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.
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).
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)
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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
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.
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.}
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.
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.
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.
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.
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.
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
Demonstration of Double EIT Using Coupled Harmonic Oscillators and RLC Circuits
ERIC Educational Resources Information Center
Harden, Joshua; Joshi, Amitabh; Serna, Juan D.
2011-01-01
Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring-mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The…
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.
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.
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.
Saturation in coupled oscillators
NASA Astrophysics Data System (ADS)
Roman, Ahmed; Hanna, James
2015-03-01
We consider a weakly nonlinear system consisting of a resonantly forced oscillator coupled to an unforced oscillator. It has long been known that, for quadratic nonlinearities and a 2:1 resonance between the oscillators, a perturbative solution of the dynamics exhibits a phenomenon known as saturation. At low forcing, the forced oscillator responds, while the unforced oscillator is quiescent. Above a critical value of the forcing, the forced oscillator's steady-state amplitude reaches a plateau, while that of the unforced oscillator increases without bound. We show that, contrary to established folklore, saturation is not unique to quadratically nonlinear systems. We present conditions on the form of the nonlinear couplings and resonance that lead to saturation. Our results elucidate a mechanism for localization or diversion of energy in systems of coupled oscillators, and suggest new approaches for the control or suppression of vibrations in engineered systems.
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.
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.
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).
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.
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…
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
Coupled Oscillators with Chemotaxis
NASA Astrophysics Data System (ADS)
Sawai, Satoshi; Aizawa, Yoji
1998-08-01
A simple coupled oscillator system with chemotaxis is introducedto study morphogenesis of cellular slime molds. The modelsuccessfuly explains the migration of pseudoplasmodium which hasbeen experimentally predicted to be lead by cells with higherintrinsic frequencies. Results obtained predict that its velocityattains its maximum value in the interface region between totallocking and partial locking and also suggest possible rolesplayed by partial synchrony during multicellular development.
Quantum dissipative effect of one dimension coupled anharmonic oscillator
Sulaiman, A.; Zen, Freddy P.
2015-04-16
Quantum dissipative effect of one dimension coupled anharmonic oscillator is investigated. The systems are two coupled harmonic oscillator with the different masses. The dissipative effect is studied based on the quantum state diffusion formalism. The result show that the anharmonic effect increase the amplitude but the lifetime of the oscillation depend on the damping coefficient and do not depend on the temperature.
NASA Astrophysics Data System (ADS)
Goryachev, Maxim; Tobar, Michael E.
2015-02-01
A new electromagnetic cavity structure, a lattice of 3D cavities consisting of an array of posts and gaps is presented. The individual cavity elements are based on the cylindrical re-entrant (or Klystron) cavity. We show that these cavities can also be thought of as 3D split-ring resonators, which is confirmed by applying symmetry transformations, each of which is an electromagnetic resonator with spatially separated magnetic and electric field. The characteristics of the cavity is used to mimic phonon behaviour of a one-dimensional (1D) chain of atoms. It is demonstrated how magnetic field coupling can lead to phonon-like dispersion curves with acoustical and optical branches. The system is able to reproduce a number of effects typical to 1D lattices exhibiting acoustic vibration, such as band gaps, phonon trapping, and effects of impurities. In addition, quasicrystal emulations predict the results expected from this class of ordered structures. The system is easily scalable to simulate two-dimensional and 3D lattices and shows a new way to engineer arrays of coupled microwave resonators with a variety of possible applications to hybrid quantum systems proposed.
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.
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.
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.
Coupled opto-electronic oscillator
NASA Technical Reports Server (NTRS)
Yao, X. Steve (Inventor); Maleki, Lute (Inventor)
1999-01-01
A coupled opto-electronic oscillator that directly couples a laser oscillation with an electronic oscillation to simultaneously achieve a stable RF oscillation at a high frequency and ultra-short optical pulsation by mode locking with a high repetition rate and stability. Single-mode selection can be achieved even with a very long opto-electronic loop. A multimode laser can be used to pump the electronic oscillation, resulting in a high operation efficiency. The optical and the RF oscillations are correlated to each other.
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
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.
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.
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.
Phase chaos in coupled oscillators.
Popovych, Oleksandr V; Maistrenko, Yuri L; Tass, Peter A
2005-06-01
A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos is a common property of networks of oscillators of very different natures, such as phase oscillators, limit-cycle oscillators, and chaotic oscillators, e.g., Rössler systems. PMID:16089804
Phase chaos in coupled oscillators
NASA Astrophysics Data System (ADS)
Popovych, Oleksandr V.; Maistrenko, Yuri L.; Tass, Peter A.
2005-06-01
A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos is a common property of networks of oscillators of very different natures, such as phase oscillators, limit-cycle oscillators, and chaotic oscillators, e.g., Rössler systems.
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
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…
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
NASA Astrophysics Data System (ADS)
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016-09-01
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Dynamics in the Kuramoto model with a bi-harmonic coupling function
NASA Astrophysics Data System (ADS)
Yuan, Di; Cui, Haitao; Tian, Junlong; Xiao, Yi; Zhang, Yingxin
2016-09-01
We study a variant of the Kuramoto model with a bi-harmonic coupling function, in which oscillators with positive first harmonic coupling strength are conformists and oscillators with negative first harmonic coupling strength are contrarians. We show that the model displays different synchronous dynamics and different dynamics may be characterized by the phase distributions of oscillators. There exist stationary synchronous states, travelling wave states, π state and, most interestingly, another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π with a constant amplitude and a constant period in oscillating π state. Finally, the bifurcation diagram of the model in the parameter space is presented.
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.
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.
Magnetically Coupled Magnet-Spring Oscillators
ERIC Educational Resources Information Center
Donoso, G.; Ladera, C. L.; Martin, P.
2010-01-01
A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of…
Globally coupled noisy oscillators with inhomogeneous periodic forcing
NASA Astrophysics Data System (ADS)
Gabbay, Michael; Larsen, Michael L.; Tsimring, Lev S.
2004-12-01
We study the collective properties of an array of nonlinear noisy oscillators driven by nonidentical periodic signals. We consider the case of a globally coupled array of harmonically forced, weakly nonlinear oscillators where there is a constant difference between the phases of the forcing signals applied to adjacent oscillators. This system is a prototypical model of a nonlinear phased array receiver. We derive analytical results for the array output in the limit of a large number of oscillators for the noise-free and noisy cases. Numerical simulations show good agreement with the theoretical analysis.
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.
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
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
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…
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.
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.)
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…
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
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Green, Stephen; Lehner, Luis
2015-04-01
Motivated by the fluid/gravity correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein's equation to the equations of motion of a series of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism with an asymptotically AdS black-brane spacetime, where the equations of motion for the oscillators are shown to be equivalent to the Navier-Stokes equation for the boundary fluid in the mode-expansion picture. We thereby expand on the explicit correspondence connecting the fluid and gravity sides for this particular physical set-up. Perhaps more importantly, we expect this formalism to remain valid in more general spacetimes, including those without a fluid/gravity correspondence. In other words, although born out of the correspondence, the formalism survives independently of it and has a much wider range of applicability.
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
Stochastic switching in delay-coupled oscillators.
D'Huys, Otti; Jüngling, Thomas; Kinzel, Wolfgang
2014-09-01
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation, which allows us to analytically compute the distribution of frequencies and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators. PMID:25314515
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.
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.
Coupled oscillator model for nonlinear gravitational perturbations
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Green, Stephen R.; Lehner, Luis
2015-04-01
Motivated by the gravity-fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although born out of the gravity-fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, we expect its introduction to simplify the often highly technical analytical exploration of nonlinear gravitational dynamics.
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.
Interaction function of oscillating coupled neurons
Dodla, Ramana; Wilson, Charles J.
2013-01-01
Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses, and parameterizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms. PMID:24229210
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.
Dynamical robustness of coupled heterogeneous oscillators
NASA Astrophysics Data System (ADS)
Tanaka, Gouhei; Morino, Kai; Daido, Hiroaki; Aihara, Kazuyuki
2014-05-01
We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.
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?
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.
Reentrant transition in coupled noisy oscillators.
Kobayashi, Yasuaki; Kori, Hiroshi
2015-01-01
We report on a synchronization-breaking instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the pacemaker more frequently and the phase slip rate increases, which may not be observed in averaged phase models such as the Kuramoto model. Investigation of the corresponding Fokker-Planck equation enables us to obtain the reentrant transition line between the synchronized state and the phase slip state. We verify our theory using the Brusselator model, suggesting that this reentrant transition can be found in a wide range of limit cycle oscillators. PMID:25679676
Phase and amplitude dynamics of nonlinearly coupled oscillators
NASA Astrophysics Data System (ADS)
Cudmore, P.; Holmes, C. A.
2015-02-01
This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type of nonlinear coupling. We show that this system exhibits synchronisation, where all oscillators are rotating at the same rate, and that in the synchronised state the system has a regular structure related to the distribution of the frequencies of the individual oscillators. Using a geometric description, we show how changes in the non-linear coupling function can cause pitchfork and saddle-node bifurcations which create or destroy stable and unstable synchronised solutions. We apply these results to show how in-phase and anti-phase solutions are created in a system with a bi-modal distribution of frequencies.
Generation of even harmonics in coupled quantum dots
Guo Shifang; Duan Suqing; Yang Ning; Chu Weidong; Zhang Wei
2011-07-15
Using the spatial-temporal symmetry principle we developed recently, we propose an effective scheme for even-harmonics generation in coupled quantum dots. The relative intensity of odd and even harmonic components in the emission spectrum can be controlled by tuning the dipole couplings among the dots, which can be realized in experiments by careful design of the nanostructures. In particular, pure 2nth harmonics and (2n+1)th harmonics (where n is an integer) can be generated simultaneously with polarizations in two mutual perpendicular directions in our systems. An experimental design of the coupled dots system is presented.
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.
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)
Synchronization in chaotic oscillators by cyclic coupling
NASA Astrophysics Data System (ADS)
Olusola, O. I.; Njah, A. N.; Dana, S. K.
2013-07-01
We introduce a type of cyclic coupling to investigate synchronization of chaotic oscillators. We derive analytical solutions of the critical coupling for stable synchronization under the cyclic coupling for the Rössler system and the Lorenz oscillator as paradigmatic illustration. Based on the master stability function (MSF) approach, the analytical results on critical coupling are verified numerically. An enhancing effect in terms of lowering the critical coupling or enlarging the synchronization window in a critical coupling space is noticed. The cyclic coupling is also applied in other models, Hindmarsh-Rose model, Sprott system, Chen system and forced Duffing system to confirm the enhancing effect. The cyclic coupling allows tuning of two coupling constants in reverse directions when an optimal control of synchronization is feasible.
Recent Developments in the Analysis of Couple Oscillator Arrays
NASA Technical Reports Server (NTRS)
Pogorzelski, Ronald J.
2000-01-01
This presentation considers linear arrays of coupled oscillators. Our purpose in coupling oscillators together is to achieve high radiated power through the spatial power combining which results when the oscillators are injection locked to each other. York, et. al. have shown that, left to themselves, the ensemble of injection locked oscillators oscillate at the average of the tuning frequencies of all the oscillators. Coupling these arrays achieves high radiated power through coherent spatial power combining. The coupled oscillators are usually designed to produce constant aperture phase. Oscillators are injection locked to each other or to a master oscillator to produce coherent radiation. Oscillators do not necessarily oscillate at their tuning frequency.
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.
Arrays of coupled chemical oscillators.
Forrester, Derek Michael
2015-01-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a "worship". Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning. PMID:26582365
Arrays of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Forrester, Derek Michael
2015-11-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning.
Arrays of coupled chemical oscillators
Forrester, Derek Michael
2015-01-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning. PMID:26582365
Period variability of coupled noisy oscillators
NASA Astrophysics Data System (ADS)
Mori, Fumito; Kori, Hiroshi
2013-03-01
Period variability, quantified by the standard deviation (SD) of the cycle-to-cycle period, is investigated for noisy phase oscillators. We define the checkpoint phase as the beginning or end point of one oscillation cycle and derive an expression for the SD as a function of this phase. We find that the SD is dependent on the checkpoint phase only when oscillators are coupled. The applicability of our theory is verified using a realistic model. Our work clarifies the relationship between period variability and synchronization from which valuable information regarding coupling can be inferred.
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
Designing the Dynamics of Globally Coupled Oscillators
NASA Astrophysics Data System (ADS)
Orosz, G.; Moehlis, J.; Ashwin, P.
2009-09-01
A method for designing cluster states with prescribed stability is presented for coupled phase oscillator systems with all-to-all coupling. We determine criteria for the coupling function that ensure the existence and stability of a large variety of clustered configurations. We show that such criteria can be satisfied by choosing Fourier coefficients of the coupling function. We demonstrate that using simple trigonometric and localized coupling functions one can realize arbitrary patterns of stable clusters and that the designed systems are capable of performing finite state computation. The design principles may be relevant when engineering complex dynamical behavior of coupled systems, e.g. the emergent dynamics of artificial neural networks, coupled chemical oscillators and robotic swarms.
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.
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…
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.
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…
Synchronization of coupled Boolean phase oscillators
NASA Astrophysics Data System (ADS)
Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.
2014-04-01
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.
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.
Dispersion dipoles for coupled Drude oscillators
NASA Astrophysics Data System (ADS)
Odbadrakh, Tuguldur T.; Jordan, Kenneth D.
2016-01-01
We present the dispersion-induced dipole moments of coupled Drude oscillators obtained from two approaches. The first approach evaluates the dipole moment using the second-order Rayleigh-Schrödinger perturbation theory wave function allowing for dipole-dipole and dipole-quadrupole coupling. The second approach, based on response theory, employs an integral of the dipole-dipole polarizability of one oscillator and the dipole-dipole-quadrupole hyperpolarizability of the other oscillator over imaginary frequencies. The resulting dispersion dipoles exhibit an R-7 dependence on the separation between the two oscillators and are connected to the leading-order C6/R6 dispersion energy through the electrostatic Hellmann-Feynman theorem.
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.
Mode coupling in spin torque oscillators
NASA Astrophysics Data System (ADS)
Zhang, Steven S.-L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-09-01
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau-Lifshitz-Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators.
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression. PMID:26066224
Mixed-mode oscillation suppression states in coupled oscillators
NASA Astrophysics Data System (ADS)
Ghosh, Debarati; Banerjee, Tanmoy
2015-11-01
We report a collective dynamical state, namely the mixed-mode oscillation suppression state where the steady states of the state variables of a system of coupled oscillators show heterogeneous behaviors. We identify two variants of it: The first one is a mixed-mode death (MMD) state, which is an interesting oscillation death state, where a set of variables show dissimilar values, while the rest arrive at a common value. In the second mixed death state, bistable and monostable nontrivial homogeneous steady states appear simultaneously to a different set of variables (we refer to it as the MNAD state). We find these states in the paradigmatic chaotic Lorenz system and Lorenz-like system under generic coupling schemes. We identify that while the reflection symmetry breaking is responsible for the MNAD state, the breaking of both the reflection and translational symmetries result in the MMD state. Using a rigorous bifurcation analysis we establish the occurrence of the MMD and MNAD states, and map their transition routes in parameter space. Moreover, we report experimental observation of the MMD and MNAD states that supports our theoretical results. We believe that this study will broaden our understanding of oscillation suppression states; subsequently, it may have applications in many real physical systems, such as laser and geomagnetic systems, whose mathematical models mimic the Lorenz system.
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…
D3-Equivariant coupled advertising oscillators model
NASA Astrophysics Data System (ADS)
Zhang, Chunrui; Zheng, Huifeng
2011-04-01
A ring of three coupled advertising oscillators with delay is considered. Using the symmetric functional differential equation theories, the multiple Hopf bifurcations of the equilibrium at the origin are demonstrated. The existence of multiple branches of bifurcating periodic solution is obtained. Numerical simulation supports our analysis results.
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
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.
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.
Nonlinearly coupled localized plasmon resonances: Resonant second-harmonic generation
NASA Astrophysics Data System (ADS)
Ginzburg, Pavel; Krasavin, Alexey; Sonnefraud, Yannick; Murphy, Antony; Pollard, Robert J.; Maier, Stefan A.; Zayats, Anatoly V.
2012-08-01
The efficient resonant nonlinear coupling between localized surface plasmon modes is demonstrated in a simple and intuitive way using boundary integral formulation and utilizing second-order optical nonlinearity. The nonlinearity is derived from the hydrodynamic description of electron plasma and originates from the presence of material interfaces in the case of small metal particles. The coupling between fundamental and second-harmonic modes is shown to be symmetry selective and proportional to the spatial overlap between polarization dipole density of the second-harmonic mode and the square of the polarization charge density of the fundamental mode. Particles with high geometrical symmetry will convert a far-field illumination into dark nonradiating second-harmonic modes, such as quadrupoles. Effective second-harmonic susceptibilities are proportional to the surface-to-volume ratio of a particle, emphasizing the nanoscale enhancement of the effect.
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.
Synchronization Dynamics of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Tompkins, Nathan
The synchronization dynamics of complex networks have been extensively studied over the past few decades due to their ubiquity in the natural world. Prominent examples include cardiac rhythms, circadian rhythms, the flashing of fireflies, predator/prey population dynamics, mammalian gait, human applause, pendulum clocks, the electrical grid, and of the course the brain. Detailed experiments have been done to map the topology of many of these systems and significant advances have been made to describe the mathematics of these networks. Compared to these bodies of work relatively little has been done to directly test the role of topology in the synchronization dynamics of coupled oscillators. This Dissertation develops technology to examine the dynamics due to topology within networks of discrete oscillatory components. The oscillatory system used here consists of the photo-inhibitable Belousov-Zhabotinsky (BZ) reaction water-in-oil emulsion where the oscillatory drops are diffusively coupled to one another and the topology is defined by the geometry of the diffusive connections. Ring networks are created from a close-packed 2D array of drops using the Programmable Illumination Microscope (PIM) in order to test Turing's theory of morphogenesis directly. Further technology is developed to create custom planar networks of BZ drops in more complicated topologies which can be individually perturbed using illumination from the PIM. The work presented here establishes the validity of using the BZ emulsion system with a PIM to study the topology induced effects on the synchronization dynamics of coupled chemical oscillators, tests the successes and limitations of Turing's theory of morphogenesis, and develops new technology to further probe the effects of network topology on a system of coupled oscillators. Finally, this Dissertation concludes by describing ongoing experiments which utilize this new technology to examine topology induced transitions of synchronization
Enhanced second harmonic generation from coupled asymmetric plasmonic metal nanostructures
NASA Astrophysics Data System (ADS)
Yildiz, Bilge Can; Emre Tasgin, Mehmet; Kurtulus Abak, Musa; Coskun, Sahin; Emrah Unalan, Husnu; Bek, Alpan
2015-12-01
We experimentally demonstrate that two coupled metal nanostructures (MNSs), a silver nanowire and bipyramid, can produce ∼30 times enhanced second harmonic generation compared to the particles alone. We develop a simple theoretical model, presenting the path interference effects in the nonlinear response of coupled MNSs. We show that the reason for such an enhancement can be the occurrence of a Fano resonance due to the coupling of the converter MNS to the long-lived mode of the attached MNS.
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.
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.
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…
Synchronization of weakly coupled oscillators: coupling, delay and topology
NASA Astrophysics Data System (ADS)
Mallada, Enrique; Tang, Ao
2013-12-01
There are three key factors in a system of coupled oscillators that characterize the interaction between them: coupling (how to affect), delay (when to affect) and topology (whom to affect). The existing work on each of these factors has mainly focused on special cases. With new angles and tools, this paper makes progress in relaxing some assumptions on these factors. There are three main results in this paper. Firstly, by using results from algebraic graph theory, a sufficient condition is obtained that can be used to check equilibrium stability. This condition works for arbitrary topology, generalizing existing results and also leading to a sufficient condition on the coupling function which guarantees that the system will reach synchronization. Secondly, it is known that identical oscillators with sin () coupling functions are guaranteed to synchronize in phase on a complete graph. Our results prove that in many cases certain structures such as symmetry and concavity, rather than the exact shape of the coupling function, are the keys for global synchronization. Finally, the effect of heterogenous delays is investigated. Using mean field theory, a system of delayed coupled oscillators is approximated by a non-delayed one whose coupling depends on the delay distribution. This shows how the stability properties of the system depend on the delay distribution and allows us to predict its behavior. In particular, we show that for sin () coupling, heterogeneous delays are equivalent to homogeneous delays. Furthermore, we can use our novel sufficient instability condition to show that heterogeneity, i.e. wider delay distribution, can help reach in-phase synchronization.
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
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.
Predicting synchrony in heterogeneous pulse coupled oscillators
NASA Astrophysics Data System (ADS)
Talathi, Sachin S.; Hwang, Dong-Uk; Miliotis, Abraham; Carney, Paul R.; Ditto, William L.
2009-08-01
Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.
Model reduction for networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.
2015-05-01
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach, an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary differential equation with n ≪ N , constituting an immense reduction in complexity. The onset of both local and global synchronisation is reproduced to good numerical accuracy, and we are able to describe both soft and hard transitions. By introducing two collective coordinates, the approach is able to describe the interaction of two partially synchronised clusters in the case of bimodally distributed native frequencies. Furthermore, our approach allows us to accurately describe finite size scalings of the critical coupling strength. We corroborate our analytical results by comparing with numerical simulations of the Kuramoto model with all-to-all coupling networks for several distributions of the native frequencies.
NASA Astrophysics Data System (ADS)
Schmidt, Lennart; Krischer, Katharina
2015-06-01
We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex dynamics. Furthermore, we investigate localized turbulence and discuss whether it can be categorized as a chimera state.
Four mass coupled oscillator guitar model.
Popp, John E
2012-01-01
Coupled oscillator models have been used for the low frequency response (50 to 250 Hz) of a guitar. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players' hands. The model presented has improved these models in three ways, (1) a fourth oscillator includes the guitar body, (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses used to calculate the responses, including resonances and phases, directly, and (3) one of the three resultant resonances varies with neck and side mass and can also be modeled as a bar mode of the neck and body. The calculated and measured resonances and phases agree reasonably well. PMID:22280705
Effect of acoustic coupling on random and harmonic plate vibrations
NASA Technical Reports Server (NTRS)
Frendi, Abdelkader; Robinson, Jay
1993-01-01
The effect of acoustic coupling on random and harmonic plate vibrations is studied using two numerical models. In the coupled model, the plate response is obtained by integration of the nonlinear plate equation coupled with the nonlinear Euler equations for the surrounding acoustic fluid. In the uncoupled model, the nonlinear plate equation with an equivalent linear viscous damping term is integrated to obtain the response of the plate subject to the same excitation field. For a low-level, narrow-band excitation, the two models predict the same plate response spectra. As the excitation level is increased, the response power spectrum predicted by the uncoupled model becomes broader and more shifted towards the high frequencies than that obtained by the coupled model. In addition, the difference in response between the coupled and uncoupled models at high frequencies becomes larger. When a high intensity harmonic excitation is used, causing a nonlinear plate response, both models predict the same frequency content of the response. However, the level of the harmonics and subharmonics are higher for the uncoupled model. Comparisons to earlier experimental and numerical results show that acoustic coupling has a significant effect on the plate response at high excitation levels. Its absence in previous models may explain the discrepancy between predicted and measured responses.
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.
Control of Oscillation Patterns in a Symmetric Coupled Biological Oscillator System
NASA Astrophysics Data System (ADS)
Takamatsu, Atsuko; Tanaka, Reiko; Yamamoto, Takatoki; Fujii, Teruo
2003-08-01
A chain of three-oscillator system was constructed with living biological oscillators of phasmodial slime mold, Physarum polycehalum and the oscillation patterns were analyzed by the symmetric Hopf bifurcation theory using group theory. Multi-stability of oscillation patterns was observed, even when the coupling strength was fixed. This suggests that the coupling strength is not an effective parameter to obtain a desired oscillation pattern among the multiple patterns. Here we propose a method to control oscillation patterns using resonance to external stimulus and demonstrate pattern switching induced by frequency resonance given to only one of oscillators in the system.
Thermal energies of classical and quantum damped oscillators coupled to reservoirs
NASA Astrophysics Data System (ADS)
Philbin, T. G.; Anders, J.
2016-05-01
We consider the global thermal state of classical and quantum harmonic oscillators that interact with a reservoir. Ohmic damping of the oscillator can be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic damping is conveniently treated with a continuum reservoir of harmonic oscillators. Using the diagonalized Hamiltonian of the total system, we calculate a number of thermodynamic quantities for the damped oscillator: the mean force internal energy, mean force free energy, and another internal energy based on the free-oscillator Hamiltonian. The classical mean force energy is equal to that of a free oscillator, for both Ohmic and non-Ohmic damping no matter how strong the coupling to the reservoir. In contrast, the quantum mean force energy depends on the details of the damping and diverges for strictly Ohmic damping. These results give additional insight into the steady-state thermodynamics of open systems with arbitrarily strong coupling to a reservoir, complementing results for energies derived within dynamical approaches (e.g. master equations) in the weak-coupling regime.
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.
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
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
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.
Active Coupled Oscillators in the Inner Ear
NASA Astrophysics Data System (ADS)
Strimbu, Clark Elliott
Auditory and vestibular systems are endowed with an active process that enables them to detect signals as small as a few Angstroms; they also exhibit frequency selectivity; show strong nonlinearities; and can exhibit as spontaneous activity. Much of this active process comes from the sensory hair cells at the periphery of the auditory and vestibular systems. Each hair cell is capped by an eponymous hair bundle, a specialized structure that transduces mechanical forces into electrical signals. Experiments on mechanically decoupled cells from the frog sacculus have shown that individual hair bundles behave in an active manner analogous to an intact organ suggesting a common cellular basis for the active processes seen in many species. In particular, mechanically decoupled hair bundles show rapid active movements in response to transient stimuli and exhibit spontaneous oscillations. However, a single mechanosensitive hair cell is unable to match the performance of an entire organ. In vivo, hair bundles are often coupled to overlying membranes, gelatinous extracellular matrices. We used an in vitro preparation of the frog sacculus in which the otolithic membrane has been left intact. Under natural coupling conditions, there is a strong degree of correlation across the saccular epithelium, suggesting that the collective response of many cells contributes to the extreme sensitivity of this organ. When the membrane is left intact, the hair bundles do not oscillate spontaneously, showing that the natural coupling and loading tunes them into a quiescent regime. However, when stimulated by a pulse, the bundles show a rapid biphasic response that is abolished when the transduction channels are blocked. The active forces generated by the bundles are sufficient to move the overlying membrane.
Synchronization using environmental coupling in mercury beating heart oscillators
NASA Astrophysics Data System (ADS)
Singla, Tanu; Montoya, Fernando; Rivera, M.; Tajima, Shunsuke; Nakabayashi, Seiichiro; Parmananda, P.
2016-06-01
We report synchronization of Mercury Beating Heart (MBH) oscillators using the environmental coupling mechanism. This mechanism involves interaction of the oscillators with a common medium/environment such that the oscillators do not interact among themselves. In the present work, we chose a modified MBH system as the common environment. In the absence of coupling, this modified system does not exhibit self sustained oscillations. It was observed that, as a result of the coupling of the MBH oscillators with this common environment, the electrical and the mechanical activities of both the oscillators synchronized simultaneously. Experimental results indicate the emergence of both lag and the complete synchronization in the MBH oscillators. Simulations of the phase oscillators were carried out in order to better understand the experimental observations.
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.
Transitional behavior in hydrodynamically coupled oscillators
NASA Astrophysics Data System (ADS)
Box, S.; Debono, L.; Phillips, D. B.; Simpson, S. H.
2015-02-01
In this article we consider the complete set of synchronized and phase-locked states available to pairs of hydrodynamically coupled colloidal rotors, consisting of spherical beads driven about circular paths in the same, and in opposing senses. Oscillators such as these have previously been used as coarse grained, minimal models of beating cilia. Two mechanisms are known to be important in establishing synchrony. The first involves perturbation of the driving force, and the second involves deformation of the rotor trajectory. We demonstrate that these mechanisms are of similar strength, in the regime of interest, and interact to determine observed behavior. Combining analysis and simulation with experiments performed using holographic optical tweezers, we show how varying the amplitude of the driving force perturbation leads to a transition from synchronized to phase-locked states. Analogies with biological systems are discussed, as are implications for the design of biomimetic devices.
Harmonic trap resonance enhanced synthetic atomic spin-orbit coupling
NASA Astrophysics Data System (ADS)
Wu, Ling-Na; Luo, Xinyu; Xu, Zhi-Fang; Ueda, Masahito; Wang, Ruquan; You, Li
2016-05-01
The widely adopted scheme for synthetic atomic spin-orbit coupling (SOC) is based on the momentum sensitive Raman coupling, which is easily implemented in one spatial dimension. Recently, schemes based on pulsed or periodically modulating gradient magnetic field (GMF) were proposed and the main characteristic features have subsequently been demonstrated. The present work reports an experimental discovery and the associated theoretical understanding of tuning the SOC strength synthesized with GMF through the motional resonance of atomic center-of-mass in a harmonic trap. In some limits, we observe up to 10 times stronger SOC compared to the momentum impulse from GMF for atoms in free space.
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.
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.
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.
Periodic patterns in a ring of delay-coupled oscillators
NASA Astrophysics Data System (ADS)
Perlikowski, P.; Yanchuk, S.; Popovych, O. V.; Tass, P. A.
2010-09-01
We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses.
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
Phase patterns of coupled oscillators with application to wireless communication
Arenas, A.
2008-01-02
Here we study the plausibility of a phase oscillators dynamical model for TDMA in wireless communication networks. We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end. The results open the door for new communication protocols in a continuous interacting networks of wireless communication devices.
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.
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.
Surprises of the Transformer as a Coupled Oscillator System
ERIC Educational Resources Information Center
Silva, J. P.; Silvestre, A. J.
2008-01-01
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both…
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.
A Fresh Look at Coupled-Oscillator Spatial Power Combining
NASA Technical Reports Server (NTRS)
Pearson, L.W.; Pogorzelski, R. J.
1998-01-01
Quasi-optical oscillators were proposed a little more than ten years ago as a means of developing the power levels needed for applications at millimeter frequencies using large numbers of individual semiconductor devices each of which produces only a modest amount of power [J.W. Mink, IEEE Trans. MTT., vol. 34, p. 273, 19861. An operating system was demonstrated soon after [Z.B. Popovic et. al, Int. J. Infrared and Millimeter Waves, v. 9, p. 647, 1988] in the form of a so-called grid oscillator. This device constituted a rectangular array of oscillating devices that are mutually coupled so that they oscillator coherently. The interconnecting lines in one direction serve as radiators so that the oscillators radiate directly, and the radiated fields add. Subsequently, coupled oscillators using resonant transmission line lengths was demonstrated by Mortazawi and Itoh [IEEE Trans. MTT., vol. 38, p. 86,1990). In recent work, coupled-oscillator power combiners have received less attention, with amplifier/combiners receiving more attention. Specific weaknesses of spatial-combining oscillators have motivated this transition. Namely, the oscillators employ low-Q resonators (resulting in low signal quality) and no clear means of modulation has been identified until recently. In this presentation, we review coupled-oscillator combiners in broad terms, indicating the features that make particular systems viable. We indicate how these features can be reconciled to functional requirements for system applications. Comparisons are drawn between two approaches to obtain mutual coupling: One employs low-Q oscillator circuits at each site, with concomitantly high propensity for the oscillators to couple. The other approach employs moderate-Q oscillators at each site with the concomitant requirement to tune the oscillators so that they share a range of frequencies over which they can couple and lock. In either case, precise frequency control and modulation can be achieved through
Harmonically trapped atoms with spin–orbit coupling
NASA Astrophysics Data System (ADS)
Zhu, Chuanzhou; Dong, Lin; Pu, Han
2016-07-01
We study harmonically trapped one-dimensional atoms subjected to an equal combination of Rashba and Dresselhaus spin–orbit coupling induced by Raman transition. We first examine the wave function and the degeneracy of the single-particle ground state, followed by a study of two weakly interacting bosons or fermions. For the two-particle ground state, we focus on the effects of the interaction on the degeneracy, the spin density profiles, and the density–density correlation functions. Finally we show how these studies help us to understand the many-body properties of the system.
Spin Number Coherent States and the Problem of Two Coupled Oscillators
NASA Astrophysics Data System (ADS)
Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.
2015-07-01
From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters. Supported by SNI-México, COFAA-IPN, EDD-IPN, EDI-IPN, SIP-IPN Project No. 20150935
Collective phase response curves for heterogeneous coupled oscillators
NASA Astrophysics Data System (ADS)
Hannay, Kevin M.; Booth, Victoria; Forger, Daniel B.
2015-08-01
Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakaguchi-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.
Stable and transient multicluster oscillation death in nonlocally coupled networks
NASA Astrophysics Data System (ADS)
Schneider, Isabelle; Kapeller, Marie; Loos, Sarah; Zakharova, Anna; Fiedler, Bernold; Schöll, Eckehard
2015-11-01
In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation, which works well for large coupling ranges but fails for coupling ranges, which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.
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.
Symmetry-broken states on networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Jiang, Xin; Abrams, Daniel M.
2016-05-01
When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here, we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-broken coexistent states are analogous to those dubbed "chimera states," which can occur when identical oscillators are coupled to one another in identical ways.
Phase dynamics of coupled oscillators reconstructed from data
NASA Astrophysics Data System (ADS)
Rosenblum, Michael; Kralemann, Bjoern; Pikovsky, Arkady
2013-03-01
We present a technique for invariant reconstruction of the phase dynamics equations for coupled oscillators from data. The invariant description is achieved by means of a transformation of phase estimates (protophases) obtained from general scalar observables to genuine phases. Staring from the bivariate data, we obtain the coupling functions in terms of these phases. We discuss the importance of the protophase-to-phase transformation for characterization of strength and directionality of interaction. To illustrate the technique we analyse the cardio-respiratory interaction on healthy humans. Our invariant approach is confirmed by high similarity of the coupling functions obtained from different observables of the cardiac system. Next, we generalize the technique to cover the case of small networks of coupled periodic units. We use the partial norms of the reconstructed coupling functions to quantify directed coupling between the oscillators. We illustrate the method by different network motifs for three coupled oscillators. We also discuss nonlinear effects in coupling.
Synchronization of optically coupled resonant tunneling diode oscillators
NASA Astrophysics Data System (ADS)
Romeira, Bruno; Figueiredo, José M. L.; Ironside, Charles N.; Quintana, José M.
2013-11-01
We experimentally investigate the synchronous response of two fiber-optic coupled optoelectronic circuit oscillators based on resonant tunneling diodes (RTDs). The fiber-optic synchronization link employs injection of a periodic oscillating optical modulated signal generated by a master RTD-laser diode (LD) oscillator to a slave RTD-photodetector (PD) oscillator. The synchronous regimes were evaluated as a function of frequency detuning and optical injection strength. The results show the slave RTD-PD oscillator follows the frequency and noise characteristics of the master RTD-LD oscillator resulting in two oscillators with similar phase noise characteristics exhibiting single side band phase noise levels below -100 dBc/Hz at 1 MHz offset from the carrier frequency. Optical synchronization of RTD-based optoelectronic circuit oscillators have many applications spanning from sensing, to microwave generation, and data transmission.
Temperature of a decoherent oscillator with strong coupling.
Unruh, W G
2012-09-28
The temperature of an oscillator coupled to the vacuum state of a heat bath via Ohmic coupling is non-zero, as measured by the reduced density matrix of the oscillator. This study shows that the actual temperature, as measured by a thermometer, is still zero (or, in the thermal state of the bath, the temperature of the bath). The decoherence temperature is due to 'false-decoherence', with a correlation between the oscillator and the heat bath causing the decoherence, but the heat baths state dragged along with the state of the oscillator. PMID:22908337
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
Laser cooling of a harmonic oscillator's bath with optomechanics
NASA Astrophysics Data System (ADS)
Xu, Xunnong; Taylor, Jacob
Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
Helicopter detection using harmonics and seismic-acoustic coupling
NASA Astrophysics Data System (ADS)
Damarla, T. Raju; Ufford, David
2008-04-01
Unattended ground sensors (UGS) are routinely used to collect intelligence, surveillance, and reconnaissance (ISR) information. Unattended ground sensors consisting of microphone array and geophone are employed to detect rotary wing aircraft. This paper presents an algorithm for the detection of helicopters based on a fusion of rotor harmonics and acoustic-seismic coupling. The main rotor blades of helicopters operate at a fixed RPM to prevent stalling or mechanical damage. In addition, the seismic spectrum is dominated by the acoustic-seismic coupling generated by these rotors; much more so than ground vehicles and other targets where mechanical coupling and a more broadband acoustic source are strong factors. First, an autocorrelation detection method identifies the constant fundamental generated by the helicopter main rotor. Second, key matching frequencies between the acoustic and seismic spectrum are used to locate possible coupled components. Detection can then be based on the ratio of the coupled seismic energy to total seismic energy. The results of the two methods are fused over a few seconds time to provide an initial and continued detection of a helicopter within the sensor range. Performance is measured on data as a function of range and sound pressure level (SPL).
Wang, Yongqiang; Hori, Yutaka; Hara, Shinji; Doyle, Francis J.
2013-01-01
Most biological rhythms are generated by a population of cellular oscillators coupled through intercellular signaling. Recent experimental evidence shows that the collective period may differ significantly from the autonomous period in the presence of intercellular delays. The phenomenon has been investigated using delay-coupled phase oscillators, but the proposed phase model contains no direct biological mechanism, which may weaken the model's reliability in unraveling biophysical principles. Based on a published gene regulatory oscillator model, we analyze the collective period of delay-coupled biological oscillators using the multivariable harmonic balance technique. We prove that, in contradiction to the common intuition that the collective period increases linearly with the coupling delay, the collective period turns out to be a periodic function of the intercellular delay. More surprisingly, the collective period may even decrease with the intercellular delay when the delay resides in certain regions. The collective period is given in a closed-form in terms of biochemical reaction constants and thus provides biological insights as well as guidance in synthetic-biological-oscillator design. Simulation results are given based on a segmentation clock model to confirm the theoretical predictions. PMID:25346544
Disentanglement of two harmonic oscillators in relativistic motion
Lin, S.-Y.; Chou, C.-H.; Hu, B. L.
2008-12-15
We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time ('sudden death'). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob's proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice's coordinate, but the shorter in Rob's coordinate.
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.
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.
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
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.
A Simplified Theory of Coupled Oscillator Array Phase Control
NASA Technical Reports Server (NTRS)
Pogorzelski, R. J.; York, R. A.
1997-01-01
Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.
A common lag scenario in quenching of oscillation in coupled oscillators
NASA Astrophysics Data System (ADS)
Suresh, K.; Sabarathinam, S.; Thamilmaran, K.; Kurths, Jürgen; Dana, Syamal K.
2016-08-01
A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from the conventional lag synchronization. We present numerical as well as experimental evidence of this unknown kind of lag scenario when the lag increases with coupling and at a critically large value at a critical coupling strength, amplitude death emerges in two largely mismatched oscillators. This is analogous to amplitude death in identical systems with increasingly large coupling delay. In support, we use examples of the Chua oscillator and the Bonhoeffer-van der Pol system. Furthermore, we confirm this lag scenario during the onset of amplitude death in identical Stuart-Landau system under various instantaneous coupling forms, repulsive, conjugate, and a type of nonlinear coupling.
A common lag scenario in quenching of oscillation in coupled oscillators.
Suresh, K; Sabarathinam, S; Thamilmaran, K; Kurths, Jürgen; Dana, Syamal K
2016-08-01
A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from the conventional lag synchronization. We present numerical as well as experimental evidence of this unknown kind of lag scenario when the lag increases with coupling and at a critically large value at a critical coupling strength, amplitude death emerges in two largely mismatched oscillators. This is analogous to amplitude death in identical systems with increasingly large coupling delay. In support, we use examples of the Chua oscillator and the Bonhoeffer-van der Pol system. Furthermore, we confirm this lag scenario during the onset of amplitude death in identical Stuart-Landau system under various instantaneous coupling forms, repulsive, conjugate, and a type of nonlinear coupling. PMID:27586600
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.
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)].
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.
Disentanglement of two harmonic oscillators in relativistic motion
NASA Astrophysics Data System (ADS)
Lin, Shih-Yuin; Chou, Chung-Hsien; Hu, B. L.
2008-12-01
We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time (“sudden death”). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob’s proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice’s coordinate, but the shorter in Rob’s coordinate.
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.
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.
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.
Classification of attractors for systems of identical coupled Kuramoto oscillators
Engelbrecht, Jan R.; Mirollo, Renato
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Senthilkumar, D. V.; Suresh, K.; Chandrasekar, V. K.; Zou, Wei; Dana, Syamal K.; Kathamuthu, Thamilmaran; Kurths, Jürgen
2016-04-01
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators.
Senthilkumar, D V; Suresh, K; Chandrasekar, V K; Zou, Wei; Dana, Syamal K; Kathamuthu, Thamilmaran; Kurths, Jürgen
2016-04-01
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results. PMID:27131491
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
NASA Astrophysics Data System (ADS)
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A.
2013-05-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses.
Oscillations and Synchronization in a System of Three Reactively Coupled Oscillators
NASA Astrophysics Data System (ADS)
Kuznetsov, Alexander P.; Turukina, Ludmila V.; Chernyshov, Nikolai Yu.; Sedova, Yuliya V.
We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features of the reactive coupling are discussed.
Entanglement of two harmonic modes coupled by angular momentum
Rebon, L.; Rossignoli, R.
2011-11-15
We examine the entanglement induced by an angular momentum coupling between two harmonic systems. The Hamiltonian corresponds to that of a charged particle in a uniform magnetic field in an anisotropic quadratic potential or, equivalently, to that of a particle in a rotating quadratic potential. We analyze both the vacuum and thermal entanglement, thereby obtaining analytic expressions for the entanglement entropy and negativity through the Gaussian state formalism. It is shown that vacuum entanglement diverges at the edges of the dynamically stable sectors, increasing with the angular momentum and saturating for strong fields, whereas at finite temperature entanglement is nonzero just within a finite field or frequency window and no longer diverges. Moreover, the limit temperature for entanglement is finite in the whole stable domain. The thermal behavior of the Gaussian quantum discord and its difference from the negativity is also discussed.
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…
Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators
NASA Technical Reports Server (NTRS)
Golubitsky, Martin; Stewart, Ian
1986-01-01
The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.
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
Perceptual grouping by entrainment in coupled Kuramoto oscillator networks.
Meier, Martin; Haschke, Robert; Ritter, Helge J
2014-01-01
In this article we present a network composed of coupled Kuramoto oscillators, which is able to solve a broad spectrum of perceptual grouping tasks. Based on attracting and repelling interactions between these oscillators, the network dynamics forms various phase-synchronized clusters of oscillators corresponding to individual groups of similar input features. The degree of similarity between features is determined by a set of underlying receptive fields, which are learned directly from the feature domain. After illustrating the theoretical principles of the network, the approach is evaluated in an image segmentation task. Furthermore, the influence of a varying degree of sparse couplings is evaluated. PMID:24571099
Suppression and revival of oscillation in indirectly coupled limit cycle oscillators
NASA Astrophysics Data System (ADS)
Sharma, P. R.; Kamal, N. K.; Verma, U. K.; Suresh, K.; Thamilmaran, K.; Shrimali, M. D.
2016-09-01
We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.
Coupling a Bose condensate to micromechanical oscillators
NASA Astrophysics Data System (ADS)
Kemp, Chandler; Fox, Eli; Flanz, Scott; Vengalattore, Mukund
2011-05-01
We describe the construction of a compact apparatus to investigate the interaction of a spinor Bose-Einstein condensate and a micromechanical oscillator. The apparatus uses a double magneto-optical trap, Raman sideband cooling, and evaporative cooling to rapidly produce a 87Rb BEC in close proximity to a high Q membrane. The micromotion of the membrane results in small Zeeman shifts at the location of the BEC due to a magnetic domain attached to the oscillator. Detection of this micromotion by the condensate results in a backaction on the membrane. We investigate prospects of using this backaction to generate nonclassical states of the mechanical oscillator. This work was funded by the DARPA ORCHID program.
Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch
NASA Astrophysics Data System (ADS)
Pisarchik, A. N.; Jaimes-Reátegui, R.
2015-11-01
A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles "stabilization of chaos by chaos," i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively.
Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch.
Pisarchik, A N; Jaimes-Reátegui, R
2015-11-01
A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles "stabilization of chaos by chaos," i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively. PMID:26651632
Dynamics of globally delay-coupled neurons displaying subthreshold oscillations.
Masoller, Cristina; Torrent, M C; García-Ojalvo, Jordi
2009-08-28
We study an ensemble of neurons that are coupled through their time-delayed collective mean field. The individual neuron is modelled using a Hodgkin-Huxley-type conductance model with parameters chosen such that the uncoupled neuron displays autonomous subthreshold oscillations of the membrane potential. We find that the ensemble generates a rich variety of oscillatory activities that are mainly controlled by two time scales: the natural period of oscillation at the single neuron level and the delay time of the global coupling. When the neuronal oscillations are synchronized, they can be either in-phase or out-of-phase. The phase-shifted activity is interpreted as the result of a phase-flip bifurcation, also occurring in a set of globally delay-coupled limit cycle oscillators. At the bifurcation point, there is a transition from in-phase to out-of-phase (or vice versa) synchronized oscillations, which is accompanied by an abrupt change in the common oscillation frequency. This phase-flip bifurcation was recently investigated in two mutually delay-coupled oscillators and can play a role in the mechanisms by which the neurons switch among different firing patterns. PMID:19620122
Synchronization-based computation through networks of coupled oscillators
Malagarriga, Daniel; García-Vellisca, Mariano A.; Villa, Alessandro E. P.; Buldú, Javier M.; García-Ojalvo, Jordi; Pons, Antonio J.
2015-01-01
The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates. PMID:26300765
Synchronization-based computation through networks of coupled oscillators.
Malagarriga, Daniel; García-Vellisca, Mariano A; Villa, Alessandro E P; Buldú, Javier M; García-Ojalvo, Jordi; Pons, Antonio J
2015-01-01
The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates. PMID:26300765
Coupled chemical oscillators and emergent system properties.
Epstein, Irving R
2014-09-25
We review recent work on a variety of systems, from the nanometre to the centimetre scale, including microemulsions, microfluidic droplet arrays, gels and flow reactors, in which chemical oscillators interact to generate novel spatiotemporal patterns and/or mechanical motion. PMID:24835430
Two-beam high-order harmonics from solids: Coupling mechanisms
Tarasevitch, A.; Wieczorek, J.; Kohn, R.; Bovensiepen, U.; Linde, D. von der
2010-11-15
The polarization of the two beam (driver-probe) high-order harmonic generation from solids is measured. The experiments, together with computer simulations, allow us to distinguish two different coupling mechanisms of the driver and the probe, resulting in different harmonic efficiencies and spectral slopes. We find that in the nonrelativistic regime the coupling is mostly due to the nonlinear plasma density modulation.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-03-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and technology, is illustrated through concrete examples of coupled biological cell models.
NASA Technical Reports Server (NTRS)
Holliday, Ezekiel S. (Inventor)
2014-01-01
Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.
Phase response curves elucidating the dynamics of coupled oscillators.
Granada, A; Hennig, R M; Ronacher, B; Kramer, A; Herzel, H
2009-01-01
Phase response curves (PRCs) are widely used in circadian clocks, neuroscience, and heart physiology. They quantify the response of an oscillator to pulse-like perturbations. Phase response curves provide valuable information on the properties of oscillators and their synchronization. This chapter discusses biological self-sustained oscillators (circadian clock, physiological rhythms, etc.) in the context of nonlinear dynamics theory. Coupled oscillators can synchronize with different frequency ratios, can generate toroidal dynamics (superposition of independent frequencies), and may lead to deterministic chaos. These nonlinear phenomena can be analyzed with the aid of a phase transition curve, which is intimately related to the phase response curve. For illustration purposes, this chapter discusses a model of circadian oscillations based on a delayed negative feedback. In a second part, the chapter provides a step-by-step recipe to measure phase response curves. It discusses specifications of this recipe for circadian rhythms, heart rhythms, neuronal spikes, central pattern generators, and insect communication. Finally, it stresses the predictive power of measured phase response curves. PRCs can be used to quantify the coupling strength of oscillations, to classify oscillator types, and to predict the complex dynamics of periodically driven oscillations. PMID:19216921
Delayed feedback control of synchronization in weakly coupled oscillator networks
NASA Astrophysics Data System (ADS)
Novičenko, Viktor
2015-08-01
We study control of synchronization in weakly coupled oscillator networks by using a phase-reduction approach. Starting from a general class of limit-cycle oscillators we derive a phase model, which shows that delayed feedback control changes effective coupling strengths and effective frequencies. We derive the analytical condition for critical control gain, where the phase dynamics of the oscillator becomes extremely sensitive to any perturbations. As a result the network can attain phase synchronization even if the natural interoscillatory couplings are small. In addition, we demonstrate that delayed feedback control can disrupt the coherent phase dynamic in synchronized networks. The validity of our results is illustrated on networks of diffusively coupled Stuart-Landau and FitzHugh-Nagumo models.
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.
NASA Astrophysics Data System (ADS)
Chartrand, Thomas; Goldman, Mark S.; Lewis, Timothy J.
2015-03-01
Although the inferior olive is known to contribute to the generation of timing and error signals for motor control, the specific role of its distinctive spatiotemporal activity patterns is still controversial. Olivary neurons display regular, sometimes synchronized oscillations of subthreshold membrane potential, driven in part by the highest density of electrical coupling of any brain region. We show that a reduced model of coupled phase oscillators is sufficient to reproduce and study experimental observations previously only demonstrated in more complex models. These include stable phase differences, variability of entrainment frequency, wave propagation, and cluster formation. Using the phase-response curve (PRC) of a conductance-based model of olivary neurons, we derive our phase model according to the theory of weakly-coupled oscillators. We retain the heterogeneity of intrinsic frequencies and heterogeneous, spatially constrained coupling as weak perturbations to the limit-cycle dynamics. Generalizing this model to an ensemble of coupled oscillator lattices with frequency and coupling disorder, we study the onset of entrainment and phase-locking as coupling is strengthened, including the scaling of cluster sizes with coupling strength near each phase transition.
Modeling of a bipedal robot using mutually coupled Rayleigh oscillators.
Filho, Armando C de Pina; Dutra, Max S; Raptopoulos, Luciano S C
2005-01-01
The objective of the work presented here was the modeling of a bipedal robot using a central pattern generator (CPG) formed by a set of mutually coupled Rayleigh oscillators. We analyzed a 2D model, with the three most important determinants of gait, that performs only motions parallel to the sagittal plane. Using oscillators with integer relation of frequency, we determined the transient motion and the stable limit cycles of the network formed by the three oscillators, showing the behavior of the knee angles and the hip angle. A comparison of the plotted graphs revealed that the system provided excellent results when compared to experimental analysis. Based on the results of the study, we come to the conclusion that the use of mutually coupled Rayleigh oscillators can represent an excellent method of signal generation, allowing their application for feedback control of a walking machine. PMID:15580522
Coupled domain wall oscillations in magnetic cylindrical nanowires
Murapaka, Chandrasekhar; Goolaup, S.; Purnama, I.; Lew, W. S.
2015-02-07
We report on transverse domain wall (DW) dynamics in two closely spaced cylindrical nanowires. The magnetostatically coupled DWs are shown to undergo an intrinsic oscillatory motion along the nanowire length in addition to their default rotational motion. In the absence of external forces, the amplitude of the DW oscillation is governed by the change in the frequency of the DW rotation. It is possible to sustain the DW oscillations by applying spin-polarized current to the nanowires to balance the repulsive magnetostatic coupling. The current density required to sustain the DW oscillation is found to be in the order of 10{sup 5 }A/cm{sup 2}. Morover, our analysis of the oscillation reveals that the DWs in cylindrical nanowires possess a finite mass.
GENERAL: Bursting Ca2+ Oscillations and Synchronization in Coupled Cells
NASA Astrophysics Data System (ADS)
Ji, Quan-Bao; Lu, Qi-Shao; Yang, Zhuo-Qin; Duan, Li-Xia
2008-11-01
A mathematical model proposed by Grubelnk et al. [Biophys. Chew,. 94 (2001) 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca2+ oscillations. Intracel-lular bursting calcium oscillations of point-point, point-cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca2+ oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point-cycle type.
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.
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.
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.
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.
Sharp versus smooth synchronization transition of locally coupled oscillators
NASA Astrophysics Data System (ADS)
Ciszak, M.; Montina, A.; Arecchi, F. T.
2008-07-01
We provide a general condition for the occurrence of a sudden transition to synchronization in an array of oscillators mutually coupled via the nearest neighbors. At the onset of synchronization a specific constraint must be fulfilled: precisely, the response time of a single system to signals from the adjacent sites must be smaller than the refractory period. We verify this criterion in some models for neuronal dynamics, namely, in excitable systems driven by noise as well as in chaotic oscillators.
Numerically induced bursting in a set of coupled neuronal oscillators
NASA Astrophysics Data System (ADS)
Medetov, Bekbolat; Weiß, R. Gregor; Zhanabaev, Zeinulla Zh.; Zaks, Michael A.
2015-03-01
We present our numerical observations on dynamics in the system of two linearly coupled FitzHugh-Nagumo oscillators close to the destabilization of the state of rest. Under the considered parameter values the system, if integrated sufficiently accurately, converges to small-scale periodic oscillations. However, minor numerical inaccuracies, which occur already at the default precision of the standard Runge-Kutta solver, lead to a breakup of periodicity and an onset of large-scale aperiodic bursting.
Vanag, Vladimir K; Smelov, Pavel S; Klinshov, Vladimir V
2016-02-21
The dynamic regimes in networks of four almost identical spike oscillators with pulsatile coupling via inhibitor are systematically studied. We used two models to describe individual oscillators: a phase-oscillator model and a model for the Belousov-Zhabotinsky reaction. A time delay τ between a spike in one oscillator and the spike-induced inhibitory perturbation of other oscillators is introduced. Diagrams of all rhythms found for three different types of connectivities (unidirectional on a ring, mutual on a ring, and all-to-all) are built in the plane C(inh)-τ, where C(inh) is the coupling strength. It is shown analytically and numerically that only four regular rhythms are stable for unidirectional coupling: walk (phase shift between spikes of neighbouring oscillators equals the quarter of the global period T), walk-reverse (the same as walk but consecutive spikes take place in the direction opposite to the direction of connectivity), anti-phase (any two neighbouring oscillators are anti-phase), and in-phase oscillations. In the case of mutual on the ring coupling, an additional in-phase-anti-phase mode emerges. For all-to-all coupling, two new asymmetrical patterns (two-cluster and three-cluster modes) have been found. More complex rhythms are observed at large C(inh), when some oscillators are suppressed completely or generate smaller number of spikes than others. PMID:26863079