistic harmonic oscillator
NASA Technical Reports Server (NTRS)
Aldaya, Victor; Guerrero, J.
1995-01-01
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
A possible generalization of the harmonic oscillator potential
NASA Technical Reports Server (NTRS)
Levai, Geza
1995-01-01
A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.
Operation of higher harmonic oscillations in free-electron lasers.
Sei, N; Ogawa, H; Yamada, K
2012-01-01
We report for the first time the experimental achievement of a seventh-harmonic free-electron laser (FEL) oscillation. The measured FEL gains and average FEL powers for higher harmonics were identical to those calculated by a one-dimensional FEL theory. The measured linewidths of the higher-harmonic FELs were narrower than that of the fundamental FEL owing to the narrower spectral widths of the spontaneous emissions. By applying the higher-harmonic FEL oscillation to a resonator-type FEL with an advanced accelerator, an x-ray FEL oscillator can be realized at lower electron-beam energy. PMID:22274354
A Look at Damped Harmonic Oscillators through the Phase Plane
ERIC Educational Resources Information Center
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…
Driven harmonic oscillator as a quantum simulator for open systems
Piilo, Jyrki; Maniscalco, Sabrina
2006-09-15
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.
Harmonic and Anharmonic Behaviour of a Simple Oscillator
ERIC Educational Resources Information Center
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…
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
Harmonic oscillator in quantum rotational spectra: Molecules and nuclei
NASA Technical Reports Server (NTRS)
Pavlichenkov, Igor M.
1995-01-01
The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.
A harmonic oscillator having “volleyball damping”
NASA Astrophysics Data System (ADS)
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.
The Study of Damped Harmonic Oscillations Using an Electronic Counter
ERIC Educational Resources Information Center
Wadhwa, Ajay
2009-01-01
We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…
On the moment of inertia of a quantum harmonic oscillator
Khamzin, A. A. Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-04-15
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.
Calculation of four-particle harmonic-oscillator transformation brackets
NASA Astrophysics Data System (ADS)
Germanas, D.; Kalinauskas, R. K.; Mickevičius, S.
2010-02-01
A procedure for precise calculation of the three- and four-particle harmonic-oscillator (HO) transformation brackets is presented. The analytical expressions of the four-particle HO transformation brackets are given. The computer code for the calculations of HO transformation brackets proves to be quick, efficient and produces results with small numerical uncertainties. Program summaryProgram title: HOTB Catalogue identifier: AEFQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1247 No. of bytes in distributed program, including test data, etc.: 6659 Distribution format: tar.gz Programming language: FORTRAN 90 Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix RAM: 8 MB Classification: 17.17 Nature of problem: Calculation of the three-particle and four-particle harmonic-oscillator transformation brackets. Solution method: The method is based on compact expressions of the three-particle harmonics oscillator brackets, presented in [1] and expressions of the four-particle harmonics oscillator brackets, presented in this paper. Restrictions: The three- and four-particle harmonic-oscillator transformation brackets up to the e=28. Unusual features: Possibility of calculating the four-particle harmonic-oscillator transformation brackets. Running time: Less than one second for the single harmonic-oscillator transformation bracket. References:G.P. Kamuntavičius, R.K. Kalinauskas, B.R. Barret, S. Mickevičius, D. Germanas, Nuclear Physics A 695 (2001) 191.
Quantum Oscillations in an Interfacial 2D Electron Gas.
Zhang, Bingop; Lu, Ping; Liu, Henan; Lin, Jiao; Ye, Zhenyu; Jaime, Marcelo; Balakirev, Fedor F.; Yuan, Huiqiu; Wu, Huizhen; Pan, Wei; Zhang, Yong
2016-01-01
Recently, it has been predicted that topological crystalline insulators (TCIs) may exist in SnTe and Pb_{1-x}Sn_{x}Te thin films [1]. To date, most studies on TCIs were carried out either in bulk crystals or thin films, and no research activity has been explored in heterostructures. We present here the results on electronic transport properties of the 2D electron gas (2DEG) realized at the interfaces of PbTe/ CdTe (111) heterostructures. Evidence of topological state in this interfacial 2DEG was observed.
First-harmonic approximation in nonlinear chirped-driven oscillators.
Uzdin, Raam; Friedland, Lazar; Gat, Omri
2014-01-01
Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a "frequency equivalent" symmetric potential and to study the autoresonance breakdown phenomenon. PMID:24580292
An algebraic cluster model based on the harmonic oscillator basis
NASA Technical Reports Server (NTRS)
Levai, Geza; Cseh, J.
1995-01-01
We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
NASA Technical Reports Server (NTRS)
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.
Complex metabolic oscillations in plants forced by harmonic irradiance.
Nedbal, Ladislav; Brezina, Vítezslav
2002-01-01
Plants exposed to harmonically modulated irradiance, approximately 1 + cos(omegat), exhibit a complex periodic pattern of chlorophyll fluorescence emission that can be deconvoluted into a steady-state component, a component that is modulated with the frequency of the irradiance (omega), and into at least two upper harmonic components (2omega and 3omega). A model is proposed that accounts for the upper harmonics in fluorescence emission by nonlinear negative feedback regulation of photosynthesis. In contrast to simpler linear models, the model predicts that the steady-state fluorescence component will depend on the frequency of light modulation, and that amplitudes of all fluorescence components will exhibit resonance peak(s) when the irradiance frequency is tuned to an internal frequency of a regulatory component. The experiments confirmed that the upper harmonic components appear and exhibit distinct resonant peaks. The frequency of autonomous oscillations observed earlier upon an abrupt increase in CO(2) concentration corresponds to the sharpest of the resonant peaks of the forced oscillations. We propose that the underlying principles are general for a wide spectrum of negative-feedback regulatory mechanisms. The analysis by forced harmonic oscillations will enable us to examine internal dynamics of regulatory processes that have not been accessible to noninvasive fluorescence monitoring to date. PMID:12324435
34 GHz second-harmonic peniotron oscillator
NASA Astrophysics Data System (ADS)
Dressman, Lawrence Jude
Harmonic operation of gyro-devices has been proposed as a way to lower the magnetic field required to a level feasible with normal (i.e., non-superconducting) magnets. The problem is, however, that gyrotron efficiency drops dramatically at harmonics greater than two, making development of such a device of limited utility. A promising solution to this quandary is the development of a related device, the peniotron, which is believed capable of achieving both high efficiency and harmonic operation resulting in a reduction of the required axial magnetic field. Although the physics of the peniotron interaction, including its high electronic conversion efficiency, has been understood and experimentally verified, demonstration of characteristics consistent with a practical device has been more elusive. This is the goal of this effort---specifically, to demonstrate high device efficiency (defined as the actual power output as a fraction of the electron beam power) with an electron beam generated by a compact cusp electron gun consistent in size and performance with other microwave vacuum electron devices. The cavity design process revealed that the pi/2 mode couples easily to the output circular waveguide. In fact, the transition to circular waveguide produced such a low reflection coefficient that an iris was needed at the cavity output to achieve the desired Q. Integral couplers were also designed to couple directly into the slotted cavity for diagnostic purposes for simplicity in this proof-of-principle physics experiment. This eliminated the need for a high-power circular vacuum window and allowed the diagnostic coupling to be made in standard WR-28 rectangular waveguide. Although mode competition did prevent the second-harmonic peniotron mode from being tuned over its entire range of magnetic field, the peniotron mode was stable over a range sufficient to allow useful experimental data to be obtained. However, another unexpected problem which occurred during execution
Asymptotic Formula for Quantum Harmonic Oscillator Tunneling Probabilities
NASA Astrophysics Data System (ADS)
Jadczyk, Arkadiusz
2015-10-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Simulating Harmonic Oscillator and Electrical Circuits: A Didactical Proposal
ERIC Educational Resources Information Center
Albano, Giovannina; D'Apice, Ciro; Tomasiello, Stefania
2002-01-01
A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
ERIC Educational Resources Information Center
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…
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
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. (Contains 2 figures.)
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
ERIC Educational Resources Information Center
Flores-Hidalgo, G.; Barone, F. A.
2011-01-01
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
Symmetry algebra of a generalized anisotropic harmonic oscillator
NASA Technical Reports Server (NTRS)
Castanos, O.; Lopez-Pena, R.
1993-01-01
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
Probing deformed commutators with macroscopic harmonic oscillators
Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A.; Serra, Enrico; Vitali, David; Marin, Francesco
2015-01-01
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965
Probing deformed commutators with macroscopic harmonic oscillators.
Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A; Serra, Enrico; Vitali, David; Marin, Francesco
2015-01-01
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈ 22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965
Franck-Condon factors for multidimensional harmonic oscillators
NASA Astrophysics Data System (ADS)
Malmqvist, Per-Åke; Forsberg, Niclas
1998-03-01
We present a simple formula for the overlap integrals of two sets of multi-dimensional harmonic oscillators. The oscillators have in general different equilibrium points, force constants, and natural vibration modes. The formula expresses the overlap matrix in the one-dimensional case, < m'| n''>, as a so-called LU decomposition,
The q-harmonic oscillators, q-coherent states and the q-symplecton
NASA Technical Reports Server (NTRS)
Biedenharn, L. C.; Lohe, M. A.; Nomura, Masao
1993-01-01
The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.
Random reverse-cyclic matrices and screened harmonic oscillator.
Srivastava, Shashi C L; Jain, Sudhir R
2012-04-01
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner. PMID:22680453
Harmonic oscillations and their switching in elliptical optical waveguide arrays
NASA Astrophysics Data System (ADS)
Jie Zheng, Ming; San Chan, Yun; Yu, Kin Wah
2011-03-01
We have studied harmonic oscillations in an elliptical optical waveguide array in which the coupling between neighboring waveguides is varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, long-living Bloch oscillations (BO) and dipole oscillations (DO) are obtained when a linear gradient in the propagation constant is applied. Moreover, we achieve a switching from DO to BO or vice versa by ramping up the gradient profile. The various optical oscillations as well as their switching are investigated by field-evolution analysis and confirmed by Hamiltonian optics. The equally spaced eigenvalues in the propagation constant allow viable applications in transmitting images, switching and routing of optical signals.
Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions
NASA Astrophysics Data System (ADS)
Macedo, Diego Ximenes; Guedes, Ilde
2015-10-01
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 invariant method. The exact wave functions are obtained by solving the respective Milne-Pinney equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.
Time-dependent coupled harmonic oscillators: Classical and quantum solutions
NASA Astrophysics Data System (ADS)
Macedo, D. X.; Guedes, I.
2014-08-01
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 m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang
2016-07-01
This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis. PMID:26241985
First, Second Quantization and Q-Deformed Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2015-06-01
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.
BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA
Arregui, I.; Asensio Ramos, A.; Diaz, A. J.
2013-03-01
The detection of multiple mode harmonic kink oscillations in coronal loops enables us to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion under each of the hypotheses. The two models are then compared using a Bayesian model comparison scheme to assess how plausible each one is given our current state of knowledge.
Free fall and harmonic oscillations: analyzing trampoline jumps
NASA Astrophysics Data System (ADS)
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 obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.
High gain amplifiers: Power oscillations and harmonic generation
Dattoli, G.; Ottaviani, P. L.; Pagnutti, S.
2007-08-01
We discuss the power oscillations in saturated high gain free electron laser amplifiers and show that the relevant period can be written in terms of the gain length. We use simple arguments following from the solution of the pendulum equation in terms of Jacobi elliptic functions. Nontrivial effects due to nonlinear harmonic generation and inhomogeneous broadening are discussed too, as well as the saturated dynamics of short pulses.
Using Coupled Harmonic Oscillators to Model Some Greenhouse Gas Molecules
Go, Clark Kendrick C.; Maquiling, Joel T.
2010-07-28
Common greenhouse gas molecules SF{sub 6}, NO{sub 2}, CH{sub 4}, and CO{sub 2} are modeled as harmonic oscillators whose potential and kinetic energies are derived. Using the Euler-Lagrange equation, their equations of motion are derived and their phase portraits are plotted. The authors use these data to attempt to explain the lifespan of these gases in the atmosphere.
Pisot q-coherent states quantization of the harmonic oscillator
Gazeau, J.P.; Olmo, M.A. del
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.
Effective field theory in the harmonic oscillator basis
NASA Astrophysics Data System (ADS)
Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.
2016-04-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less
Information theories for time-dependent harmonic oscillator
Choi, Jeong Ryeol; Kim, Min-Soo; Kim, Daeyeoul; Maamache, Mustapha; Menouar, Salah; Nahm, In Hyun
2011-06-15
Highlights: > Information theories for the general time-dependent harmonic oscillator based on invariant operator method. > Time dependence of entropies and entropic uncertainty relation. > Characteristics of Shannon information and Fisher information. > Application of information theories to particular systems that have time-dependent behavior. - Abstract: Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville-von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.
Argand diagrams, harmonic oscillators, and record-playing tonearms
NASA Astrophysics Data System (ADS)
Piccard, Richard D.
1986-04-01
The complex analysis of the driven, damped, harmonic oscillator is reviewed for the specific case that the driving force is produced by ``wiggling the other end of the spring,'' a case which many find intuitively appealing. The solution is examined using the Cartesian and polar presentations in the complex plane. The record-playing tonearm is particularly suited as a ``practical example'' because it naturally leads to a question that is much easier to answer in terms of the Argand diagram: What will the cartridge output be?
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Optimal control of a harmonic oscillator: Economic interpretations
NASA Astrophysics Data System (ADS)
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.
Kraus representation of a damped harmonic oscillator and its application
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-10-01
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.
A 95 GHz, 4th harmonic gyro-oscillator
Hargreaves, T.A.; Scheitrum, G.P.; Bemis, T.; Higgins, L.
1994-12-31
There is currently an interest in medium power ({approximately}100 kW), compact 95 GHz amplifiers for future radar applications. Size, weight, and efficiency are critical for airborne applications. Litton has been investigating a 4th harmonic, 4-cavity gyro-amplifier. The key to success of the amplifier is the axis-encircling electron beam from a new type of electron gun, the advanced center post (ACP) gun. Gun simulations incorporating the actual magnetic field and thermal velocity spread in the emitted electrons show that axial velocity spreads of less than 2% are attainable, which is significantly better than other gun concepts. The amplifier utilizes coaxial-magnetron-type cavities operating in the {pi} mode. In this cavity, vanes extend nearly down to the electron beam`s outside diameter. The majority of the RF stored energy in the system is in the coaxial cavity, so that the resonant frequency and quality factor of each coaxial magnetron cavity may be adjusted by varying only the coaxial cavity. Several components are being tested individually. To test the cavity design, a 4th harmonic oscillator based on a coaxial magnetron cavity has been designed. Results of the oscillator testing will be presented.
Non-unique monopole oscillations of harmonically confined Yukawa systems
NASA Astrophysics Data System (ADS)
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)
Oscillations of light absorption in 2D macroporous silicon structures with surface nanocoatings
NASA Astrophysics Data System (ADS)
Karachevtseva, L.; Kuchmii, S.; Lytvynenko, O.; Sizov, F.; Stronska, O.; Stroyuk, A.
2011-02-01
We investigated the near-IR light absorption oscillations in 2D macroporous silicon structures with microporous silicon layers and CdTe, ZnO surface nanocrystals. The electro-optical effect was taken into account within the strong electric field approximation. Well-separated oscillations were observed in the spectral ranges of the surface bonds of macroporous silicon structures with surface nanocrystals. The model of the resonant electron scattering on impurity states in electric field of heterojunction “silicon-nanocoating” on macropore surface as well as realization of Wannier-Stark effect on the randomly distributed surface bonds were considered. The Wannier-Stark ladders are not broken by impurities because of the longer scattering lifetime as compared with the period of electron oscillations in an external electric field, in all spectral regions considered for macroporous silicon structures with CdTe and ZnO surface nanocrystals.
Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D
NASA Astrophysics Data System (ADS)
Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.
2015-10-01
Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
Noninvariance groups for many-particle systems: Coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Kellman, Michael E.
1984-07-01
Noninvariance groups for many-particle systems are investigated in the context of the model problem of the coupling of a pair of harmonic oscillators to give normal modes. First, a recent paper analyzing normal modes in terms of breaking of the SU(2) invariance symmetry of the uncoupled system is reviewed. Next, the noninvariance group description of the one-dimensional oscillator spectrum in terms of infinite-dimensional unitary representations of SU(1,1) is summarized. Then, the analysis of normal modes in terms of a broken noninvariance SU(2,1) group for the two-dimensional problem is carried out. First, the T, U, and V SU(2) subgroup classifications of SU(3) are reviewed in the context of representations for the three-dimensional oscillator. Second, the analogous SU(2) and SU(1,1) subgroup classification of the infinite two-dimensional spectrum is presented. The SU(1,1) groups classify infinite sequences of excitation of the symmetric and antisymmetric stretch, respectively. Then, in an alternate approach, SU(1,1) representations for the spectra of the individual oscillators are coupled, analogous to vector coupling of angular momentum. Normal modes can be obtained in this manner, but only in the limit in which an arbitrary parameter labeling the group representations takes the value infinity. The relation of these results to the theory of group contractions and their implications for the description of truncated spectra (such as coupled Morse oscillators or π-electron spectra of linear polyenes) are briefly discussed.
Entanglement dynamics for a conditionally kicked harmonic oscillator
NASA Astrophysics Data System (ADS)
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
2016-08-01
The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb–Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.
Fastest Effectively Adiabatic Transitions for a Collection of Harmonic Oscillators.
Boldt, Frank; Salamon, Peter; Hoffmann, Karl Heinz
2016-05-19
We discuss fastest effectively adiabatic transitions (FEATs) for a collection of noninteracting harmonic oscillators with shared controllable real frequencies. The construction of such transitions is presented for given initial and final equilibrium states, and the dependence of the minimum time control on the interval of achievable frequencies is discussed. While the FEAT times and associated FEAT processes are important in their own right as optimal controls, the FEAT time is an added feature which provides a measure of the quality of a shortcut to adiabaticity (STA). The FEAT time is evaluated for a previously reported experiment, wherein a cloud of Rb atoms is cooled following a STA recipe that took about twice as long as the FEAT speed limit, a time efficiency of 50%. PMID:26811863
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
NASA Astrophysics Data System (ADS)
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
2010-05-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum harmonic oscillator (QHO) + environment" is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of ≪ground state≫ are investigated by the SDM method.
Single trapped ion as a time-dependent harmonic oscillator
Menicucci, Nicolas C.; Milburn, G. J.
2007-11-15
We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al., [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result.
ERIC Educational Resources Information Center
Earl, Boyd L.
2008-01-01
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
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.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
ERIC Educational Resources Information Center
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…
Shao, Yonghong; Liu, Honghai; Qin, Wan; Qu, Junle; Peng, Xiang; Niu, Hanben
2013-01-01
We present an addressable, large-field second harmonic generation microscope by combining a 2D acousto-optical deflector with a spatial light modulator. The SLM shapes an incoming mode-locked, near-infrared Ti:Sapphire laser beam into a multifocus array, which can be rapidly scanned by changing the incident angle of the laser beam using a 2D acousto-optical deflector. Compared to the single-beam-scan technique, the multifocus array scan can increase the scanning rate and the field-of-view size with the multi-region imaging ability. PMID:24307756
Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator
NASA Astrophysics Data System (ADS)
Eshghi, M.; Sever, R.; Ikhdair, S. M.
2016-07-01
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass m(t) to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential V(t) acting on the TDM m(t) oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent mass reduces to m0.
Cooper pair of superconductivity in the coordinate representation and q-deformed harmonic oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2016-06-01
In this work we study the similarity between the wave functions of q -deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an “onion-like” layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q -deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
ERIC Educational Resources Information Center
Gauthier, N.
2004-01-01
An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…
Multielectron Correlation in High-Harmonic Generation: A 2D Model Analysis
Sukiasyan, Suren; McDonald, Chris; Destefani, Carlos; Brabec, Thomas; Ivanov, Misha Yu.
2009-06-05
We analyze the role of multielectron dynamics in high-harmonic generation spectroscopy, using an example of a two-electron system. We identify and systematically quantify the importance of correlation and exchange effects. One of the main sources for correlation is identified to be the polarization of the ion by the recombining continuum electron. This effect, which plays an important qualitative and quantitative role, seriously undermines the validity of the standard approaches to high-harmonic generation, which ignore the contribution of excited ionic states to the radiative recombination of the continuum electron.
Inverse Problem for Harmonic Oscillator Perturbed by Potential, Characterization
NASA Astrophysics Data System (ADS)
Chelkak, Dmitri; Kargaev, Pavel; Korotyaev, Evgeni
Consider the perturbed harmonic oscillator Ty=-y''+x2y+q(x)y in L2(R), where the real potential q belongs to the Hilbert space H={q', xq∈ L2(R)}. The spectrum of T is an increasing sequence of simple eigenvalues λn(q)=1+2n+μn, n >= 0, such that μn--> 0 as n-->∞. Let ψn(x,q) be the corresponding eigenfunctions. Define the norming constants νn(q)=limx↑∞log |ψn (x,q)/ψn (-x,q)|. We show that for some real Hilbert space and some subspace Furthermore, the mapping ψ:q|-->ψ(q)=({λn(q)}0∞, {νn(q)}0∞) is a real analytic isomorphism between H and is the set of all strictly increasing sequences s={sn}0∞ such that The proof is based on nonlinear functional analysis combined with sharp asymptotics of spectral data in the high energy limit for complex potentials. We use ideas from the analysis of the inverse problem for the operator -y''py, p∈ L2(0,1), with Dirichlet boundary conditions on the unit interval. There is no literature about the spaces We obtain their basic properties, using their representation as spaces of analytic functions in the disk.
Phase of the quantum harmonic oscillator with applications to optical polarization
NASA Technical Reports Server (NTRS)
Shepard, Scott R.
1993-01-01
The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.
Quantum Dynamics of a Harmonic Oscillator in a Defomed Bath in the Presence of Lamb Shift
NASA Astrophysics Data System (ADS)
Daeimohamad, M.; Mohammadi, M.
2012-10-01
In this paper, we investigate the dissipative quantum dynamics of a harmonic oscillator in the presence a deformed bath by considering the Lamb shift term. The deformed bath is modelled by a collection of deformed quantum harmonic oscillators as a generalization of Hopfield model. The Langevin equation for both the photon number and the fluctuation spectrum under the Weisskopf-Winger approximation are obtained and discussed.
Kaaouana, Takoua; de Rochefort, Ludovic; Samaille, Thomas; Thiery, Nathalie; Dufouil, Carole; Delmaire, Christine; Dormont, Didier; Chupin, Marie
2015-01-01
Cerebral microbleeds (CMBs) have emerged as a new imaging marker of small vessel disease. Composed of hemosiderin, CMBs are paramagnetic and can be detected with MRI sequences sensitive to magnetic susceptibility (typically, gradient recalled echo T2* weighted images). Nevertheless, their identification remains challenging on T2* magnitude images because of confounding structures and lesions. In this context, T2* phase image may play a key role in better characterizing CMBs because of its direct relationship with local magnetic field variations due to magnetic susceptibility difference. To address this issue, susceptibility-based imaging techniques were proposed, such as Susceptibility Weighted Imaging (SWI) and Quantitative Susceptibility Mapping (QSM). But these techniques have not yet been validated for 2D clinical data in multicenter settings. Here, we introduce 2DHF, a fast 2D phase processing technique embedding both unwrapping and harmonic filtering designed for data acquired in 2D, even with slice-to-slice inconsistencies. This method results in internal field maps which reveal local field details due to magnetic inhomogeneity within the region of interest only. This technique is based on the physical properties of the induced magnetic field and should yield consistent results. A synthetic phantom was created for numerical simulations. It simulates paramagnetic and diamagnetic lesions within a 'brain-like' tissue, within a background. The method was evaluated on both this synthetic phantom and multicenter 2D datasets acquired in standardized clinical setting, and compared with two state-of-the-art methods. It proved to yield consistent results on synthetic images and to be applicable and robust on patient data. As a proof-of-concept, we finally illustrate that it is possible to find a magnetic signature of CMBs and CMCs on internal field maps generated with 2DHF on 2D clinical datasets that give consistent results with CT-scans in a subsample of 10 subjects
The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator
ERIC Educational Resources Information Center
Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.
2008-01-01
In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…
NASA Astrophysics Data System (ADS)
Egorov, A. G.; Kamalutdinov, A. M.; Paimushin, V. N.; Firsov, V. A.
2016-03-01
A method for determining the drag coefficient of a thin plate harmonically oscillating in a viscous incompressible fluid is proposed. The method is based on measuring the amplitude of deflections of cantilever-fixed thin plates exhibiting damping flexural oscillations with a frequency corresponding to the first mode and on solving an inverse problem of calculating the drag coefficient on the basis of the experimentally found logarithmic decrement of beam oscillations.
On harmonic oscillators and their Kemmer relativistic forms
NASA Technical Reports Server (NTRS)
Debergh, Nathalie; Beckers, Jules
1993-01-01
It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.
New stochastic equation for a harmonic oscillator: Brownian motion with adhesion
NASA Astrophysics Data System (ADS)
Gitterman, M.
2010-11-01
In addition to the usually considered stochastic harmonic oscillator with an external random force (Brownian motion) or with random frequency and random damping, we consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some (random) time after the collision, thereby changing the oscillator mass. We have calculated the first two moments and the Lyapunov exponent, which describes the stability of the fixed point. This model can be useful for the analysis of chemical and biological solutions as well as for nano-technological devices.
Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths
NASA Astrophysics Data System (ADS)
Pigeon, Simon; Fusco, Lorenzo; Xuereb, André; De Chiara, Gabriele; Paternostro, Mauro
2015-07-01
We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to N dissipative baths by using an approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyze the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.
The finite harmonic oscillator and its associated sequences
Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir
2008-01-01
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684
The finite harmonic oscillator and its associated sequences.
Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir
2008-07-22
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684
Entanglement scaling in classical and quantum harmonic oscillator lattices
Audenaert, K.; Eisert, J.; Plenio, M. B.; Cramer, M.
2006-11-15
We consider entanglement properties of ground and thermal states of harmonic lattice systems. A theorem connecting entanglement between a region and the rest of the lattice with the surface area of the boundary between the two regions is presented for systems in arbitrary spatial dimensions. The behavior of the block entanglement in the field limit is analysed and a logarithmic divergence is recovered.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
NASA Astrophysics Data System (ADS)
Sugawara-Tanabe, Kazuko
2011-05-01
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters δ and γ. The special cases with tan γ = 1/√3 (γ = 30°) and √3 /5(γ˜19°) are discussed.
On the effects of a screw dislocation and a linear potential on the harmonic oscillator
NASA Astrophysics Data System (ADS)
Bueno, M. J.; Furtado, C.; Bakke, K.
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.
NASA Astrophysics Data System (ADS)
Falaye, B. J.; Dong, Shi-Hai; Oyewumi, K. J.; Ilaiwi, K. F.; Ikhdair, S. M.
2015-10-01
We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [x̂,p̂] = iℏ(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ˜SO(2, 1) algebra is satisfied by the operators ℒ±̂ and ℒẑ.
The impact damped harmonic oscillator in free decay
NASA Technical Reports Server (NTRS)
Brown, G. V.; North, C. M.
1987-01-01
The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P
2015-01-01
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems. PMID:25525161
A 2-D oscillating flow analysis in Stirling engine heat exchangers
NASA Technical Reports Server (NTRS)
Ahn, Kyung H.; Ibrahim, Mounir B.
1991-01-01
A two-dimensional oscillating flow analysis was conducted, simulating the gas flow inside Stirling heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re(max) = 1920 (Va = 80), 10800 (Va = 272), 19300 (Va = 272), and 60800 (Va = 126). The results are compared with experimental results of previous investigators. Also, predictions of the flow regime on present oscillating flow conditions were checked by comparing velocity amplitudes and phase differences with those from laminar theory and quasi-steady profile. A high Reynolds number k-epsilon turbulence model was used for turbulent oscillating pipe flow. Finally, performance evaluation of the K-epsilon model was made to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.
A 2-D oscillating flow analysis in Stirling engine heat exchangers
NASA Technical Reports Server (NTRS)
Ahn, Kyung H.; Ibrahim, Mounir B.
1991-01-01
A two dimensional oscillating flow analysis was conducted, simulating the gas flow inside Stirling heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re(max) = 1920 (Va = 80), 10800 (Va = 272), 19300 (Va = 272), and 60800 (Va = 126). The results are compared with experimental results of previous investigators. Also, predictions of the flow regime on present oscillating flow conditions were checked by comparing velocity amplitudes and phase differences with those from laminar theory and quasi-steady profile. A high Reynolds number k-epsilon turbulence model was used for turbulent oscillating pipe flow. Finally, performance evaluation of the K-epsilon model was made to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.
Generation of high power sub-terahertz radiation from a gyrotron with second harmonic oscillation
Saito, Teruo; Yamada, Naoki; Ikeuti, Shinji; Tatematsu, Yoshinori; Ikeda, Ryosuke; Ogawa, Isamu; Idehara, Toshitaka; Ogasawara, Shinya; Manuilov, Vladimir N.; Shimozuma, Takashi; Kubo, Shin; Nishiura, Masaki; Tanaka, Kenji; Kawahata, Kazuo
2012-06-15
New power records of second harmonic gyrotron oscillation have been demonstrated in the sub-THz band. The first step gyrotron of demountable type had succeeded in oscillation with power more than 50 kW at 350 GHz and nearly 40 kW at 390 GHz [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009)]. Then, the second step gyrotron of sealed-off type was manufactured. A cavity mode was carefully selected to avoid mode competition with a neighboring fundamental harmonic mode. Matching of the selected mode with the electron gun was also circumspectly considered. The second step gyrotron has attained higher power radiation than the first gyrotron. The maximum single mode power was 62 kW at 388 GHz. Then, the electron gun was modified for use of a different cavity mode with a higher coupling coefficient than that for the 62 kW mode. The new mode proved single mode oscillation power of 83 kW at about 389 GHz. These results are new second-harmonic-oscillation power records for sub-THz gyrotrons. The present study constitutes foundations of development of high power second harmonic sub-THz gyrotron for application to collective Thomson scattering measurement on fusion plasmas, especially on high-density plasmas such as those produced in LHD [N. Ohyabu et al., Phys. Rev. Lett. 97, 055002 (2006)]. This paper reports the design consideration to realize high power single mode gyrotron oscillation at second harmonic and the examination of oscillation characteristics of the gyrotron.
ERIC Educational Resources Information Center
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Structure and Behavior of the Edge Harmonic Oscillation in Quiescent H-Mode Plasmas on DIII-D
NASA Astrophysics Data System (ADS)
McKee, G. R.; Yan, Z.; Burrell, K. H.; Garofalo, A. M.; Grierson, B. A.; Solomon, W. M.
2013-10-01
The edge harmonic oscillation (EHO) is a steady-state, pedestal-localized instability that is observed in high-performance, ELM-free Quiescent H-mode plasmas. The spatiotemporal characteristics of the EHO have been measured in QH-mode plasmas with a 2D BES array that measures low-k density fluctuations. The skewness of the fluctuation distribution increases radially from -0.5 to +1 near the separatrix, consistent with the radially varying and highly non-sinusoidal harmonic structure. These fluctuation characteristics are qualitatively consistent with an outward particle transport driven by the EHO. The density fluctuation (ñ / n) profile peaks inside the pedestal, near ρ = 0.90-0.95, and is observed from ρ = 0 . 85 to the separatrix; the fundamental frequency is typically in the range of 5-15 kHz. The radial structure of the oscillation has a monotonically varying phase shift of approximately 180 degrees across the outer plasma region that changes direction with plasma current, suggesting that the mode structure is impacted by the high edge toroidal rotation velocity. Work supported by the US Department of Energy under DE-FG02-08ER54999, DE-FC02-04ER54698, and DE-AC02-09CH11466.
Fisher Information and Shannon Entropy in Confined 1D Harmonic Oscillator
Stevanovic, Ljiljana
2010-01-21
Study of the linear harmonic oscillator confined in the square well with impenetrable walls is of great interest since its application for modeling parabolic quantum well semiconductor heterostructures. Fisher information and Shannon entropy, as a complexity measure for its ground and some excited energy levels are reported here.
Optical-parametric-oscillator solitons driven by the third harmonic.
Lutsky, Vitaly; Malomed, Boris A
2004-12-01
We introduce a model of a lossy second-harmonic-generating (chi(2)) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the fundamental-frequency (FF) wave may also contain a quadratic self-driving term, which is generated by the cubic nonlinearity of the medium. Unlike previously studied phase-matched models of chi(2) cavities driven at the second harmonic or at FF, the present one admits an exact analytical solution for the soliton, at a special value of the gain parameter. Two families of solitons are found in a numerical form, and their stability area is identified through numerical computation of the perturbation eigenvalues (stability of the zero solution, which is a necessary condition for the soliton's stability, is investigated in an analytical form). One family is a continuation of the special analytical solution. At given values of the parameters, one soliton is stable and the other one is not; they swap their stability at a critical value of the mismatch parameter. The stability of the solitons is also verified in direct simulations, which demonstrate that an unstable pulse rearranges itself into a stable one, or into a delocalized state, or decays to zero. A soliton which was given an initial boost C starts to move but quickly comes to a halt, if the boost is smaller than a critical value C(cr) . If C > C(cr) , the boost destroys the soliton (sometimes, through splitting into two secondary pulses). Interactions between initially separated solitons are investigated, too. It is concluded that stable solitons always merge into a single one. In the system with weak loss, it appears in a vibrating form, slowly relaxing to the static shape. With stronger loss, the final soliton emerges in the stationary form. PMID:15697523
Optical-parametric-oscillator solitons driven by the third harmonic
NASA Astrophysics Data System (ADS)
Lutsky, Vitaly; Malomed, Boris A.
2004-12-01
We introduce a model of a lossy second-harmonic-generating (χ(2)) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the fundamental-frequency (FF) wave may also contain a quadratic self-driving term, which is generated by the cubic nonlinearity of the medium. Unlike previously studied phase-matched models of χ(2) cavities driven at the second harmonic or at FF, the present one admits an exact analytical solution for the soliton, at a special value of the gain parameter. Two families of solitons are found in a numerical form, and their stability area is identified through numerical computation of the perturbation eigenvalues (stability of the zero solution, which is a necessary condition for the soliton’s stability, is investigated in an analytical form). One family is a continuation of the special analytical solution. At given values of the parameters, one soliton is stable and the other one is not; they swap their stability at a critical value of the mismatch parameter. The stability of the solitons is also verified in direct simulations, which demonstrate that an unstable pulse rearranges itself into a stable one, or into a delocalized state, or decays to zero. A soliton which was given an initial boost C starts to move but quickly comes to a halt, if the boost is smaller than a critical value Ccr . If C>Ccr , the boost destroys the soliton (sometimes, through splitting into two secondary pulses). Interactions between initially separated solitons are investigated, too. It is concluded that stable solitons always merge into a single one. In the system with weak loss, it appears in a vibrating form, slowly relaxing to the static shape. With stronger loss, the final soliton emerges in the stationary form.
Browne, Jacinta E; Watson, Amanda J; Hoskins, Peter R; Elliott, Alex T
2005-07-01
Tissue harmonic imaging (THI) has been reported to improve contrast resolution, tissue differentiation and overall image quality in clinical examinations. However, a study carried out previously by the authors (Brown et al. 2004) found improvements only in spatial resolution and not in contrast resolution or anechoic target detection. This result may have been due to the homogeneity of the phantom. Biologic tissues are generally inhomogeneous and THI has been reported to improve image quality in the presence of large amounts of subcutaneous fat. The aims of the study were to simulate the distortion caused by subcutaneous fat to image quality and thus investigate further the improvements reported in anechoic target detection and contrast resolution performance with THI compared with 2D conventional imaging. In addition, the effect of three different types of fat-mimicking layer on image quality was examined. The abdominal transducer of two ultrasound scanners with 2D conventional imaging and THI were tested, the 4C1 (Aspen-Acuson, Siemens Co., CA, USA) and the C5-2 (ATL HDI 5000, ATL/Philips, Amsterdam, The Netherlands). An ex vivo subcutaneous pig fat layer was used to replicate beam distortion and phase aberration seen clinically in the presence of subcutaneous fat. Three different types of fat-mimicking layers (olive oil, lard and lard with fish oil capsules) were evaluated. The subcutaneous pig fat layer demonstrated an improvement in anechoic target detection with THI compared with 2D conventional imaging, but no improvement was demonstrated in contrast resolution performance; a similar result was found in a previous study conducted by this research group (Brown et al. 2004) while using this tissue-mimicking phantom without a fat layer. Similarly, while using the layers of olive oil, lard and lard with fish oil capsules, improvements due to THI were found in anechoic target detection but, again, no improvements were found for contrast resolution for any of the
Harmonic mode competition in a terahertz gyrotron backward-wave oscillator
Kao, S. H.; Chiu, C. C.; Chang, P. C.; Wu, K. L.; Chu, K. R.
2012-10-15
Electron cyclotron maser interactions at terahertz (THz) frequencies require a high-order-mode structure to reduce the wall loss to a tolerable level. To generate THz radiation, it is also essential to employ cyclotron harmonic resonances to reduce the required magnetic field strength to a value within the capability of the superconducting magnets. However, much weaker harmonic interactions in a high-order-mode structure lead to serious mode competition problems. The current paper addresses harmonic mode competition in the gyrotron backward wave oscillator (gyro-BWO). We begin with a comparative study of the mode formation and oscillation thresholds in the gyro-BWO and gyromonotron. Differences in linear features result in far fewer 'windows' for harmonic operation of the gyro-BWO. Nonlinear consequences of these differences are examined in particle simulations of the multimode competition processes in the gyro-BWO, which shed light on the competition criteria between modes of different as well as the same cyclotron harmonic numbers. The viability of a harmonic gyro-BWO is assessed on the basis of the results obtained.
Orso, G.; Stringari, S.; Menotti, C.
2006-11-10
We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.
NASA Astrophysics Data System (ADS)
Isaac, Phillip S.; Marquette, Ian
2016-03-01
We generalize the construction of integrals of motion for quantum superintegrable models and the deformed oscillator algebra approach. This is presented in the context of 1D systems admitting ladder operators satisfying a parabosonic algebra involving reflection operators and more generally {c}λ extended oscillator algebras with grading. We apply the construction on two-dimensional {c}λ oscillators. We also introduce two new superintegrable Hamiltonians that are the anisotropic Dunkl and the singular Dunkl oscillators. Integrals are constructed by extending the approach of Daskaloyannis to include grading. An algebraic derivation of the energy spectra of the two models is presented, making use of finite dimensional unitary representations. We show how the spectra divide into sectors, and make comparisons with the physical case.
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems
Schlosshauer, Maximilian; Hines, A. P.; Milburn, G. J.
2008-02-15
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four 'canonical' system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.
The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory
Gomez Vergel, Daniel Villasenor, Eduardo J.S.
2009-06-15
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a single one-dimensional time-dependent oscillator, for which we first summarize some basic results concerning the unitary implementability of the dynamics. This is done by employing techniques different from those used so far to derive the Feynman propagator. In particular, we calculate the transition amplitudes for the usual harmonic oscillator eigenstates and define suitable semiclassical states for some physically relevant models. We then explore the possible extension of this study to infinite dimensional dynamical systems. Specifically, we construct Schroedinger functional representations in terms of appropriate probability spaces, analyze the unitarity of the time evolution, and probe the existence of semiclassical states for a wide range of physical systems, particularly, the well-known Minkowskian free scalar fields and Gowdy cosmological models.
Vignat, C.; Lamberti, P. W.
2009-10-15
Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Coherent dynamics of a flux qubit coupled to a harmonic oscillator.
Chiorescu, I; Bertet, P; Semba, K; Nakamura, Y; Harmans, C J P M; Mooij, J E
2004-09-01
In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system. PMID:15356624
Surface origin of quasi-2D Shubnikov-de Haas oscillations in Bi2Te2Se
NASA Astrophysics Data System (ADS)
Kapustin, A. A.; Stolyarov, V. S.; Bozhko, S. I.; Borisenko, D. N.; Kolesnikov, N. N.
2015-08-01
Transport measurements at liquid helium temperatures were done on a number of Bi2Te2Se samples with thicknesses ranging from 30 to 200 μm in order to detect surface states. In each sample we observed Shubnikov-de Haas (SdH) oscillations and sublinear dependence of off-diagonal component of magnetoresistance tensor on magnetic field. The periods of SdH oscillations in inverse magnetic field were found to be the same within 15%. The positions of SdH oscillations are determined by the normal to surface component of magnetic field. We found that the measured conductivity can be well described by a model with two groups of electrons, 2D and 3D. The conductivity of 2D electrons was found to be relatively weakly varying from sample to sample and not depending on thickness in a systematic manner. This behavior can be explained only by their localization on the surface. Comparison of the results of magnetotransport measurements with our scanning tunneling spectroscopy results on atomically smooth Bi2Te2Se surface in ultrahigh vacuum led us to conclude that the surface electrons are separated from the bulk electrons by a depletion layer approximately 100 nm thick. This effect could provide the dominant contribution of surface electrons to conductivity in samples with thicknesses less than 200 nm.
NASA Astrophysics Data System (ADS)
Gokhale, M. H.
A spherical harmonic Fourier analysis of the maximum areas of sunspot groups listed in Ledgers I and II of Greenwich photoheliographic results for 1933 - 1954 yield significant peaks at the 11 y periodicity for some spherical harmonic modes: especially the mode (l = 6, m = 0). A similar analysis of the daily areas of the spotgroups during 1944 - 1954 yields 11 y periodicity peaks only for some non-axisymmetric modes. These results suggest that the sunspot activity may be physically related to long period global oscillations of the sun.
Quenching of vortex breakdown oscillations via harmonic modulation
NASA Astrophysics Data System (ADS)
Lopez, J. M.; Cui, Y. D.; Marques, F.; Lim, T. T.
Vortex breakdown is a phenomenon inherent to many practical problems, such as leading-edge vortices on aircraft, atmospheric tornadoes, and flame-holders in combustion devices. The breakdown of these vortices is associated with the stagnation of the axial velocity on the vortex axis and the development of a near-axis recirculation zone. For large enough Reynolds number, the breakdown can be time-dependent. The unsteadiness can have serious consequences in some applications, such as tail-buffeting in aircraft flying at high angles of attack. There has been much interest in controlling the vortex breakdown phenomenon, but most efforts have focused on either shifting the threshold for the onset of steady breakdown or altering the spatial location of the recirculation zone. There has been much less attention paid to the problem of controlling unsteady vortex breakdown. Here we present results from a combined experimental and numerical investigation of vortex breakdown in an enclosed cylinder in which low-amplitude modulations of the rotating endwall that sets up the vortex are used as an open-loop control. As expected, for very low amplitudes of the modulation, variation of the modulation frequency reveals typical resonance tongues and frequency locking, so that the open-loop control allows us to drive the unsteady vortex breakdown to a prescribed periodicity within the resonance regions. For modulation amplitudes above a critical level that depends on the modulation frequency (but still very low), the result is a periodic state synchronous with the forcing frequency over an extensive range of forcing frequencies. Of particular interest is the spatial form of this forced periodic state: for modulation frequencies less than about twice the natural frequency of the unsteady breakdown, the oscillations of the near-axis recirculation zone are amplified, whereas for modulation frequencies larger than about twice the natural frequency the oscillations of the recirculation
Oscillator Seeding of a High Gain Harmonic Generation FEL in a Radiator-First Configuration
Gandhi, P.; Wurtele, J.; Penn, G.; Reinsch, M.
2012-05-20
A longitudinally coherent X-ray pulse from a high repetition rate free electron laser (FEL) is desired for a wide variety of experimental applications. However, generating such a pulse with a repetition rate greater than 1 MHz is a significant challenge. The desired high repetition rate sources, primarily high harmonic generation with intense lasers in gases or plasmas, do not exist now, and, for the multi-MHz bunch trains that superconducting accelerators can potentially produce, are likely not feasible with current technology. In this paper, we propose to place an oscillator downstream of a radiator. The oscillator generates radiation that is used as a seed for a high gain harmonic generation (HGHG) FEL which is upstream of the oscillator. For the first few pulses the oscillator builds up power and, until power is built up, the radiator has no HGHG seed. As power in the oscillator saturates, the HGHG is seeded and power is produced. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass map is derived using a semi-analytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft X-ray FEL.
Evading surface and detector frequency noise in harmonic oscillator measurements of force gradients
Moore, Eric W.; Lee, SangGap; Hickman, Steven A.; Harrell, Lee E.; Marohn, John A.
2010-01-01
We introduce and demonstrate a method of measuring small force gradients acting on a harmonic oscillator in which the force-gradient signal of interest is used to parametrically up-convert a forced oscillation below resonance into an amplitude signal at the oscillator’s resonance frequency. The approach, which we demonstrate in a mechanically detected electron spin resonance experiment, allows the force-gradient signal to evade detector frequency noise by converting a slowly modulated frequency signal into an amplitude signal. PMID:20733934
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid E-mail: siqbal@sns.nust.edu.pk
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
NASA Astrophysics Data System (ADS)
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
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.
The Harmonic Oscillator Influenced by Gravitational Wave in Noncommutative Quantum Phase Space
NASA Astrophysics Data System (ADS)
Yakup, Rehimhaji; Dulat, Sayipjamal; Li, Kang; Hekim, Mamatabdulla
2014-04-01
Dynamical property of harmonic oscillator affected by linearized gravitational wave (LGW) is studied in a particular case of both position and momentum operators which are noncommutative to each other. By using the generalized Bopp's shift, we, at first, derived the Hamiltonian in the noncommutative phase space (NPS) and, then, calculated the time evolution of coordinate and momentum operators in the Heisenberg representation. Tiny vibration of flat Minkowski space and effect of NPS let the Hamiltonian of harmonic oscillator, moving in the plain, get new extra terms from it's original and noncommutative space partner. At the end, for simplicity, we take the general form of the LGW into gravitational plain wave, obtain the explicit expression of coordinate and momentum operators.
Corrections to the Born-Oppenheimer approximation for a harmonic oscillator
NASA Astrophysics Data System (ADS)
Patterson, Chris W.
1993-02-01
We derive simple expressions for the energy corrections to the Born-Oppenheimer approximation valid for a harmonic oscillator. We apply these corrections to the electronic and rotational ground state of H+2 and show that the diabatic energy corrections are linearly dependent on the vibrational quantum numbers as seen in recent variational calculations [D. A. Kohl and E. J. Shipsey, J. Chem. Phys. 84, 2707 (1986)].
Truncated harmonic oscillator and Painlevé IV and V equations
NASA Astrophysics Data System (ADS)
Fernández C, David J.; Morales-Salgado, V. S.
2015-06-01
Quantum systems described by second and third order polynomial Heisenberg algebras are obtained applying supersymmetric quantum mechanics to the harmonic oscillator with an infinite potential barrier. These systems are linked with the Painlevé IV and V equations, respectively, thus several solutions of these non-linear second-order differential equations will be found, along with a chain of Bäcklund transformations connecting such solutions.
RLC circuit realization of a q-deformed harmonic oscillator with time dependent mass
NASA Astrophysics Data System (ADS)
Batouli, J.; El Baz, M.; Maaouni, A.
2015-08-01
We consider an RLC circuit type realization of a q-deformed harmonic oscillator. The differential equations of motion characterizing this circuit are derived, and it is shown that the RLC circuit gets modified as a result of the q-deformation. The natural frequency, the capacitance and the external power source are all modified and become q-dependent. The energy aspects of the circuit are also studied and the effects of the deformation are shown.
Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator
Chen Xi; Muga, J. G.
2010-11-15
We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes ('shortcuts to adiabaticity') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano
2008-03-01
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these "curved" harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK)-type approach, with two free parameters κ1,κ2 which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere S2, hyperbolic plane H2, AntiDeSitter sphere AdS1+1, and DeSitter sphere dS1+1) appear in this family, with Euclidean and Minkowski spaces as flat particular cases. We solve the equations of motion for the curved harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: by direct integration, by obtaining the general CK version of Binet's equation, and finally as a consequence of its superintegrable character. The orbits are conics with center at the potential origin on any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents pertinent results of the theory of conics on spaces of constant curvature.
NASA Astrophysics Data System (ADS)
Wang, Fei; Nie, Wei; Feng, Xunli; Oh, C. H.
2016-07-01
The correlated emission lasing (CEL) is experimentally demonstrated in harmonic oscillators coupled via a single three-level artificial atom [Phys. Rev. Lett. 115, 223603 (2015), 10.1103/PhysRevLett.115.223603] in which two-mode entanglement only exists in a certain time period when the harmonic oscillators are resonant with the atomic transitions. Here we examine this system and show that it is possible to obtain the steady-state entanglement when the two harmonic oscillators are resonant with Rabi sidebands. Applying dressed atomic states and Bogoliubov-mode transformation, we obtain the analytical results of the variance sum of a pair of Einstein-Podolsky-Rosen (EPR)-like operators. The stable entanglement originates from the dissipation process of the Bogoliubov modes because the atomic system can act as a reservoir in dressed state representation. We also show that the entanglement is robust against the dephasing rates of the superconducing atom, which is expected to have important applications in quantum information processing.
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
NASA Astrophysics Data System (ADS)
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.
Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams
NASA Technical Reports Server (NTRS)
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.
Containment control for coupled harmonic oscillators with multiple leaders under directed topology
NASA Astrophysics Data System (ADS)
Xu, Chengjie; Zheng, Ying; Su, Housheng; Wang, Hua O.
2015-02-01
This paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology. Using tools from matrix, graph and stability theories, necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous-time and sampled-data-based protocols, respectively. When the continuous-time protocol is used, it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time. When the sampled-data-based protocol is used, it is shown that the containment can be achieved if and only if: (1) an appropriate sampling period is chosen and (2) for every follower, there exists at least one leader that has a directed path to that follower at any time. And we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case. Finally, numerical simulations are presented to illustrate the theoretical findings.
ERIC Educational Resources Information Center
Andrews, David L.; Romero, Luciana C. Davila
2009-01-01
The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory
Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun
2010-09-15
We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by {approx}5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.
Wood, William E.; Osseward, Peter J.; Roseberry, Thomas K.; Perkel, David J.
2013-01-01
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. PMID:24312654
Schutt, Carolyn E; Ibsen, Stuart; Benchimol, Michael; Hsu, Mark; Esener, Sadik
2015-06-15
A new optical contrast agent has been developed by exposing dye-loaded microbubbles to a rapidly-cooled thermal treatment to homogenize the dye distribution across the surface. Ultrasound causes these microbubbles to oscillate in size which changes the self-quenching efficiency of the dye molecules creating a "blinking" signal. We demonstrate for the first time that these microbubbles can reproducibly generate second, third, and even fourth harmonic fluorescence intensity modulations, in addition to the fundamental frequency of the driving ultrasound. Detecting these harmonic signals could produce a higher signal-to-noise ratio for fluorescence imaging in medical applications by allowing fundamental frequency interference and artifacts to be filtered out. PMID:26076274
A TE{sub 21} second-harmonic gyrotron backward-wave oscillator with slotted structure
Chen, N. C.; Yu, C. F.; Chang, T. H.
2007-12-15
Second-harmonic gyrotron backward-wave oscillator (gyro-BWO) with a reduced magnetic field strength is a tunable source in the millimeter wave regime, but it has long been impeded by the severe mode competition as a result of low efficiency and narrow bandwidth. This study employs a slotted structure functioning as a mode selective circuit to suppress the lower order transverse modes. In addition, a two-step tapered waveguide is adopted to stabilize the higher-order transverse modes and axial modes. Some important characteristics of the slotted gyro-BWO will be analyzed and discussed. As a calculated result, the interaction efficiency is improved and the stable tuning range is broadened. A stable, Ka-band, slotted second-harmonic gyro-BWO is capable of producing an efficiency of 23% with a 3 dB tuning bandwidth of 9% at 5 A and 100 kV.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Menikoff, Ralph
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.
Generalized Hopf Fibration and Geometric SO(3) Reduction of the 4DOF Harmonic Oscillator
NASA Astrophysics Data System (ADS)
van der Meer, J. C.; Crespo, F.; Ferrer, S.
2016-04-01
It is shown that the generalized Hopf map ℍ × ℍ → ℍ × ℝ × ℝ quaternion formulation can be interpreted as an SO(3) orbit map for a symplectic SO(3) action. As a consequence the generalized Hopf fibration S7 → S4 appears in the SO(3) geometric symplectic reduction of the 4DOF isotropic harmonic oscillator. Furthermore it is shown how the Hopf fibration and associated twistor fibration play a role in the geometry of the Kepler problem and the rigid body problem.
Protective measurement of the wave function of a single squeezed harmonic-oscillator state
NASA Astrophysics Data System (ADS)
Alter, Orly; Yamamoto, Yoshihisa
1996-05-01
A scheme for the "protective measurement"
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
NASA Technical Reports Server (NTRS)
Kazansky, A. K.; Ostrovsky, Valentin N.
1995-01-01
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
NASA Astrophysics Data System (ADS)
Hoover, Wm. G.; Hoover, Carol G.
2012-02-01
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.
NASA Astrophysics Data System (ADS)
Afshar, Davood; Motamedinasab, Amin; Anbaraki, Azam; Jafarpour, Mojtaba
2016-02-01
In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.
The sojourn time of the inverted harmonic oscillator on the noncommutative plane
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Ren, Zhong-Zhou; Ju, Guo-Xing; Long, Chao-Yun
2011-10-01
The sojourn time of the Gaussian wavepacket that is stationed at the center of the inverted harmonic oscillator is investigated on the noncommutative plane in detail. In ordinary commutative space quantum mechanics, the sojourn time of the Gaussian wavepacket is always a monotonically decreasing function of the curvature parameter ω of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of ω with a minimum at an inflection point ω0. Furthermore, if ω is larger than a certain critical value the sojourn time will become infinity. Thus, the ordinary intuitive physical picture about the relation between the sojourn time and the shape of the inverted oscillator potential is changed when the spatial noncommutativity is considered.
Fox, Ronald F.; Vela-Arevalo, Luz V.
2002-11-01
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.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-03-01
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-01-01
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation. PMID:26382493
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-02-01
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
Bocko, M.F.; Onofrio, R.
1996-07-01
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 {ital et} {ital al}., 1980, Rev. Mod. Phys. {bold 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} {ital 1996 The American Physical Society.}
Purity and decoherence in the theory of a damped harmonic oscillator.
Isar, A; Sandulescu, A; Scheid, W
1999-12-01
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon. PMID:11970551
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-11-01
In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.
Confined One Dimensional Harmonic Oscillator as a Two-Mode System
Gueorguiev, V G; Rau, A P; Draayer, J P
2005-07-11
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.
NASA Astrophysics Data System (ADS)
Federman, Steven Robert; Heidarian, Negar; Irving, Richard; Ritchey, Adam M.; Ellis, David; Cheng, Song; Curtis, Larry; Furman, Walter
2016-06-01
We conducted beam-foil measurements on levels producing Pb II lines at 1203.6 and 1433.9 Å. These were supplemented by archival data from the Hubble Space Telescope (HST) covering the Pb II transitions. The oscillator strengths derived from our experimental lifetimes are generally consistent with recent large-scale theoretical results, as well as our own relativistic calculations. Our analysis of the HST spectra confirms the relative strengths of the two lines. However, the oscillator strength obtained for the line at 1433 Å is significantly smaller than earlier theoretical values used to derive the interstellar lead abundance, leading to an increase of 0.43 dex in this quantity. We will present our results for Pb II and compare them with others from the literature.
NASA Astrophysics Data System (ADS)
Shaari, M. F.; Abu Bakar, H.; Nordin, N.; Saw, S. K.; Samad, Z.
2013-12-01
Contractile body is an alternative mechanism instead of rotating blade propeller to generate water jet for locomotion. The oscillating motion of the actuator at different frequencies varies the pressure and volume of the pressure chamber in time to draw in and jet out the water at a certain mass flow rate. The aim of this research was to analyze the influence of the actuating frequency of the fluid flow in the pressure chamber of the thruster during this inflation-deflation process. A 70mm × 70mm × 18mm (L × W × T) 2D water jet thruster was fabricated for this purpose. The contractile function was driven using two lateral pneumatic actuators where the fluid flow analysis was focused on the X-Y plane vector. Observation was carried out using a video camera and Matlab image measurement technique to determine the volume of the flowing mass. The result demonstrated that the greater actuating frequency decreases the fluid flow rate and the Reynolds number. This observation shows that the higher frequency would give a higher mass flow rate during water jet generation.
Plenio, M. B.; Almeida, J.; Huelga, S. F.
2013-12-21
We demonstrate that the coupling of excitonic and vibrational motion in biological complexes can provide mechanisms to explain the long-lived oscillations that have been obtained in nonlinear spectroscopic signals of different photosynthetic pigment protein complexes and we discuss the contributions of excitonic versus purely vibrational components to these oscillatory features. Considering a dimer model coupled to a structured spectral density we exemplify the fundamental aspects of the electron-phonon dynamics, and by analyzing separately the different contributions to the nonlinear signal, we show that for realistic parameter regimes purely electronic coherence is of the same order as purely vibrational coherence in the electronic ground state. Moreover, we demonstrate how the latter relies upon the excitonic interaction to manifest. These results link recently proposed microscopic, non-equilibrium mechanisms to support long lived coherence at ambient temperatures with actual experimental observations of oscillatory behaviour using 2D photon echo techniques to corroborate the fundamental importance of the interplay of electronic and vibrational degrees of freedom in the dynamics of light harvesting aggregates.
NASA Technical Reports Server (NTRS)
Defacio, B.; Vannevel, Alan; Brander, O.
1993-01-01
A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.
NASA Astrophysics Data System (ADS)
Zhao, Liyun; Zhou, Jin; Wu, Quanjun
2016-01-01
This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.
Revised calculation of four-particle harmonic-oscillator transformation brackets matrix
NASA Astrophysics Data System (ADS)
Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.
2013-02-01
In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_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.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version
Harmonic oscillator states with integer and non-integer orbital angular momentum
NASA Astrophysics Data System (ADS)
Land, Martin
2011-12-01
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
Squeezing induced in a harmonic oscillator by a sudden change in mass or frequency
NASA Astrophysics Data System (ADS)
Abdalla, M. Sebawe; Colegrave, R. K.
1993-08-01
The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the influence of an external agency which causes the mass parameter to change from M0 to M1 in a short time ɛ. Then the frequency changes from ω0 to ω1=(M0/M1)ω0+O(ɛ2). In the limit ɛ-->0, no squeezing or loss of coherence occurs. If M1/M0=1+/-η (0<η<<1), then a squeezing of order ɛ2η occurs. If M1/M0 is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.
NASA Astrophysics Data System (ADS)
Kuwata, S.
2016-02-01
For the Fourier transform: ℱ of a non-integrablefunction φ, we exploit theresolvent ℛ forthe harmonic oscillator Hamiltonian, where the integral kernel for ℛ can be represented using the confluent hypergeometric function. Due to the commutativity of ℱ and ℛ, ℱ can be regarded by ℛ-1ℱℛ. In the case of φ(x) = 1, for example, it follows that(ℛφ)(x) is continuous on ℝ and that (ℛφ)(x) ≃ x-2(|x| → ∞)), so that ℛφ turns outto be integrable over ℝ. The finding that(ℱℛ)φ is exponentially localized indicatesthat the mapℱℛ:φ ↦ ¢ can be used as data compression of φ. Moreover, the inverse map:ℛ-1ℱ-1:¢ ↦ φ is well defined, which implies that the data decompression into φ can be made in a numerical calculation friendly way.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
NASA Technical Reports Server (NTRS)
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
1995-01-01
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved. PMID:19123623
Alternative descriptions of wave and particle aspects of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Schuch, Dieter
1993-01-01
The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.
GENERAL: Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential
NASA Astrophysics Data System (ADS)
Hu, Xian-Quan; Luo, Guang; Wu, Zhi-Min; Niu, Lian-Bin; Ma, Yan
2010-02-01
A new ring-shaped non-harmonic oscillator potential is proposed. The precise hound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 (2005) 94. The positive energy states of system are discussed and the conclusions are made properly.
Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Tanimura, Yoshitaka
2002-10-01
Vibrational relaxation of a harmonic oscillator nonlinearly coupled to a heat bath is investigated by the Gaussian-Markovian quantum Fokker-Planck equation approach. The system-bath interaction is assumed to be linear in the bath coordinate, but linear plus square in the system coordinate modeling the elastic and inelastic relaxation mechanisms. Interplay of the two relaxation processes induced by the linear-linear and square-linear interactions in Raman or infrared spectra is discussed for various system-bath couplings, temperatures, and correlation times for the bath fluctuations. The one-quantum coherence state created through the interaction with the pump laser pulse relaxes through different pathways in accordance with the mechanisms of the system-bath interactions. Relations between the present theory, Redfield theory, and stochastic theory are also discussed.
On the Mössbauer studies of harmonically bound quantum oscillators in Brownian motion
NASA Astrophysics Data System (ADS)
Razdan, A.
1999-03-01
In many biological systems like whole cells, membranes or proteins and some of the polymeric systems, dynamics reveals itself in Mössbauer spectra as a non Lorentzian behaviour above some particular temperature which is characteristic of the system. Moreover mean square displacement and line width show temperature dependence above the characteristic temperature. Brownian motion of harmonically bound oscillator has been able to explain the non-Lorentzian behaviour. In the present paper, a quantum picture of the above model is discussed and lineshape is expressed as the closed form for the extreme overdamping case. In addition to the non-Lorentzian behaviour, the present model also predicts a temperature dependence of mean square displacement and linewidth.
Some properties of an infinite family of deformations of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Quesne, Christiane
2010-12-01
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians Hk on the plane, depending on a positive real parameter k. Two algebraic extensions of Hk are described. The first one, based on the elements of the dihedral group D2k and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of Hk for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of Hk of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
Some properties of an infinite family of deformations of the harmonic oscillator
Quesne, Christiane
2010-12-23
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians H{sub k} on the plane, depending on a positive real parameter k. Two algebraic extensions of H{sub k} are described. The first one, based on the elements of the dihedral group D{sub 2k} and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of H{sub k} for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of H{sub k} of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
Rigatos, Gerasimos G.
2007-09-06
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of importance for the realization of quantum computing machines. To this end, this paper studies neural structures with weights that follow the model of the quantum harmonic oscillator. These weights correspond to diffusing particles, which interact to each other as the theory of Brownian motion predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of the number of attractors. Spectral analysis shows that the stochastic weights satisfy an equation which is analogous to the principle of uncertainty.
Bose–Einstein condensation in a two-component Bose gas with harmonic oscillator interaction
NASA Astrophysics Data System (ADS)
Abulseoud, A. A.; Abbas, A. H.; Galal, A. A.; El-Sherbini, Th M.
2016-07-01
In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose–Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
ERIC Educational Resources Information Center
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath.
Joutsuka, Tatsuya; Ando, Koji
2011-05-28
The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed. PMID:21639460
High efficiency fourth-harmonic generation from nanosecond fiber master oscillator power amplifier
NASA Astrophysics Data System (ADS)
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.
Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator.
Hornstein, Melissa K; Bajaj, Vikram S; Griffin, Robert G; Temkin, Richard J
2006-06-01
We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE(0,6,1) mode near 460 GHz. The gyrotron also operates in the second harmonic TE(2,6,1) mode at 456 GHz and in the TE(2,3,1) fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE(0,6,1) mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T. PMID:17710187
Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator
Hornstein, Melissa K.; Bajaj, Vikram S.; Griffin, Robert G.; Temkin, Richard J.
2007-01-01
We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE0,6,1 mode near 460 GHz. The gyrotron also operates in the second harmonic TE2,6,1 mode at 456 GHz and in the TE2,3,1 fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE0,6,1 mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T. PMID:17710187
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.
1984-01-01
A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.
ERIC Educational Resources Information Center
Nicolaides, Cleanthes A.; Constantoudis, Vasilios
2009-01-01
In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to epsilon[subscript n] = nhv, n = 0, 1, 2..., and [double integral]dp[subscript x] dx = h. By referring to just these two relations, we show how the adoption of "cycle-averaged phase-space states" (CAPSSs) leads to the…
NASA Astrophysics Data System (ADS)
Ita, B. I.; Obong, H. P.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.
Cari, C. Suparmi, A.
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.
Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming.
Chen, Zhiyong; Zheng, Min; Friesen, W Otto; Iwasaki, Tetsuya
2008-12-01
Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength. PMID:18663565
Lerche, Ernesto; Van Eester, Dirk
2011-12-23
Fourier analysis in the poloidal direction is a standard ingredient in present-day 2D wave equation solvers describing radio frequency waves in hot tokamak plasmas. Although a powerful and elegant technique, Fourier analysis has the disadvantage that a large number of modes is needed to describe the field pattern on a magnetic surface if a short wavelength mode exists on any - even very small - subpart of the particle trajectory. The present paper examines the potential of a method that does not suffer from this drawback: a finite element technique relying on simple linear or cubic area base functions that are defined on irregular elementary surfaces of triangular shape. The wave equation is solved in its weak Galerkin variational form and for realistic 2D tokamak geometry, accounting for the toroidal curvature but assuming the toroidal angle is ignorable, allowing to study the wave pattern for each of the independent toroidal modes excited by the antenna individually.The locally uniform full hot plasma dielectric tensor to all orders in finite Larmor radius was adopted. As the main intended application is the study of fast wave behavior (heating and current drive) at arbitrary harmonics, the wave vector complex amplitude appearing in the dielectric tensor is determined through a local dispersion root evaluation. High frequency fast wave propagation and damping is provided as an illustration in view of possible application of this type of current drive in future high density reactor-like tokamaks.
NASA Astrophysics Data System (ADS)
Dixon, George Jefferies
Spike-mode oscillation of a single-frequency, internally-doubled Nd:YAG laser under conditions of square -wave pump modulation is a potentially interesting technique for increasing the average harmonic conversion efficiency. To investigate this mode of operation, we have designed and built a unidirectional, Nd:YAG ring laser prototype which is capable of single-longitudinal mode oscillation at pump powers which are substantially above threshold. Initial study of this laser with diode-laser-array pumping yielded a maximum continuous-wave (cw) 1064-nm output power of 72 mW at an optical conversion efficiency exceeding 14%. Intracavity second harmonic generation was studied by inserting a crystal of potassium titanyl phosphate (KTP) inside the resonator and replacing the infrared output coupler with a mirror which was highly reflecting at 1064 nm and had high transmission at the 532-nm second harmonic. A maximum cw harmonic output power of 12 mW was observed from the laser at a pump power of 473 mW. Spike-mode oscillation could be achieved in the intracavity-doubled laser through square wave current modulation of the diode laser pump. Under optimal conditions, the average harmonic conversion efficiency was increased by over 100% under spiked conditions. Spike-mode oscillation with significant intracavity nonlinear coupling was observed to differ substantially from that of laser without the nonlinear crystal. The power-dependent harmonic output coupling had the effect of damping out relaxation oscillations and substantially limiting the peak spiked power. It was also observed to increase the amplitude and temporal stability of the spike pulse train and significantly increase the frequency range over which spiked oscillation would occur. A set of coupled rate equations relating the single -mode intracavity field to the gain in the laser medium was used to model the spike-mode oscillations of the intracavity -doubled ring. Numerical methods were used to obtain solutions
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
Majima, H. Suzuki, A.
2011-12-15
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 (-{gamma}x) 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)+({gamma})/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){sup 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.
H.K. Park, N.C. Luhmann, Jr, A.J.H. Donné, C.W. Domier, T. Munsat, M.J. Van de Pol, and the TEXTOR Team
2007-11-26
Two dimensional (2-D) images of electron temperature fluctuations with high temporal and spatial resolution have been employed to study the sawtooth oscillation (m/n=1/1 mode) in Toroidal EXperiment for Technology Oriented Research (TEXTOR) tokamak plasmas. 2-D imaging data revealed new physics which were not available in previous studies based on the 1-D electron temperature measurement and X-ray tomography. Review of the physics of the sawtooth oscillation is given by comparative studies with prominent theoretical models suggest that a new physics paradigm is needed to describe the reconnection physics of the sawtooth oscillation. The new insights are: A pressure driven instability (not a ballooning mode) leads to the X-point reconnection process. The reconnection process is identified as a random 3-D local reconnection process with a helical structure. The reconnection time scale is similar for different types of sawtooth oscillation ("kink" and tearing type) and is significantly faster than the resistive time scale. Heat flow from the core to the outside of the inversion radius during the reconnection process is highly collective rather than stochastic.
NASA Astrophysics Data System (ADS)
Ashhab, Sahel
2015-03-01
The Landau-Zener (LZ) problem is a standard paradigm for studying energy transfer and adiabatic passage protocols. We consider the LZ problem for a two level system when this system interacts with one harmonic oscillator mode that is initially set to a finite-temperature thermal equilibrium state. The oscillator could represent an external mode that is strongly coupled to the system, e.g. an ionic oscillation mode in a molecule, or it could represent a prototypical uncontrolled environment. We analyze the system's occupation probabilities at the final time in a number of different regimes, varying the system and oscillator frequencies, their coupling strength and the temperature. In particular we find some surprising non-monotonic dependence on the coupling strength and temperature.
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Demarie, Tommaso F.; Linjordet, Trond; Menicucci, Nicolas C.; Brennen, Gavin K.
2014-08-01
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology.
Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.
2015-11-01
In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.
NASA Astrophysics Data System (ADS)
Fidler, Andrew F.; Engel, Gregory S.
2013-10-01
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time. PMID:27575089
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
NASA Astrophysics Data System (ADS)
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
NASA Technical Reports Server (NTRS)
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.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.
2016-07-01
In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ⩽ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E × B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.
Ikeda, Tatsushi; Ito, Hironobu; Tanimura, Yoshitaka
2015-06-01
We explore and describe the roles of inter-molecular vibrations employing a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear infrared absorption (1D IR), we calculated 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are compared with results obtained from the LL+SL BO model applied through use of hierarchal Fokker-Planck equations with non-perturbative and non-Markovian noise. We find that all of the qualitative features of the 2D profiles of the signals obtained from the MD simulations are reproduced with the LL+SL BO model, indicating that this model captures the essential features of the inter-molecular motion. We analyze the fitted 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The origins of the echo peaks of the librational motion and the elongated peaks parallel to the probe direction are elucidated using optical Liouville paths. PMID:26049441
NASA Astrophysics Data System (ADS)
Wang, W.-M.
2008-01-01
We prove that the 1- d quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper [EV] in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corresponding nonlinear equation.
NASA Astrophysics Data System (ADS)
Leadenham, S.; Erturk, A.
2014-11-01
Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is
Surface origin of quasi-2D Shubnikov–de Haas oscillations in Bi{sub 2}Te{sub 2}Se
Kapustin, A. A. Stolyarov, V. S.; Bozhko, S. I.; Borisenko, D. N.; Kolesnikov, N. N.
2015-08-15
Transport measurements at liquid helium temperatures were done on a number of Bi{sub 2}Te{sub 2}Se samples with thicknesses ranging from 30 to 200 μm in order to detect surface states. In each sample we observed Shubnikov–de Haas (SdH) oscillations and sublinear dependence of off-diagonal component of magnetoresistance tensor on magnetic field. The periods of SdH oscillations in inverse magnetic field were found to be the same within 15%. The positions of SdH oscillations are determined by the normal to surface component of magnetic field. We found that the measured conductivity can be well described by a model with two groups of electrons, 2D and 3D. The conductivity of 2D electrons was found to be relatively weakly varying from sample to sample and not depending on thickness in a systematic manner. This behavior can be explained only by their localization on the surface. Comparison of the results of magnetotransport measurements with our scanning tunneling spectroscopy results on atomically smooth Bi{sub 2}Te{sub 2}Se surface in ultrahigh vacuum led us to conclude that the surface electrons are separated from the bulk electrons by a depletion layer approximately 100 nm thick. This effect could provide the dominant contribution of surface electrons to conductivity in samples with thicknesses less than 200 nm.
NASA Astrophysics Data System (ADS)
Muralidhar, K.
2014-03-01
Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass and bivector spin has been derived in the form . Where, is the angular velocity bivector of complex rotations, is the velocity of light. The unit vector acts as an operator on the idempotents and to give the eigen values The constant represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed.
NASA Astrophysics Data System (ADS)
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.
Hou, Gary Y.; Provost, Jean; Grondin, Julien; Wang, Shutao; Marquet, Fabrice; Bunting, Ethan; Konofagou, Elisa E.
2015-01-01
Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a recently developed High-Intensity Focused Ultrasound (HIFU) treatment monitoring method. HMIFU utilizes an Amplitude-Modulated (fAM = 25 Hz) HIFU beam to induce a localized focal oscillatory motion, which is simultaneously estimated and imaged by confocally-aligned imaging transducer. HMIFU feasibilities have been previously shown in silico, in vitro, and in vivo in 1-D or 2-D monitoring of HIFU treatment. The objective of this study is to develop and show the feasibility of a novel fast beamforming algorithm for image reconstruction using GPU-based sparse-matrix operation with real-time feedback. In this study, the algorithm was implemented onto a fully integrated, clinically relevant HMIFU system composed of a 93-element HIFU transducer (fcenter = 4.5MHz) and coaxially-aligned 64-element phased array (fcenter = 2.5MHz) for displacement excitation and motion estimation, respectively. A single transmit beam with divergent beam transmit was used while fast beamforming was implemented using a GPU-based delay-and-sum method and a sparse-matrix operation. Axial HMI displacements were then estimated from the RF signals using a 1-D normalized cross-correlation method and streamed to a graphic user interface. The present work developed and implemented a sparse matrix beamforming onto a fully-integrated, clinically relevant system, which can stream displacement images up to 15 Hz using a GPU-based processing, an increase of 100 fold in rate of streaming displacement images compared to conventional CPU-based conventional beamforming and reconstruction processing. The achieved feedback rate is also currently the fastest and only approach that does not require interrupting the HIFU treatment amongst the acoustic radiation force based HIFU imaging techniques. Results in phantom experiments showed reproducible displacement imaging, and monitoring of twenty two in vitro HIFU treatments using the new 2D system showed a
NASA Astrophysics Data System (ADS)
Kriisa, Annika; Liu, H.-C.; Samaraweera, R. L.; Heimbeck, M. S.; Everitt, H. O.; Wegscheider, W.; Mani, R. G.
Microwave-induced zero-resistance-states in the photo-excited GaAs/AlGaAs system evolve from the minima of microwave photo-excited ``quarter-cycle shifted'' magnetoresistance oscillations. Such magnetoresistance oscillations are known to exhibit nodes at cyclotron resonance (hf = ℏωc) and cyclotron resonance harmonics (hf = nℏωc). Further, the effective mass extracted from the radiation-induced magnetoresistance oscillations is known to differ from the canonical effective mass ratio for electrons in the GaAs/AlGaAs system. In an effort to reconcile this difference, we have looked for cyclotron resonance in the microwave reflection from the high mobility 2DES and attempted to correlate the observations with observed oscillatory magnetoresistance over the 30 <= f <= 330 GHz band. The results of such a study will be reported here. DOE-BES, Mat'l. Sci. & Eng. Div., DE-SC0001762; ARO W911NF-14-2-0076; ARO W911NF-15-1-0433.
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
ERIC Educational Resources Information Center
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
From weakly to strongly interacting 2D Fermi gases
NASA Astrophysics Data System (ADS)
Dyke, Paul; Fenech, Kristian; Lingham, Marcus; Peppler, Tyson; Hoinka, Sascha; Vale, Chris
2014-05-01
We study ultracold 2D Fermi gases of 6Li formed in a highly oblate trapping potential. The potential is generated by a cylindrically focused, blue detuned TEM01 mode laser beam. Weak magnetic field curvature provides highly harmonic confinement in the radial direction and we can readily produce single clouds with an aspect ratio of 230. Our experiments investigate the dimensional crossover from 3D to 2D for a two component Fermi gas in the Bose-Einstein Condensate to Bardeen Cooper Schrieffer crossover. Observation of an elbow in measurements of the cloud width vs. atom number is consistent with populating only the lowest transverse harmonic oscillator state for weak attractive interactions. This measurement is extended to the strongly interacting region using the broad Feshbach resonance at 832 G. We also report our progress towards measurement of the 2D equation of state for an interacting 2D Fermi gas via in-situ absorption imaging.
2-D and 3-D oscillating wing aerodynamics for a range of angles of attack including stall
NASA Technical Reports Server (NTRS)
Piziali, R. A.
1994-01-01
A comprehensive experimental investigation of the pressure distribution over a semispan wing undergoing pitching motions representative of a helicopter rotor blade was conducted. Testing the wing in the nonrotating condition isolates the three-dimensional (3-D) blade aerodynamic and dynamic stall characteristics from the complications of the rotor blade environment. The test has generated a very complete, detailed, and accurate body of data. These data include static and dynamic pressure distributions, surface flow visualizations, two-dimensional (2-D) airfoil data from the same model and installation, and important supporting blockage and wall pressure distributions. This body of data is sufficiently comprehensive and accurate that it can be used for the validation of rotor blade aerodynamic models over a broad range of the important parameters including 3-D dynamic stall. This data report presents all the cycle-averaged lift, drag, and pitching moment coefficient data versus angle of attack obtained from the instantaneous pressure data for the 3-D wing and the 2-D airfoil. Also presented are examples of the following: cycle-to-cycle variations occurring for incipient or lightly stalled conditions; 3-D surface flow visualizations; supporting blockage and wall pressure distributions; and underlying detailed pressure results.
NASA Technical Reports Server (NTRS)
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.
Teichmann, Karen; Wenderoth, Martin; Prüser, Henning; Pierz, Klaus; Schumacher, Hans W; Ulbrich, Rainer G
2013-08-14
InAs quantum dots embedded in an AlAs matrix inside a double barrier resonant tunneling diode are investigated by cross-sectional scanning tunneling spectroscopy. The wave functions of the bound quantum dot states are spatially and energetically resolved. These bound states are known to be responsible for resonant tunneling phenomena in such quantum dot diodes. The wave functions reveal a textbook-like one-dimensional harmonic oscillator behavior showing up to five equidistant energy levels of 80 meV spacing. The derived effective oscillator mass of m* = 0.24m0 is 1 order of magnitude higher than the effective electron mass of bulk InAs that we attribute to the influence of the surrounding AlAs matrix. This underlines the importance of the matrix material for tailored QD devices with well-defined properties. PMID:23777509
NASA Astrophysics Data System (ADS)
KartaloğLu, Tolga; Figen, Z. Gürkan; Aytür, Orhan
2003-02-01
We report a simple ad hoc method for designing an aperiodic grating structure to quasi-phase match two arbitrary second-order nonlinear processes simultaneously within the same electric-field-poled crystal. This method also allows the relative strength of the two processes to be adjusted freely, thereby enabling maximization of the overall conversion efficiency. We also report an experiment that is based on an aperiodically poled lithium niobate crystal that was designed by use of our method. In this crystal, parametric oscillation and second-harmonic generation are simultaneously phase matched for upconversion of a femtosecond Ti:sapphire laser to 570 nm. This self-doubling optical parametric oscillator provides an experimental verification of our design method.
NASA Astrophysics Data System (ADS)
Bamler, Robert; Rosch, Achim
2015-06-01
The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum-generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning δ ω of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by interspecies interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of interspecies interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, 1 /τ ∝(δω ) 2/Γ , where Γ is a single-particle scattering rate.
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Tanimura, Yoshitaka
2004-01-01
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.
Kato, Tsuyoshi; Tanimura, Yoshitaka
2004-01-01
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model. PMID:15267286
3/4-Fractional Superdiffusion in a System of Harmonic Oscillators Perturbed by a Conservative Noise
NASA Astrophysics Data System (ADS)
Bernardin, Cédric; Gonçalves, Patrícia; Jara, Milton
2016-05-01
We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.
NASA Astrophysics Data System (ADS)
Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.
2014-04-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.
Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E
2014-01-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.
NASA Technical Reports Server (NTRS)
Bgattacharyya, Sudip; Strohmayer, E.
2005-01-01
We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.
NASA Astrophysics Data System (ADS)
Aghaei, S.; Chenaghlou, A.
2015-01-01
In this paper, we study the Dirac equation with spin and pseudospin symmetry by the quadratic algebra approach for the 4-dimensional harmonic oscillator. By realization of the quadratic algebras in the deformed oscillator algebra, we obtain the relativistic energy spectrum. Also, by regarding the generalized Kustaanheimo-Stiefel transformation, we obtain the relativistic energy spectrum for the charge-dyon system with the U(1) monopole.
Ayvaz, Muzaffer; Demiralp, Metin
2012-12-10
This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.
An Ultrahigh-order-mode, Higher-harmonic Coaxial Gyrotron Oscillator in Sub-terahertz Wave Range
NASA Astrophysics Data System (ADS)
Zhang, Hui-Bo; Zhang, Shi-Chang
2013-12-01
A coaxial cavity gyrotron oscillator at a frequency of 0.34 THz is studied, which operates with a quite low magnetic field of 4.55 Tesla at the third cyclotron harmonic of the ultrahigh-order mode TE43,4. Properly choosing the depth of the longitudinal corrugations on the inner rod and optimizing the electron-beam position significantly suppress the mode competition. Nonlinear multimode simulations show the feasibility of the single-mode operation with an output power of 163 kW by using an electron beam with a voltage of 70kV and a current of 30A, which corresponds to an interaction efficiency of 9.2 % with maxim density of ohmic losses 2.9 kW/cm2.
NASA Astrophysics Data System (ADS)
Carlos Castro-Palacio, Juan; Velázquez-Abad, Luisberis; Giménez, Marcos H.; Monsoriu, Juan A.
2013-06-01
We have used a mobile phone acceleration sensor, and the Accelerometer Monitor application for Android, to collect data in physics experiments on free and damped oscillations. Results for the period, frequency, spring constant, and damping constant agree very well with measurements obtained by other methods. These widely available sensors are likely to find increased use in instructional laboratories.
NASA Astrophysics Data System (ADS)
Castellanos-Gomez, A.
2013-01-01
A simple strobe setup with the potential to study higher-order eigenmodes and multifrequency oscillations in micromechanical resonators is described. It requires standard equipment, commonly found in many laboratories, and it can thus be employed for public demonstrations of mechanical resonances. Moreover, the work presented here can be used by undergraduate students and/or teachers to prepare practical work in laboratory courses at physics or engineering universities. The dynamics of a micromachined cantilever is analysed as an example. In fact, using our stroboscopic setup, the first and second flexural eigenmodes, as well as a multifrequency oscillation composed by a superposition of both modes, have been successfully filmed with a conventional optical microscope equipped with a digital camera.
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Rañada, Manuel F.
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
NASA Astrophysics Data System (ADS)
Lorenz, Ulf; Saalfrank, Peter
2015-02-01
System-bath problems in physics and chemistry are often described by Markovian master equations. However, the Markov approximation, i.e., neglect of bath memory effects is not always justified, and different measures of non-Markovianity have been suggested in the literature to judge the validity of this approximation. Here we calculate several computable measures of non-Markovianity for the non-trivial problem of a harmonic oscillator coupled to a large number of bath oscillators. The Multi Configurational Time Dependent Hartree method is used to provide a numerically converged solution of the system-bath Schrödinger equation, from which the appropriate quantities can be calculated. In particular, we consider measures based on trace-distances and quantum discord for a variety of initial states. These quantities have proven useful in the case of two-level and other small model systems typically encountered in quantum optics, but are less straightforward to interpret for the more complex model systems that are relevant for chemical physics. Supplementary material in the form of one zip file available from the Journal web page at http://dx.doi.org/10.1140/epjd/e2014-50727-8
NASA Astrophysics Data System (ADS)
Monnier, B.; Naguib, A. M.; Koochesfahani, M. M.
2015-04-01
Reported herein is an investigation of the influence of the structural flexibility of sinusoidally pitching airfoils on the pattern of vorticity shed into the wake. For rigid airfoils, it is well known that, depending on the oscillation frequency and amplitude, this pattern takes the form of the classical or reverse von Kármán vortex street. The pattern may be characterized by the vortex circulation ( Γ o ), vortex-to-vortex streamwise and cross-stream spacing ( a and b, respectively), and vortex core radius ( R). In the present work, these four parameters are obtained from particle image velocimetry measurements in the wake of airfoils consisting of a rigid "head" and flexible "tail" at chord Reynolds number of 2010 for different tail flexibilities. The results show that flexible airfoils exhibit the switch from classical to reverse von Kármán vortex street (i.e., change in the sign of b) at a reduced frequency of oscillation lower than their rigid counterpart. At a given oscillation frequency, the Strouhal number at which this switch occurs is smallest for a given airfoil structural flexibility; which becomes stiffer with increasing frequency. Using Strouhal number based on the actual trailing edge oscillation amplitude, reasonable scaling is found of the dependence of not only b but also Γ o , a and R on the motion and structure parameters for all airfoils investigated. These results are complemented with analyses using a vortex array model, which together with the identified scaling of the wake vortex parameters, provide basis for the computation of the net thrust acting on the airfoil.
Stanislavsky, A A
2004-11-01
We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillator ensemble: these oscillators differ a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows one to draw a parallel in the dispersion analysis for media described by a fractional oscillator and an ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed. PMID:15600586
NASA Astrophysics Data System (ADS)
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Phase of the Riemann ζ function and the inverted harmonic oscillator
NASA Astrophysics Data System (ADS)
Bhaduri, R. K.; Khare, Avinash; Law, J.
1995-07-01
The Argand diagram is used to display some characteristics of the Riemann ζ function. The zeros of the ζ function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. The behavior of the phase of the ζ function on and off the line of zeros is studied. Up to some distance from the line of the complex zeros, the phase angle is shown to still retain their memory. The Argand plots also lead to an analogy with the scattering amplitude and an approximate rule for the location of the zeros. The smooth phase of the ζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
NASA Technical Reports Server (NTRS)
Durisen, R. H.
1978-01-01
The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.
NASA Astrophysics Data System (ADS)
Harko, Tiberiu; Liang, Shi-Dong
2016-06-01
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\\'enard and generalized Li\\'enard type, which physically describe important oscillator systems. By using a method inspired by quantum mechanics, and which consist on the deformation of the phase space coordinates of the harmonic oscillator, we generalize the equation of motion of the classical linear harmonic oscillator to several classes of strongly non-linear differential equations. The first integrals, and a number of exact solutions of the corresponding equations are explicitly obtained. The devised method can be further generalized to derive explicit general solutions of nonlinear second order differential equations unrelated to the harmonic oscillator. Applications of the obtained results for the study of the travelling wave solutions of the reaction-convection-diffusion equations, and of the large amplitude free vibrations of a uniform cantilever beam are also presented.
NASA Astrophysics Data System (ADS)
StankevičiÅ«tÄ--, K.; PipinytÄ--, I.; Vengelis, J.; MarcinkevičiÅ«tÄ--, A.; Å uminas, R.; Grigonis, R.; Eckardt, R. C.; Sirutkaitis, V.
2013-09-01
We present experimental data obtained during investigation of synchronously pumped optical parametric oscillators (SPOPO's) pumped by fundamental (1030 nm) and second harmonic (515 nm) radiation of mode-locked Yb:KGW laser, providing 105 fs pulses at 76 MHz repetition rate with an average power of 4 W. Different nonlinear crystals such as beta barium borate (BBO), and periodically poled lithium niobate (PPLN) and MgO doped PPLN (MgO:PPLN) were tested to estimate wavelength tuning capabilities and SPOPO's efficiency. Rotation of BBO nonlinear crystal and SPOPO's cavity length variation and, in the case of SPOPO based on PPLN, change of grating period and cavity length allowed signal wavelength tuning in 630 - 1030 nm and 1350 - 1700 nm spectral ranges, respectively. Parametric light conversion from pump power to signal power efficiency was as high as 25 %. Including the idler pulses the tuning ranges were from 630 to 2400 nm and from 1350 to 4000 nm in case of BBO and PPLN crystals, respectively. SPOPO based on BBO wsithout intracavity group velocity dispersion (GVD) compensation generates longer than transform limited pulses, so SPOPO based on BBO with dispersive prisms were investigated.
NASA Astrophysics Data System (ADS)
Papangelo, A.; Ciavarella, M.
2015-03-01
Due to the nonlinearity of the Coulomb friction law, even the simplest models of interfaces in contact show a very rich dynamic solution. It is often desirable, especially if the frequency of loading is only a fraction of the first natural frequency of the system, to replace a full dynamic analysis with a quasi-static one, which obviously is much simpler to obtain. In this work, we study a simple Coulomb frictional oscillator with harmonic tangential load, but with constant normal load. It is found that the quasi-static solution (which has only 2 stops) captures approximately the displacement peak as long as the forcing frequency is low enough for the dynamic solution to have 2 or, even better, more than 2 stops. Instead, the velocity peak is not correctly estimated, since the velocity becomes highly irregular due to the stick-slip stops, whose number increases without limit for zero frequency. In this sense, the classical quasi-static solution, obtaining by cancelling inertia terms in the equilibrium equations, does not coincide with the limit of the full dynamic solution at low frequencies. The difference is not eliminated by adding a small amount of viscous damping, as only with critical damping, the dynamic solution is very close to the quasi-static one. Additional discrepancies arise above a limit frequency whose value depends on the ratio of the tangential load to the limit one for sliding, and correspond to when the dynamic solution turns from 2 to 0 stop per cycle.
Neural network solution of the Schrödinger equation for a two-dimensional harmonic oscillator
NASA Astrophysics Data System (ADS)
Androsiuk, J.; Kułak, L.; Sienicki, K.
1993-07-01
We present computer simulations of a neural network capable of learning to perform transformations generated by the Schrödinger equation required to find eigenenergies of a two-dimensional harmonic oscillator. We show that this task can be achieved by a not fully connected back-propagation neural network containing 49 input neurons, 3 hidden layer neurons and 1 output neuron. The investigated neural network turns out to be capable of predicting eigenenergies with an average error of less than one percent. We demonstrate that the CPU time required to teach a neural network of performing the transformation produced by the Schrödinger equation is about 2 min to reach 41000 learning iterations, thus making foreseeable a direct application of a neural network in this and other more complex physical and chemical problems. A discussion of the errors due to the generalization of acquired knowledge is presented and related to a limited number of examples in learning mode and the number of neurons in the hidden layer. Decreasing the number of neurons in the hidden layer increases the apparent ability of the neural network for generalization.
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-01
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. PMID:21164914
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.
1980-01-01
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
Noguera, Norman; Rózga, Krzysztof
2015-07-15
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
NASA Astrophysics Data System (ADS)
Taghipour, Javad; Dardel, Morteza
2015-10-01
Steady state dynamical behavior of two degrees of freedom (DOF) system composed of a harmonically excited nonlinear oscillator coupled with a single DOF nonlinear energy sink (NES) is studied in comparison with the behavior of a system consisting of a nonlinear oscillator coupled with a two-DOF NES subjected to external harmonic excitation. First, an optimized set of parameters was obtained using optimization for the two-DOF system. Results show that the system with one NES has low robustness to the changes of the parameters and external force. By adding a degree of freedom to the first system, the steady state behavior of the resulting three-DOF system was investigated. Conclusions illustrated that increasing the degrees of freedom of the NES would increase the robustness of the system to the changes in system parameters and amplitude of external force.
NASA Astrophysics Data System (ADS)
Quesne, C.
2016-02-01
The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper (Quesne, 2015) [1], are extended by the inclusion of an isotonic term.
Steele, Richard H
2008-03-01
This article introduces quantum physics into biology in an intuitive and non-intimidating manner. It extends the quantum aspects of harmonic oscillators, and electromagnetic fields, to their functional roles in biology. Central to this process are the De Broglie wave-particle duality equation, and the adiabatic invariant parameters, magnetic moment, angular momentum and magnetic flux, determined by Ehrenfest as imposing quantum constraints on the dynamics of charges in motion. In mechanisms designed to explain the generation of low-level light emissions in biology we have adopted a biological analog of the electrical circuitry modeled on the parallel plated capacitor, traversed by helical protein structures, capable of generating electromagnetic radiation in the optical spectral region. The charge carrier required for the emissions is an accelerating electron driven, in a cyclotron-type mechanism, by ATP-induced reverse electron transfer with the radial, emission, components, mediated by coulombic forces within the helical configurations. Adenine, an essential nucleotide constituent of DNA, was examined with its long wavelength absorption maximum determining the energetic parameters for the calculations. The calculations were made for a virtual 5-turn helix where each turn of the helix emits a different frequency, generating a biological quantum series. The components of six adiabatic invariant equations were found to be embedded in Planck's constant rendering them discrete, finite, non-random, non-statistical-Planck's constant precludes probability. A mechanism for drug-induced hallucination is described that might provide insights as to the possible role of electromagnetic fields in consciousness. Sodium acceleration through a proposed nerve membrane helical channel generated electromagnetic emissions in the microwave region in confirmation of reported microwave emission for active nerves and may explain saltatory nerve conduction. Theoretical calculations for a
Oishi, T.; Kado, S.; Yoshinuma, M.; Ida, K.; Akiyama, T.; Minami, T.; Nagaoka, K.; Shimizu, A.; Okamura, S.; Tanaka, S.
2006-10-15
In the present study, a coherent density fluctuation similar to the edge harmonic oscillation (EHO) in tokamaks was observed in the edge transport barrier discharge in the Compact Helical System (CHS) [K. Matsuoka et al., Plasma Physics and Controlled Nuclear Fusion Research, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 2, pp. 441] using beam emission spectroscopy (BES). The fluctuation had both fundamental (f=4.5 kHz) and second-harmonic (2f=9 kHz) frequencies. EHO in CHS had a peak amplitude at approximately {rho}=0.95. The mode has a continuous phase shift in the radial direction. If this is interpreted as the radial propagation, the mode propagates in the outer radial direction at an apparent phase velocity of several hundreds of meters per second, which is a characteristic similar to the radial phase shift of EHO in tokamaks.
Guo, H.Z.; Rodgers, J.; Hoppe, D.J.
1995-12-31
Phase-locking in a 34.5 GHz special complex cavity gyrotron oscillator operating at the second harmonic of the electron cyclotron frequency was studied. Injection of the locking power was made via a quasi-optical circulator connected to the gyrotron output. Locking bandwidth was measured by comparing the phase of the injection signal and output signal using a balanced mixer. Locking was observed with input power level as low as 40 dB below the gyrotron output power. The locking bandwidth is, however, narrower than in gyrotrons operating at the fundamental cyclotron frequency which may be attributed to the longer resonant cavity in the second harmonic gyrotron and the corresponding larger value of external quality factor. The measurements are roughly in agreement with predictions of Adler`s phase-locking equation which is given for the system in terms of powers propagating in the output waveguide toward and away from the gyrotron cavity.
NASA Astrophysics Data System (ADS)
Stoitsov, M. V.; Dobaczewski, J.; Nazarewicz, W.; Ring, P.
2005-04-01
We describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogolyubov calculations with Skyrme-forces and zero-range pairing interaction using Harmonic-Oscillator and/or Transformed Harmonic-Oscillator states. The particle-number symmetry is approximately restored using the Lipkin-Nogami prescription, followed by an exact particle number projection after the variation. The program can be used in a variety of applications, including systematic studies of wide ranges of nuclei, both spherical and axially deformed, extending all the way out to nucleon drip lines. Program summaryTitle of the program: HFBTHO (v1.66p) Catalogue number: ADUI Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI Licensing provisions: none Computers on which the program has been tested: Pentium-III, Pentium-IV, AMD-Athlon, IBM Power 3, IBM Power 4, Intel Xeon Operating systems: LINUX, Windows Programming language used: FORTRAN-95 Memory required to execute with typical data: 59 MB when using N=20 No. of bits in a word: 64 No. of processors used: 1 Has the code been vectorized?: No No. of bytes in distributed program, including test data, etc.: 195 285 No. of lines in distributed program: 12 058 Distribution format: tar.gz Nature of physical problem: The solution of self-consistent mean-field equations for weakly bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasiparticle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the Transformed Harmonic Oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Method of solution: The program uses the axially Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes