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).
Markovian evolution of strongly coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Joshi, Chaitanya; Öhberg, Patrik; Cresser, James D.; Andersson, Erika
2014-12-01
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
Oscillation death and revival by coupling with damped harmonic oscillator
NASA Astrophysics Data System (ADS)
Varshney, Vaibhav; Saxena, Garima; Biswal, Bibhu; Prasad, Awadhesh
2017-09-01
Dynamics of nonlinear oscillators augmented with co- and counter-rotating linear damped harmonic oscillator is studied in detail. Depending upon the sense of rotation of augmenting system, the collective dynamics converges to either synchronized periodic behaviour or oscillation death. Multistability is observed when there is a transition from periodic state to oscillation death. In the periodic region, the system is found to be in mixed synchronization state, which is characterized by the newly defined "relative phase angle" between the different axes.
Heat transport along a chain of coupled quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
de Oliveira, Mário J.
2017-04-01
I study the heat transport properties of a chain of coupled quantum harmonic oscillators in contact at its ends with two heat reservoirs at distinct temperatures. My approach is based on the use of an evolution equation for the density operator which is a canonical quantization of the classical Fokker-Planck-Kramers equation. I set up the evolution equation for the covariances and obtain the stationary covariances at the stationary states from which I determine the thermal conductance in closed form when the interparticle interaction is small. The conductance is finite in the thermodynamic limit implying an infinite thermal conductivity.
Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.
Wei, Bo; Xiao, Feng; Dai, Ming-Zhe
2016-08-30
The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.
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.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
Leaci, Paola; Ortolan, Antonello
2007-12-15
We discuss limitations in precision measurements of a weak classical force coupled to quantum mechanical systems, the so-called standard quantum limit (SQL). Among the several contexts exploiting the measurement of classical signals, gravitational wave (GW) detection is of paramount importance. In this framework, we analyze the quantum limited sensitivity of a free test mass, a quantum mechanical harmonic oscillator, two harmonic oscillators with equal masses and different resonance frequencies, and finally two mechanical oscillators with different masses and resonating at the same frequency. The sensitivity analysis of the latter two cases illustrates the potentialities of back-action reduction and classical impedance matching schemes, respectively. By examining coupled quantum oscillators as detectors of classical signals, we found a viable path to approach the SQL for planned or operating GW detectors, such as DUAL and AURIGA.
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
2004-09-09
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.
Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Guimarães, Pedro H.; Landi, Gabriel T.; de Oliveira, Mário J.
2017-04-01
We have determined the thermal conductance of a system consisting of a two-level atom coupled to two quantum harmonic oscillators in contact with heat reservoirs at distinct temperatures. The calculation of the heat flux as well as the atomic population and the rate of entropy production are obtained by the use of a quantum Fokker-Planck-Kramers equation and by a Lindblad master equation. The calculations are performed for small values of the coupling constant. The results coming from both approaches show that the conductance is proportional to the coupling constant squared and that, at high temperatures, it is proportional to the inverse of temperature.
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.
Hwang, Myung-Joong; Choi, Mahn-Soo
2010-08-15
The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.
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.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
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.
Entanglement in a continuously measured two-level system coupled to a harmonic oscillator
Hernandez-Concepcion, E.; Alonso, D.; Brouard, S.
2009-05-15
The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the 'relative entropy of entanglement' (REE) in the one-energy-excitation manifold of the reduced TLS+HO system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.
Rodriguez-Gallardo, M.; Arias, J. M.; Gomez-Camacho, J.; Moro, A. M.; Johnson, R. C.; Tostevin, J. A.; Thompson, I. J.
2008-06-15
The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, {sup 6}He+{sup 12}C at 229.8 MeV, {sup 6}He+{sup 64}Zn at 10 and 13.6 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV, induced by the Borromean nucleus {sup 6}He. Both the Coulomb and nuclear interactions with a target are taken into account.
Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.; Perez-Bernal, F.
2009-11-15
A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+{sup 58}Ni at 80 MeV, {sup 6}Li+{sup 40}Ca at 156 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.
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. © 2011 American Institute of Physics
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.}
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.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Galilean covariant harmonic oscillator
NASA Technical Reports Server (NTRS)
Horzela, Andrzej; Kapuscik, Edward
1993-01-01
A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.
NASA Astrophysics Data System (ADS)
Xu, Shi-Min; Xu, Xing-Lei; Li, Hong-Qi
2008-06-01
The intermediate representation (namely intermediate coordinate-momentum representation) | x> λ, ν are introduced and employed to research the expression of the operator tauhat{p}+σhat{x} in intermediate representation | x> λ, ν . The systematic Hamilton operator hat{H} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ, ν, τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator | x> λ, ν λ, ν < x|, and the Radon transformation of Wigner function is just a margin distribution.
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.
Charge transfer and coherence dynamics of a tunnelling system coupled to an harmonic oscillator.
Paganelli, S; Ciuchi, S
2008-06-11
We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be considered as an extended bath, it produces decoherence because of the large number of states involved in the dynamics. In the case in which the oscillator is initially displaced, a coherent dynamics of charge entangled with oscillator modes takes place. Coherency is, however, degraded as far as the oscillator mass increases, producing an increasingly large recoherence time. Calculations are carried on by exact diagonalization and compared with two semiclassical approximations. The role of the quantum effects are highlighted in the long time dynamics, where semiclassical approaches give rise to a dissipative behaviour. Moreover, we find that the oscillator dynamics has to be taken into account, even in a semiclassical approximation, in order to reproduce a thermally activated enhancement of the transition probability.
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.
Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I
2001-06-01
New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.
NASA Astrophysics Data System (ADS)
Vanhimbeeck, Marc
In this thesis a technique is developed to determine the low-energy eigensolutions of an unspecified few-level system which is coupled both linearly and quadratically to a finite collection of harmonic oscillators. The method is based on the second-order symmetrized Trotter-Suzuki approximation for e^{lambda} ^{H} with H standing for the Hamiltonian of the quantum mechanical system. Taking lambda = -beta (real), we use e ^{beta}^{H} as a projection operator which sorts out the low-energy eigenstates from the decomposition of an initially randomly constructed system-state. Once the eigenstates are found, a second approximation on the time propagator e ^{-itH} is applied in order to determine some relevant time-correlation functions for the systems under study. Next to a general formulation of the theory we also provide a study of some example systems. The coupled two-level system is shown to account phenomenologically for the anomalous isotope shift which was observed in the Raman spectrum of the tunneling Li^+ defect in KCl. Furthermore, we examine the low-energy eigenvalues and Ham-reduction factors for some of the cubic Jahn-Teller (JT) systems. The triplet systems T otimes tau _2 and T otimes epsilon are studied with a linear JT-interaction but for the E otimes epsilon doublet system a quadratic warping is included in the description. The results are in good agreement with the literature and confirm the applicability of the method.
Covariant harmonic oscillators: 1973 revisited
NASA Technical Reports Server (NTRS)
Noz, M. E.
1993-01-01
Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.
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…
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…
Harmonic oscillator and nuclear pseudospin
Lisboa, Ronai; Malheiro, Manuel; Castro, Antonio S. de; Alberto, Pedro; Fiolhais, Manuel
2004-12-02
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either {sigma} = S + V or {delta} = V - S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case {sigma} = 0, for which pseudospin symmetry is exact.
The harmonic oscillator behind all aberrations
Wolf, Kurt Bernardo
2010-12-23
The group-theoretical structure of the harmonic oscillator appears in many guises. Originally developed by Marcos Moshinsky among several others for applications in nuclear physics, we point out here that the harmonic oscillator structure appears in aberrations of geometric optics, particularly in their classification by rank, symplectic spin and weight. And further, the finite harmonic oscillator appears again in the nonlinear transformations of finite Hamiltonian systems, when applied to the parallel processing of signals.
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.
Coherent states for the nonlinear harmonic oscillator
Ghosh, Subir
2012-06-15
Wave packets for the quantum nonlinear oscillator are considered in the generalized coherent state framework. To first order in the nonlinearity parameter the coherent state behaves very similar to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features (such as the squeezed state nature) of the coherent state have been discussed.
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.
Instanton solutions on the polymer harmonic oscillator
NASA Astrophysics Data System (ADS)
Austrich-Olivares, Joan A.; Garcia-Chung, Angel; Vergara, J. David
2017-06-01
We have computed, using instanton methods, the first allowed energy band for the polymer harmonic oscillator. The eigenvalues within the band are labelled by a discrete parameter λ which results from the non-separability of the polymer Hilbert space. It is shown throughout the article the role played by λ in the full quantization of the polymer harmonic oscillator. The result is consistent with the band structure of the standard quantum pendulum but with pure point spectrum. Consequently, an effective infinite degeneracy emerges in the formal limit μ/l0 \\to 0 where l 0 is the characteristic length of the vacuum eigenfunction of a quantum harmonic oscillator.
Relation of squeezed states between damped harmonic and simple harmonic oscillators
NASA Technical Reports Server (NTRS)
Um, Chung-In; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.
Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process
NASA Astrophysics Data System (ADS)
Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki
2017-03-01
We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
Condition for minimal harmonic oscillator action
NASA Astrophysics Data System (ADS)
Moriconi, M.
2017-08-01
We provide an elementary proof that the action for the physical trajectory of the one-dimensional harmonic oscillator is guaranteed to be a minimum if and only if τ<π/ω , where τ is the elapsed time and ω is the oscillator's natural frequency.
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…
Background independent duals of the harmonic oscillator.
Husain, Viqar
2006-06-09
We show that a class of topological field theories are quantum duals of the harmonic oscillator. This is demonstrated by establishing a correspondence between the creation and annihilation operators and nonlocal gauge invariant observables of the topological field theory. The example is used to discuss some issues concerning background independence and the relation of vacuum energy to the problem of time in quantum gravity.
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.
Finite quantum kinematics of the harmonic oscillator
Shiri-Garakani, Mohsen; Finkelstein, David Ritz
2006-03-15
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
Caligiuri, Luigi Maxmilian
2015-01-01
The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.
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.
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.
Enhancing energy harvesting by coupling monostable oscillators
NASA Astrophysics Data System (ADS)
Peña Rosselló, Julián I.; Wio, Horacio S.; Deza, Roberto R.; Hänggi, Peter
2017-02-01
The performance of a ring of linearly coupled, monostable nonlinear oscillators is optimized towards its goal of acting as energy harvester - through piezoelectric transduction - of mesoscopic fluctuations, which are modeled as Ornstein-Uhlenbeck noises. For a single oscillator, the maximum output voltage and overall efficiency are attained for a soft piecewise-linear potential (providing a weak attractive constant force) but they are still fairly large for a harmonic potential. When several harmonic springs are linearly and bidirectionally coupled to form a ring, it is found that counter-phase coupling can largely improve the performance while in-phase coupling worsens it. Moreover, it turns out that few (two or three) coupled units perform better than more.
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.
Finite quantum theory of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shiri-Garakani, Mohsen
We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N low-lying states with nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/-l. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/-l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
Avoiding dissipation in a system of three quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta
2013-03-01
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.
Increase of Boltzmann entropy in a quantum forced harmonic oscillator
NASA Astrophysics Data System (ADS)
Campisi, Michele
2008-11-01
Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.
Increase of Boltzmann entropy in a quantum forced harmonic oscillator.
Campisi, Michele
2008-11-01
Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.
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
NASA Astrophysics Data System (ADS)
Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.
2016-04-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Finally, many-body coupled-cluster calculations of nuclei up to ^{132}Sn converge fast for the ground-state energies and radii in feasible model spaces.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; ...
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
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-leading order. Finally, many-body coupled-cluster calculations of nuclei up to ^{132}Sn converge fast for the ground-state energies and radii in feasible model spaces.
NASA Astrophysics Data System (ADS)
Tay, Buang Ann
The eigenvalue problem of Kossakowski-Linblad's kinetic equation associated with the reduced density matrix of a harmonic oscillator interacting with a thermal bath in equilibrium is solved. The solution gives rise to a complete orthogonal eigenbasis endowed with Hilbert space structure that has a weighted norm. We find that the eigenfunctions at finite temperature can be obtained from the eigenfunction at zero temperature through a hyperbolic rotation on the position variables. This transformation enables the extension of the simple harmonic oscillator density matrix to that of a finite temperature. We further investigate the decay of these extended states under our dissipative kinetic equation. Furthermore, the Hilbert space structure enables the proof of a H -theorem in this system. We apply the eigenbasis expansion of an initial state to analyze decoherence as well as coherence processes. We find that coherence process occurs at a longer time scale compared to decoherence process. The time scales of both processes are estimated with the eigenbasis expansion. In the same way we analyze the evolution of the coherent state. We show that in addition to the ordinary decay time, we found another time scale which is defined by the time when the motion of the peak of the coherent state become comparative to the width of the coherent state. In contrast to the ordinary decay time this new relaxation time depends on the initial value of the momentum of the oscillator. We also find that our eigenbasis is applicable to a class of non-linear interactions, with a slight extension of the form of transport coefficients due to the non-linear interactions.
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.
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
2012-01-02
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.
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 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…
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…
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
2017-01-01
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.
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.
Self Phase-Locked Sub-Harmonic Optical Parametric Oscillators
NASA Astrophysics Data System (ADS)
Zondy, J.-J.; Laclau, V.; Bancel, A.; Douillet, A.; Tallet, A.; Ressayre, E.; Le Berre, M.
2002-04-01
We analyse a novel class of non-degenerate, doubly (DRO) or triply (TRO) resonant optical parametric oscillators (OPOs) producing signal and idler waves that are sub-harmonics of the pump frequency (3ω → 2ω, ω), and subject to an additional resonant coupling via the second-harmonic generation (SHG) of the idler wave (ω + ω → 2ω). At exact 3 ÷ 2 ÷ 1 non-degeneracy, self phase-locking among the three waves is theoretically predicted, freezing the well-known quantum phase diffusion noise in conventional oscillators. Three possible phase states corresponding to the same intensity state emerge. When slightly detuned from the 3 ÷ 2 ÷ 1 point, and under some specific conditions, the OPO:SHG cascading is expected to lead to a passively mode-locked cw-OPO providing two frequency combs peaked around the signal and idler frequencies. We report our attempt to observe both types of self-phase-locked (SPL) operation in a single-grating (OPO-only section) periodically poled lithium niobate (PPLN) oscillator, under the very weak self injection-locking by non-phase matched spontaneous idler SHG.
Coupled oscillators on evolving networks
NASA Astrophysics Data System (ADS)
Singh, R. K.; Bagarti, Trilochan
2016-12-01
In this work we study coupled oscillators on evolving networks. We find that the steady state behavior of the system is governed by the relative values of the spread in natural frequencies and the global coupling strength. For coupling strong in comparison to the spread in frequencies, the system of oscillators synchronize and when coupling strength and spread in frequencies are large, a phenomenon similar to amplitude death is observed. The network evolution provides a mechanism to build inter-oscillator connections and once a dynamic equilibrium is achieved, oscillators evolve according to their local interactions. We also find that the steady state properties change by the presence of additional time scales. We demonstrate these results based on numerical calculations studying dynamical evolution of limit-cycle and van der Pol oscillators.
Isar, A.; Sandulescu, A. ); Scheid, W. )
1990-05-01
In the frame of the Lindblad theory of open quantum systems, the spherical harmonic oscillator with opening operators linear in the coordinates and the momenta of the considered system is analyzed. Explicit expressions for the damping of the energy, angular momentum and its projection, including the coupling of the harmonic oscillator due to the environment, are obtained.
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
Heat and work fluctuations for a harmonic oscillator.
Sabhapandit, Sanjib
2012-02-01
The formalism of Kundu et al. [J. Stat. Mech. P03007 (2011)], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-τ form of the moment generating function
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
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016-09-15
The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
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.
Driven damped harmonic oscillator resonance with an Arduino
NASA Astrophysics Data System (ADS)
Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.
2017-07-01
In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.
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.
Harmonic coupling of steady-state visual evoked potentials.
Krusienski, Dean J; Allison, Brendan Z
2008-01-01
Steady-state visual evoked potentials (SSVEPs) are oscillating components of the electroencephalogram (EEG) that are detected over the occipital areas, having frequencies corresponding to visual stimulus frequencies. SSVEPs have been demonstrated to be reliable control signals for operating a brain-computer interface (BCI). This study uses offline analyses to investigate the characteristics of SSVEP harmonic amplitude and phase coupling and the impact of using this information to construct a matched filter for continuously tracking the signal.
Experimental demonstration of a technique for generation of arbitrary harmonic oscillator states.
NASA Astrophysics Data System (ADS)
Ben-Kish, A.; Demarco, B.; Rowe, M.; Meyer, V.; Britton, J.; Itano, W. M.; Jelenković, B. M.; Langer, C.; Leibfried, D.; Rosenband, T.; Wineland, D. J.
2002-05-01
Synthesizing arbitrary quantum states is at the heart of such diverse fields as quantum computation and reaction control in chemistry. For harmonic oscillator states, particular interactions (in general, non-linear) can be used to generate special states such as squeezed states. However, it is usually intractable to realize the interactions required to create arbitrary states. Law and Eberly [1] have devised a technique for arbitrary harmonic oscillator state generation that couples the oscillator to a two-level atomic or spin system and applies a sequence of operations that use simple interactions. We demonstrate the general features of this technique on the harmonic motion of a single trapped ^9Be^+ ion and extend it to the generation of arbitrary spin-oscillator states [2]. [1] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996). [2] B. Kneer and C. K. Law, Phys. Rev. A 57, 2096 (1998).
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…
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…
Harmonic phase detector for phase locking of cryogenic terahertz oscillators
NASA Astrophysics Data System (ADS)
Kalashnikov, Konstantin V.; Khudchenko, Andrey V.; Koshelets, Valery P.
2013-09-01
We present a simple and effective way to phase lock terahertz cryogenic oscillators. Extreme nonlinearity of a superconductor-insulator-superconductor tunnel junction allows its implementation as a cryogenic high-harmonic phase detector (HPD), which is used both for mixing a terahertz oscillator signal with a microwave reference and for generating a phase error feedback signal that is directly applied to the oscillator for its phase locking. An integration of the HPD with a cryogenic flux-flow oscillator results in synchronization bandwidth as wide as 70 MHz (significantly exceeding conventional room-temperature system bandwidth), providing phase locking of 84% emitted power for 15 MHz oscillator linewidth.
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.
Digitization of the harmonic oscillator in extended relativity
NASA Astrophysics Data System (ADS)
Friedman, Yaakov
2013-06-01
Extended relativistic dynamics (ERD) admits only solutions that have speed bounded by the speed of light c and acceleration bounded by an assumed universal maximal acceleration am. Here we explore the harmonic oscillator under ERD. For oscillators with small natural frequency ω, we recover the classical solutions, while for large ω, the solutions differ significantly from the classical one. The solutions for large ω are a ‘digitization’ of the standard signals of the classical harmonic oscillator. The spectrum of these signals coincides with the energy spectrum of the quantum harmonic oscillator. While for small ω, the thermal radiation is a wave type, for large ω, it becomes pulses of radiation. This provides a possible explanation for the difference in the blackbody radiation for small and large ω and is another indication of the validity of ERD.
Coupled harmonic systems as quantum buses in thermal environments
NASA Astrophysics Data System (ADS)
Nicacio, F.; Semião, F. L.
2016-09-01
In this work, we perform a careful study of a special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to establish simple effective Hamiltonians and Liouvillians allowing an accurate description of the dynamics of the external oscillators regardless of the topology of the network. By simple, we mean an effective description using just a few degrees of freedom. With the methodology developed here, we are able to treat general topologies and, under certain structural conditions, to also include the interaction with external environments. In order to illustrate the predictability of the simplified dynamics, we present a comparative study with the predictions of the numerically obtained exact description in the context of propagation of energy through the network.
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…
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…
Synchronizing quantum harmonic oscillators through two-level systems
NASA Astrophysics Data System (ADS)
Militello, Benedetto; Nakazato, Hiromichi; Napoli, Anna
2017-08-01
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of N oscillators and M (
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
NASA Astrophysics Data System (ADS)
Blaizot, J. P.; Schulz, H.
1982-03-01
We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schrödinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory.
Searching for robust quantum memories in many coupled oscillators
NASA Astrophysics Data System (ADS)
Bosco de Magalhães, A. R.
2011-11-01
The relation between microscopic symmetries in the system-environment interaction and the emergence of robust states is studied for many linearly coupled harmonic oscillators. Different types of symmetry, which are introduced into the model as terms in the coupling constants between each system's oscillator and a common reservoir, lead to distinct robust modes. Since these modes are partially or completely immune to the symmetric part of the environmental noise, they are good candidates for building quantum memories. A comparison of the model investigated here, with bilinear system-reservoir coupling, and a model where such coupling presents an exponential dependence on the variables of interest is performed.
Generic behavior of coupled oscillators
NASA Astrophysics Data System (ADS)
Hogg, T.; Huberman, B. A.
1984-01-01
There exist a number of interesting physical problems, such as the ac-driven, dc SQUID (superconducting quantum interference device) or convection in conducting fluids, which can be described by the dynamics of driven coupled oscillators. In order to study their behavior as a function of coupling strength and nonlinearity, we have considered the dynamics of two coupled maps belonging to the same universality class as the oscillators. We have analytically determined some of the parameter values for which they exhibit locked states as well as bifurcations into aperiodic behavior. Furthermore, we found a set of codimension-two bifurcations into quasiperiodic orbits near which the rotation number becomes vanishingly small. These bifurcations are characterized by the existence of periodic regimes interrupted by episodes of phase slippage. Finally, we show the effect of thermal fluctuations on the bifurcation diagram by computing the Lyapunov exponent in the presence of external and parametric noise.
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.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
2009-08-14
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
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.
Coupled oscillators and Feynman's three papers
NASA Astrophysics Data System (ADS)
Kim, Y. S.
2007-05-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.
Quantum kicked harmonic oscillator in contact with a heat bath
NASA Astrophysics Data System (ADS)
Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.
2017-02-01
We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law.
Measuring nonlinear functionals of quantum harmonic oscillator states.
Pregnell, K L
2006-02-17
Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and nonlinear functionals of an arbitrary oscillator state. This leads to many applications including purity tests, eigenvalue estimation, entropy, and distance measures--all without the need for nonlinear interactions or complete state reconstruction. Remarkably, experimental realization of the proposed scheme is already within the reach of current technology with linear optics.
Observations of Harmonic Oscillations and ELM Magnetic Precursors in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Fredrickson, E.; Bell, R.; Tritz, K.; Maingi, R.; Takahashi, H.
2010-11-01
Recent experiments in the National Spherical Torus Experiment (NSTX) demonstrated the progressive suppression of edge localized modes (ELMs) with increasing lithium deposition. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n harmonics more frequent. Signatures of these harmonic oscillations with a significant edge component were observed in both the high-n Mirnov magnetic and soft X-ray diagnostics of NSTX. Two distinct sets of harmonic oscillations can be observed during some ELM-free periods. The harmonic oscillations are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. NSTX magnetic diagnostics also observe distinctive signatures of ELMs. Transient n = 1 and n = 2 mode bursts and occasional higher n modes with frequency in the 30 to 90 kHz range occurred simultaneous with the increase in fast Da signal. These bursts of n = 1 and n = 2 modes resemble a model simulation of ELMs by T. Evans in which a bifurcation of magnetic topology is driven by nonlinear feedback amplification of thermoelectric currents from linear peeling-ballooning modes.
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.)
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
NASA Astrophysics Data System (ADS)
Nogueira, Pedro H. F.; de Castro, Antonio S.
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions.
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.
Nonequilibrium work distribution of a quantum harmonic oscillator.
Deffner, Sebastian; Lutz, Eric
2008-02-01
We calculate analytically the work distribution of a quantum harmonic oscillator with arbitrary time-dependent angular frequency. We provide detailed expressions for the work probability density for adiabatic and nonadiabatic processes, in the limits of low and high temperature. We further verify the validity of the quantum Jarzynski equality.
Macroscopic detection of deformed QM by the harmonic oscillator
NASA Astrophysics Data System (ADS)
Maziashvili, Michael
2017-08-01
Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations (to the first order in deformation parameter as it has been pointed out in Bawaj et al. (2015)). For this reason, we take an alternate way for estimating the effect and discuss its possible observational manifestations in macrophysics.
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
ERIC Educational Resources Information Center
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
ERIC Educational Resources Information Center
Flores-Hidalgo, G.; Barone, F. A.
2011-01-01
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
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…
Renormalized reaction and relaxation rates for harmonic oscillator model
NASA Astrophysics Data System (ADS)
Gorbachev, Yuriy E.
2017-07-01
The thermal dissociation process is considered within the method of solving the kinetic equations for spatially inhomogeneous reactive gas mixtures developed in the previous papers. For harmonic oscillator model explicit expressions for reaction and relaxation rates in the renormalized form are derived.
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
2010-05-01
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
Equity prices as a simple harmonic oscillator with noise
NASA Astrophysics Data System (ADS)
Ataullah, Ali; Tippett, Mark
2007-08-01
The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.
Harmonic Emission from High Power Gyrotron Oscillators.
1984-05-01
rd ( 0. () 2 4 39 . * .. . . a.. . . As discussed in Section 2.1, for the Gaussian ki k1l Leff/2. This relationship with the near cutoff and near...linear changes in I he IF fre- quency by equat ion (3.1). The tlilne scale onl the sCope was cal ibra 1 ed by changing 93 RD -A145 621 HARMONIC EMISSION...cial mi. lin’neaatra pro~ rd helpful in findin~g the comrwq RI: bmpfel "lr kriw" Ife .1.1. eftoai -Olvtoo %*a- fairlh *lattir In ’feur (&*#ft. *vrfil
Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator
NASA Astrophysics Data System (ADS)
Rosu, H. C.; Cornejo-Pérez, O.; Chen, P.
2012-12-01
Interesting nonsingular parametric oscillators which are Darboux-related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) “oscillator” for which the obtained Darboux partners show transient underdamped features.
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
Geometric phase and nonadiabatic effects in an electronic harmonic oscillator.
Pechal, M; Berger, S; Abdumalikov, A A; Fink, J M; Mlynek, J A; Steffen, L; Wallraff, A; Filipp, S
2012-04-27
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
Sano
2000-02-01
Equilibrium and nonequilibrium properties of a chain of colliding harmonic oscillators (ding-dong model) are investigated. Our chain is modeled as harmonically bounded particles that can only interact with neighboring particles by hard-core interaction. Between the collisions, particles are just independent harmonic oscillators. We are especially interested in the stationary nonequilibrium state of the ding-dong model coupled with two stochastic heat reservoirs (not thermostated) at the ends, whose temperature is different. We check the Gallavotti-Cohen fluctuation theorem [G. Gallavoti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)] and also the Evans-Searles identity [D. Evans and D. Searles, Phys. Rev. E. 50, 1994 (1994)] numerically. It is verified that the former theorem is satisfied for this system, although the system is not a thermostated system.
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
NASA Astrophysics Data System (ADS)
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.
Pisot q-coherent states quantization of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Gazeau, J. P.; del Olmo, M. A.
2013-03-01
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.
Quantum harmonic oscillator: an elementary derivation of the energy spectrum
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2017-03-01
An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.
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.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis.
Kienzler, D; Lo, H-Y; Negnevitsky, V; Flühmann, C; Marinelli, M; Home, J P
2017-07-21
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the sqrt[n] scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n=6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis
NASA Astrophysics Data System (ADS)
Kienzler, D.; Lo, H.-Y.; Negnevitsky, V.; Flühmann, C.; Marinelli, M.; Home, J. P.
2017-07-01
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the √{n } scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n =6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator.
Horowitz, Jordan M
2012-03-01
I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.
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.
Dynamical properties of the delta-kicked harmonic oscillator.
Kells, G A; Twamley, J; Heffernan, D M
2004-01-01
We propose an efficient procedure for numerically evolving the quantum dynamics of delta-kicked harmonic oscillator. The method allows for longer and more accurate simulations of the system as well as a simple procedure for calculating the system's Floquet eigenstates and quasienergies. The method is used to examine the dynamical behavior of the system in cases where the ratio of the kicking frequency to the system's natural frequency is both rational and irrational.
Energy-dependent harmonic oscillator in noncommutative space
NASA Astrophysics Data System (ADS)
Benchikha, A.; Merad, M.; Birkandan, T.
2017-06-01
In noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is studied by solving the Schrödinger equation in polar coordinates. The presence of the noncommutativity in space coordinates and the dependence on energy for the potential yield energy-dependent mass and potential. The correction of normalization condition is calculated and the parameter-dependences of the results are studied graphically.
Coherent and squeezed states for the 3D harmonic oscillator
NASA Astrophysics Data System (ADS)
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
2017-01-01
A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.
An analogue of the Berry phase for simple harmonic oscillators
NASA Astrophysics Data System (ADS)
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Generalized relativistic harmonic oscillator in minimal length quantum mechanics
NASA Astrophysics Data System (ADS)
Castro, L. B.; E Obispo, A.
2017-07-01
We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature are obtained as particular cases.
Alpha clustering near nuclear surface and harmonic-oscillator excitations
NASA Astrophysics Data System (ADS)
Horiuchi, W.; Suzuki, Y.
2017-06-01
We quantify how it is difficult to describe an alpha(α)-cluster state with single-particle harmonic-oscillator (HO) bases in the low-lying16O states by counting the number of HO quanta of12 C+n+n+p+p five-body wave functions. We also discuss how many HO quanta are needed for describing a localized α cluster near the nuclear surface towards understanding of the shell and cluster coexistence in heavier nuclei.
Collision-induced squeezing in a harmonic oscillator
NASA Technical Reports Server (NTRS)
Lee, Hai-Woong
1993-01-01
The concept of squeezing has so far been applied mainly to light, as is evidenced by the number of research works on the subject of squeezed light. Since, in quantum mechanics, both light and the simple harmonic oscillator are described within the same mathematical framework, there is of course no difficulty in applying the concept to the simple harmonic oscillator as well. In fact, the theoretical development of squeezed states and squeezed light owes much to the physical insights that one obtains as the analogy between light and the harmonic oscillator is exploited. The example presented shows clearly that two states with different phases in general have different degrees of squeezing, even if they have the same state distribution. This means that, even if one considers collision processes that produce the same state distribution, the degree of squeezing obtained during and after the collisions can be quite different, depending on how the phases phi(sub n) of the probability amplitudes develop in time as the collisions proceed. It is therefore evident that, for a detailed study of collision-induced squeezing, further study on the time development of the phases in collisions and its relation to collision parameters such as potential energy surfaces and collision energy is needed.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
Coupled oscillators with parity-time symmetry
NASA Astrophysics Data System (ADS)
Tsoy, Eduard N.
2017-02-01
Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed.
Emergence of a negative resistance in noisy coupled linear oscillators
NASA Astrophysics Data System (ADS)
Quiroz-Juárez, M. A.; Aragón, J. L.; León-Montiel, R. de J.; Vázquez-Medina, R.; Domínguez-Juárez, J. L.; Quintero-Torres, R.
2016-12-01
We report on the experimental observation of an emerging negative resistance in a system of coupled linear electronic RLC harmonic oscillators under the influence of multiplicative noise with long correlation time. When two oscillators are coupled by a noisy inductor, an analysis in the Fourier space of the electrical variables unveils the presence of an effective negative resistance, which acts as an energy transport facilitator. This might constitute a simple explanation of the now fashionable problem of energy transport assisted by noise in classical systems. The experimental setup is based on the working principle of an analog computer and by itself constitutes a versatile platform for studying energy transport in noisy systems by means of coupled electrical oscillator systems.
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.
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
NASA Astrophysics Data System (ADS)
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
NASA Astrophysics Data System (ADS)
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
Emergence of amplitude and oscillation death in identical coupled oscillators.
Zou, Wei; Senthilkumar, D V; Duan, Jinqiao; Kurths, Jürgen
2014-09-01
We deduce rigorous conditions for the onset of amplitude death (AD) and oscillation death (OD) in a system of identical coupled paradigmatic Stuart-Landau oscillators. A nonscalar coupling and high frequency are beneficial for the onset of AD. In strong contrast, scalar diffusive coupling and low intrinsic frequency are in favor of the emergence of OD. Our finding contributes to clearly distinguish intrinsic geneses for AD and OD, and further substantially corroborates that AD and OD are indeed two dynamically distinct oscillation quenching phenomena due to distinctly different mechanisms.
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
Capture into resonance of coupled Duffing oscillators.
Kovaleva, Agnessa
2015-08-01
In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated.
Detecting the harmonics of oscillations with time-variable frequencies
NASA Astrophysics Data System (ADS)
Sheppard, L. W.; Stefanovska, A.; McClintock, P. V. E.
2011-01-01
A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.
Diverse routes to oscillation death in a coupled oscillator system
Suárez-Vargas, José J.; González, Jorge A.; Stefanovska, Aneta; McClintock, Peter V. E.
2010-01-01
We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory. PMID:20823952
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.
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
2015-12-01
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.
Oscillator state reconstruction via tunable qubit coupling in Markovian environments
Tufarelli, Tommaso; Bose, Sougato; Kim, M. S.
2011-06-15
We show that a parametrically coupled qubit can be used to fully reconstruct the quantum state of a harmonic oscillator even when both systems are subject to decoherence. By controlling the coupling strength of the qubit over time, the characteristic function of the oscillator at any phase-space point can be directly measured by combining the expectation values of two Pauli operators. The effect of decoherence can be filtered out from the measured data, provided a sufficient number of experimental runs are performed. In situations where full state reconstruction is not practical or not necessary, the method can still be used to estimate low-order moments of the mechanical quadratures. We also show that in the same framework it is possible to prepare superposition states of the oscillator. The model is very general but particularly appropriate for nanomechanical systems.
Complex mode dynamics of coupled wave oscillators
NASA Astrophysics Data System (ADS)
Alexander, T. J.; Yan, D.; Kevrekidis, P. G.
2013-12-01
We explore how nonlinear coherent waves localized in a few wells of a periodic potential can act analogously to a chain of coupled oscillators. We identify the small-amplitude oscillation modes of these “coupled wave oscillators” and find that they can be extended into the large amplitude regime, where some “ring” for long times. We also reveal the appearance of complex behavior such as the breakdown of Josephson-like oscillations, the destabilization of fundamental oscillation modes, and the emergence of chaotic oscillations for large amplitude excitations. We show that the dynamics may be accurately described by a discrete model with nearest-neighbor coupling, in which the lattice oscillators bear an effective mass.
Generalized Energy Equipartition in Harmonic Oscillators Driven by Active Baths
NASA Astrophysics Data System (ADS)
Maggi, Claudio; Paoluzzi, Matteo; Pellicciotta, Nicola; Lepore, Alessia; Angelani, Luca; Di Leonardo, Roberto
2014-12-01
We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.
Thermal conduction in a chain of colliding harmonic oscillators revisited.
Sano, M M; Kitahara, K
2001-11-01
Thermal conduction in a chain of colliding harmonic oscillators, sometimes called the ding-dong model, is investigated. We first argue that this system is equivalent to the Dawson plasma sheet model. Next we show the Lyapunov analysis for this system to characterize its dynamical property. Finally, we reconsider the numerical study of thermal conduction for this system using the Green-Kubo relation and the direct simulation of Fourier law. Both show that thermal conduction is normal in that kappa(N,T) approximately equals N(0), at least, at low temperature in a large system.
The effect of singular potentials on the harmonic oscillator
Filgueiras, C.; Silva, E.O.; Oliveira, W.; Moraes, F.
2010-11-15
We address the problem of a quantum particle moving under interactions presenting singularities. The self-adjoint extension approach is used to guarantee that the Hamiltonian is self-adjoint and to fix the choice of boundary conditions. We specifically look at the harmonic oscillator added of either a {delta}-function potential or a Coulomb potential (which is singular at the origin). The results are applied to Landau levels in the presence of a topological defect, the Calogero model and to the quantum motion on the noncommutative plane.
Analysis of transonic flow about harmonically oscillating airfoils and wings
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.
1980-01-01
A finite difference method for analyzing the unsteady transonic flow about harmonically oscillating wings is discussed. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting partial differential equations for small disturbances. Initial solutions were obtained using relaxation procedures, but the solution range proved to be limited in terms of Mach number and reduced frequency. Recent two-dimensional results are presented which have been obtained with direct solution procedures in which the difference equations are solved 'all at once' and these provide reasonable correlation for practical values of Mach number and reduced frequency.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
NASA Astrophysics Data System (ADS)
Sheehan, D. P.; Wright, J. H.
2006-10-01
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
Sheehan, D. P.; Wright, J. H.
2006-10-16
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Elementary derivation of the quantum propagator for the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Harmonic response of a class of finite extensibility nonlinear oscillators
NASA Astrophysics Data System (ADS)
Febbo, M.
2011-06-01
Finite extensibility oscillators are widely used to simulate those systems that cannot be extended to infinity. For example, they are used when modelling the bonds between molecules in a polymer or DNA molecule or when simulating filaments of non-Newtonian liquids. In this paper, the dynamic behavior of a harmonically driven finite extensibility oscillator is presented and studied. To this end, the harmonic balance method is applied to determine the amplitude-frequency and amplitude-phase equations. The distinguishable feature in this case is the bending of the amplitude-frequency curve to the frequency axis, making it asymptotically approach the limit of maximum elongation of the oscillator, which physically represents the impossibility of the system reaching this limit. Also, the stability condition that defines stable and unstable steady-state solutions is derived. The study of the effect of the system parameters on the response reveals that a decreasing value of the damping coefficient or an increasing value of the excitation amplitude leads to the appearance of a multi-valued response and to the existence of a jump phenomenon. In this sense, the critical amplitude of the excitation, which means here a certain value of external excitation that results in the occurrence of jump phenomena, is also derived. Numerical experiments to observe the effects of system parameters on the frequency-amplitude response are performed and compared with analytical calculations. At a low value of the damping coefficient or at a high value of excitation amplitude, the agreement is poor for low frequencies but good for high frequencies. It is demonstrated that the disagreement is caused by the neglect of higher-order harmonics in the analytical formulation. These higher-order harmonics, which appear as distinguishable peaks at certain values in the frequency response curves, are possible to calculate considering not the linearized frequency of the oscillator but its actual
Kraus representation of a damped harmonic oscillator and its application
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-10-01
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.
A method of solving simple harmonic oscillator Schroedinger equation
NASA Technical Reports Server (NTRS)
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Paal, Eugen; Virkepu, Jueri
2009-05-15
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
Reentrant transition in coupled noisy oscillators
NASA Astrophysics Data System (ADS)
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.
On quantum harmonic oscillator being subjected to absolute potential state
NASA Astrophysics Data System (ADS)
Nityayogananda, Swami
2017-01-01
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as `like-potential' energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity - this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.
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.
Transients in the synchronization of asymmetrically coupled oscillator arrays
NASA Astrophysics Data System (ADS)
Cantos, C. E.; Hammond, D. K.; Veerman, J. J. P.
2016-09-01
We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Observations of ELM Magnetic Precursors and Harmonic Oscillations in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Frederickson, E.; Bell, R.; Tritz, K.; Takahashi, H.; Maingi, R.; NSTX Collaboration
2011-10-01
Recent experiments on NSTX have shown n=1 dominant and n=2 mode ELM magnetic precursors with mode frequency in the 30 to 90 kHz range. The growing magnetic oscillations measured with the NSTX high-n Mirnov diagnostic occurred simultaneous with the onset of the increase in fast D α signal. These bursts of dominantly n=1, some n=2 and fewer higher modes resemble the predictions of a model simulation of ELMs by T. Evans in which a feedback amplification mechanism causes explosive growth of the separatrix topology driven by thermoelectric currents in flux tubes connecting the divertor plates. The n=1 mode remained dominant as wall recycling was reduced with lithium conditioning and n=3 RMP was applied, suggesting the trigger mechanism remained the same. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n Harmonics Oscillations (HOs) more frequent. The HOs are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. Work supported in part by US DOE contract no. DE-AC02-09CH11466.
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)
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-15
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
1-GHz harmonically pumped femtosecond optical parametric oscillator frequency comb.
Balskus, K; Leitch, S M; Zhang, Z; McCracken, R A; Reid, D T
2015-01-26
We present the first example of a femtosecond optical parametric oscillator frequency comb harmonically-pumped by a 333-MHz Ti:sapphire laser to achieve a stabilized signal comb at 1-GHz mode spacing in the 1.1-1.6-µm wavelength band. Simultaneous locking of the comb carrier-envelope-offset and repetition frequencies is achieved with uncertainties over 1 s of 0.27 Hz and 5 mHz respectively, which are comparable with those of 0.27 Hz and 1.5 mHz achieved for 333-MHz fundamental pumping. The phase-noise power-spectral density of the CEO frequency integrated from 1 Hz-64 kHz was 2.8 rad for the harmonic comb, 1.0 rad greater than for fundamental pumping. The results show that harmonic operation does not substantially compromise the frequency-stability of the comb, which is shown to be limited only by the Rb atomic frequency reference used.
NASA Astrophysics Data System (ADS)
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-01-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies. PMID:27886252
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-25
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Collective Modes of Coupled Phase Oscillators with Delayed Coupling
NASA Astrophysics Data System (ADS)
Ares, Saúl; Morelli, Luis G.; Jörg, David J.; Oates, Andrew C.; Jülicher, Frank
2012-05-01
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelengths. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving boundary conditions. We show that the phase profiles of collective modes depend on coupling delays.
Observation of harmonic gyro-backward-wave oscillation in a 100 GHz CARM oscillator experiment
NASA Astrophysics Data System (ADS)
McCowan, Robert B.; Sullivan, Carol A.; Gold, Steven H.; Fliflet, Arne W.
1991-02-01
A cyclotron autoresonance maser (CARM) oscillator experiment is reported, using a 600 keV, 200 A electron beam, and a whispering gallery-mode rippled-wall Bragg cavity. This device was designed to produce tens of megawatts of radiation at 100 GHz from a CARM interaction, but instead has produced only moderate powers (tens of kWs) in fundamental gyrotron modes near 35 GHz, in third-harmonic-gyro-BWO modes, and possible third-harmonic gyrotron modes at frequencies near the expected CARM frequency, with no discernable CARM radiation. The lack of observable CARM radiation is attributed to excessive ripple on the voltage waveform and to mode competition. Calculations of the spectrum and growth rate of the backward-wave oscillations are consistent with the experimental observation.
NASA Astrophysics Data System (ADS)
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.
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.
Generation of coherently coupled vibronic oscillations in carotenoids
NASA Astrophysics Data System (ADS)
Sugisaki, Mitsuru; Kosumi, Daisuke; Saito, Keisuke; Cogdell, Richard J.; Hashimoto, Hideki
2012-06-01
Coherent vibronic oscillations in the ground state of carotenoids have been investigated by means of three-pulse four-wave mixing spectroscopy. Here, we especially focused our attention on the influence of the temporal separation between the first and the second pulses, i.e., the coherent period τ, on the third-order nonlinear signals. The vibronic oscillations of the fundamental modes are clearly observed when τ is set to zero. They appear via an impulsive resonant Raman process and reflect the spectral feature of a conventional Raman spectrum very well. Interestingly, in addition to the coherent vibronic oscillations of the fundamental modes, we found that high-intensity coherent vibronic oscillations of the overtones and the coupled modes appear when a nonzero value of τ is employed. These coupled modes become dominant at a rather large coherent period of τ ˜ 60 fs. A simple extension of our previous calculations that assume electronic harmonic potentials and vibronic Brownian oscillators cannot explain the present experimental results. Instead, we propose a model that takes into consideration the mixing between singlet states and the higher-order interaction of molecular vibrations with electronic states, which is in quantitative agreement with the experimental results. Our finding opens the way to controlling even Raman inactive vibronic oscillations using light.
Coupling functions in networks of oscillators
NASA Astrophysics Data System (ADS)
Stankovski, Tomislav; Ticcinelli, Valentina; McClintock, Peter V. E.; Stefanovska, Aneta
2015-03-01
Networks of interacting oscillators abound in nature, and one of the prevailing challenges in science is how to characterize and reconstruct them from measured data. We present a method of reconstruction based on dynamical Bayesian inference that is capable of detecting the effective phase connectivity within networks of time-evolving coupled phase oscillators subject to noise. It not only reconstructs pairwise, but also encompasses couplings of higher degree, including triplets and quadruplets of interacting oscillators. Thus inference of a multivariate network enables one to reconstruct the coupling functions that specify possible causal interactions, together with the functional mechanisms that underlie them. The characteristic features of the method are illustrated by the analysis of a numerically generated example: a network of noisy phase oscillators with time-dependent coupling parameters. To demonstrate its potential, the method is also applied to neuronal coupling functions from single- and multi-channel electroencephalograph recordings. The cross-frequency δ, α to α coupling function, and the θ, α, γ to γ triplet are computed, and their coupling strengths, forms of coupling function, and predominant coupling components, are analysed. The results demonstrate the applicability of the method to multivariate networks of oscillators, quite generally.
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
The Study of a Dampened Driven Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Findley, Tiffany; Yoshida, Sanichiro; Bankston, Daniel; Lovell, Clinton
2003-03-01
The dynamics of a pendulum are studied with a suspended mirror used in a Laser Interferometer Gravitational-wave Observatory (LIGO) detector in mind. We are interested in modeling the motion of the suspended mirrors in the context of a damped driven harmonic oscillator. A model mirror was constructed and suspended by wire to a block that was driven by a mechanical oscillator. To measure the frequency dependence of the pitch and yaw motions, the mirror reflected a laser beam onto a measurement plane. A CCD camera took periodic pictures of the measurement plane, thus capturing the movement of the beam due to the movement of the mirror. These pictures were then analyzed to determine the dynamics of the pendulum at the driving frequency. The resonant frequencies and damping coefficient were estimated from free oscillations of the pendulum. The pendular motion of the three-dimensional pendulum will also be analyzed. We will compare our results with data from LIGO to understand the dynamics of the mirror.
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
2015-01-02
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. Copyright © 2015, American Association for the Advancement of Science.
Pulse-coupled BZ oscillators with unequal coupling strengths.
Horvath, Viktor; Kutner, Daniel J; Chavis, John T; Epstein, Irving R
2015-02-14
Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N : M) in which the two oscillators exhibit different numbers of peaks per cycle. The N : M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system's behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1 : 2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1 : N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.
Entrainment in coupled salt-water oscillators
NASA Astrophysics Data System (ADS)
Miyakawa, Kenji; Yamada, Kazuhiko
1999-03-01
The properties of coupling between two salt-water oscillators were studied. Two salt-water oscillators were coupled through the window of the partition wall. With an increase of the area of the window, the quasi-periodic mode, the in-phase mode, the bistable mode, and the out-of-phase mode appeared successively. A phase diagram of coupling was obtained in the plane of the area of the window and the diameter of the orifice of the cup. Furthermore, the effect of viscosity on coupling behaviors was investigated. In the boundary region between quasi-periodic coupling and in-phase coupling, the mode coupled with the phase difference of approximately π/4 was found. The experimental results were reproduced by the numerical simulation using coupled non-linear differential equations.
Quantization of a free particle interacting linearly with a harmonic oscillator.
Mainiero, Thomas; Porter, Mason A
2007-12-01
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic.
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.
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
2015-11-19
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.
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.
Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A relativistic harmonic-oscillator formalism which is mathematically simple as the nonrelativistic harmonic oscillator is given. In view of its effectiveness in describing Lorentz-deformed hadrons, the inclusion of this formalism in a first-year graduate course will make the results of high-energy experiments more understandable. (BB)
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…
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…
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…
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…
Adaptive coupling and enhanced synchronization in coupled phase oscillators
NASA Astrophysics Data System (ADS)
Ren, Quansheng; Zhao, Jianye
2007-07-01
We study the dynamics of an adaptive coupled array of phase oscillators. The adaptive law is designed in such a way that the coupling grows stronger for the pairs which have larger phase incoherence. The proposed scheme enhances the synchronization and achieves a more reasonable coupling dynamics for the network of oscillators with different intrinsic frequencies. The synchronization speed and the steady-state phase difference can be adjusted by the parameters of the adaptive law. Besides global coupling, nearest-neighbor ring coupling is also considered to demonstrate the generality of the method.
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
NASA Astrophysics Data System (ADS)
Liu, Xiaowei; Chen, Lingen; Wu, Feng; Sun, Fengrui
2009-12-01
A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
2010-05-04
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-Schroedinger (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 <
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.
Phase-space treatment of the driven quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Campos, Diógenes
2017-03-01
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
A Perturbation of the Dunkl Harmonic Oscillator on the Line
NASA Astrophysics Data System (ADS)
Álvarez López, Jesús A.; Calaza, Manuel
2015-07-01
Let J_σ be the Dunkl harmonic oscillator on R (σ>-1/2). For 00, it is proved that, if σ>u-1/2, then the operator U=J_σ+ξ|x|^{-2u}, with appropriate domain, is essentially self-adjoint in L^2({R},|x|^{2σ} dx), the Schwartz space S is a core of overline U^{1/2}, and overline U has a discrete spectrum, which is estimated in terms of the spectrum of overline{J_σ}. A generalization J_{σ,τ} of J_σ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for J_{σ,τ}, where the perturbation has an additional term involving, either the factor x^{-1} on odd functions, or the factor x on even functions. Versions of these results on R_+ are derived.
The Acoustic Simple Harmonic Oscillator: Experimental Verification and Applications
NASA Astrophysics Data System (ADS)
Matteson, Sam
2009-04-01
In his famous volume, The Sensations of Tone, published in 1877, Hermann Helmholtz introduced a resonator that was central to his investigations of acoustics. This talk revisits the device that Helmholtz described and examines it as a manifestation of an acoustic simple harmonic oscillator (SHO). The presentation demonstrates that an enclosed volume which communicates with the outside world via a narrow tube exhibits a single strong frequency response in analogy to a mechanical SHO, along with weaker resonances of the air in the short pipe that comprises the ``neck.'' The investigations, furthermore, report results of a straightforward experiment that confirms the SHO model (with damping) and that is very accessible to undergraduate students using inexpensive equipment and internet-obtainable freeware. The current work also extends the analysis to include applications of the Helmholtz Resonator to several folk instruments, namely, the ocarina, whistling, and the ``bottle band.''
Excitation with quantum light. I. Exciting a harmonic oscillator
NASA Astrophysics Data System (ADS)
Carreño, J. C. López; Laussy, F. P.
2016-12-01
We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.
Chiral potential renormalized in harmonic-oscillator space
NASA Astrophysics Data System (ADS)
Yang, C.-J.
2016-12-01
We renormalize the chiral effective field theory potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultraviolet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J -matrix method to reproduce the nucleon-nucleon scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy Tlab=100 MeV with number of HO basis nmax as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. This work serves as the input to perform ab initio calculations.
Explosive oscillation death in coupled Stuart-Landau oscillators
NASA Astrophysics Data System (ADS)
Bi, Hongjie; Hu, Xin; Zhang, Xiyun; Zou, Yong; Liu, Zonghua; Guan, Shuguang
2014-12-01
Recently, explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works have investigated Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. We observe three typical scenarios with distinct microscopic mechanism of occurrence, i.e., ordinary, hierarchical, and cluster explosive oscillation death, corresponding to different frequency distributions of oscillators. We carry out theoretical analyses and obtain the backward transition point, which is shown to be independent of the specific frequency distributions. Numerical results are consistent with the theoretical predictions.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Entanglement prethermalization in an interaction quench between two harmonic oscillators.
Ikeda, Tatsuhiko N; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
2017-02-01
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Entanglement prethermalization in an interaction quench between two harmonic oscillators
NASA Astrophysics Data System (ADS)
Ikeda, Tatsuhiko N.; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
2017-02-01
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Dynamical Recurrence and the Quantum Control of Coupled Oscillators
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Serafini, Alessio; Kim, M. S.; Burgarth, Daniel
2012-04-01
Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.
Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation
NASA Astrophysics Data System (ADS)
Hassan, S. S.; Joshi, A.; Frege, O. M.; Emam, W.
2007-09-01
A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.
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.
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.
Intense energy transfer and superharmonic resonance in a system of two coupled oscillators.
Kovaleva, Agnessa; Manevitch, Leonid; Manevitch, Elina
2010-05-01
The paper presents the analytic study of energy exchange in a system of coupled nonlinear oscillators subject to superharmonic resonance. The attention is given to complete irreversible energy transfer that occurs in a system with definite initial conditions corresponding to a so-called limiting phase trajectory (LPT). We show that the energy imparted in the system is partitioned among the principal and superharmonic modes but energy exchange can be due to superharmonic oscillations. Using the LPT concept, we construct approximate analytic solutions describing intense irreversible energy transfer in a harmonically excited Duffing oscillator and a system of two nonlinearly coupled oscillators. Numerical simulations confirm the accuracy of the analytic approximations.
Autoresonance versus localization in weakly coupled oscillators
NASA Astrophysics Data System (ADS)
Kovaleva, Agnessa; Manevitch, Leonid I.
2016-04-01
We study formation of autoresonance (AR) in a two-degree of freedom oscillator array including a nonlinear (Duffing) oscillator (the actuator) weakly coupled to a linear attachment. Two classes of systems are studied. In the first class of systems, a periodic force with constant (resonance) frequency is applied to a nonlinear oscillator (actuator) with slowly time-decreasing stiffness. In the systems of the second class a nonlinear time-invariant oscillator is subjected to an excitation with slowly increasing frequency. In both cases, the attached linear oscillator and linear coupling are time-invariant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type AR in the nonlinear actuator entails oscillations with growing amplitudes in the linear attachment while in the system of the second type energy transfer from the nonlinear actuator is insufficient to excite high-energy oscillations of the attachment. It is also shown that a slow change of stiffness may enhance the response of the actuator and make it sufficient to support oscillations with growing energy in the attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is demonstrated.
Parametric instability of two coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Denardo, Bruce; Earwood, John; Sazonova, Vera
1999-03-01
One of the two normal modes of a system of two coupled nonlinear oscillators is subject to an instability. Several demonstration apparatus of weakly coupled oscillators that exhibit the instability are described. The effect is due to one normal mode parametrically driving the other, and occurs for the broad range of systems where the nonlinearity has a cubic contribution to the restoring force of each oscillator, which includes pendulums. The instability has an amplitude threshold that increases as the coupling is increased. A naive physical approach predicts that the mode opposite to that observed should be unstable. This is resolved by a weakly nonlinear analysis which reveals that the nonlinearity causes the linear frequency of a normal mode to depend upon the finite amplitude of the other mode. Numerical simulations confirm the theory, and extend the existence of the instability and the accuracy of the theoretical amplitude threshold beyond the regime of weak nonlinearity and weak coupling.
Nonlinear dynamics of coupled oscillator arrays
NASA Astrophysics Data System (ADS)
Mosher, David
1988-03-01
The phase-locked dynamics of large oscillator arrays is currently of interest because of possible microwave directed energy applications. Straight-forward integration of the coupled dynamical equations for such arrays is computationally costly for the associated multidimensional parameter space, long integration times, various initial conditions and system configurations. Finite difference analogs of the nonlinear differential equations can reproduce their complex dynamical behavior with a 2 to 3 order-of-magnitude improvement in computational time. Here, the applicability of the finite difference technique is demonstrated by solutions of the dynamical equations for 2 coupled oscillators and rings of larger numbers. Parameter studies for these configurations suggest the values of the coupler length and coupling strength required to provide robust phase-locked operation. The finite difference technique can be extended to model large oscillator arrays with other coupling geometries, amplifier arrays, and additional physical phenomena.
Aging and clustering in globally coupled oscillators.
Daido, Hiroaki; Nakanishi, Kenji
2007-05-01
A population of coupled nonlinear oscillators may age in such a way that the fraction of non-self-oscillatory elements increases. Following our previous paper [Phys. Rev. Lett. 93, 104101 (2004)], we study the effect of aging in this sense mainly for globally coupled Stuart-Landau oscillators with the emphasis on the structure of the (K,p) phase diagram, where K is the coupling strength and p is the ratio of inactive oscillators. In addition to the aging transition reported previously, such a diagram is shown to be characterized by a hornlike region, which we call a "desynchronization horn," where active oscillators desynchronize to form a number of clusters, provided that uncoupled active oscillators are sufficiently nonisochronous. We also show that desynchronization in such a region can be captured as a type of diffusion-induced inhomogeneity based on a "swing-by mechanism." Our results suggest that the desynchronization horn with some curious properties may be a fairly common feature in aging systems of globally and diffusively coupled periodic oscillators.
NASA Astrophysics Data System (ADS)
Verreault, René
2017-08-01
In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.
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.
Amplitude envelope synchronization in coupled chaotic oscillators.
Gonzalez-Miranda, J M
2002-03-01
A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.
Adaptive elimination of synchronization in coupled oscillator
NASA Astrophysics Data System (ADS)
Zhou, Shijie; Ji, Peng; Zhou, Qing; Feng, Jianfeng; Kurths, Jürgen; Lin, Wei
2017-08-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh-Nagumo spiking oscillators and the Hindmarsh-Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy.
Synchronization of coupled nonidentical genetic oscillators
NASA Astrophysics Data System (ADS)
Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki
2006-03-01
The study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using a control theory approach, we provide a theoretical method for analysing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-09-15
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. Here, our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-09-15
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. Here, our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; ...
2016-09-15
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. Here, our resultsmore » show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.« less
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators
NASA Astrophysics Data System (ADS)
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.
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.
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…
Dynamics of mobile coupled phase oscillators
NASA Astrophysics Data System (ADS)
Uriu, Koichiro; Ares, Saúl; Oates, Andrew C.; Morelli, Luis G.
2013-03-01
We study the transient synchronization dynamics of locally coupled phase oscillators moving on a one-dimensional lattice. Analysis of spatial phase correlation shows that mobility speeds up relaxation of spatial modes and leads to faster synchronization. We show that when mobility becomes sufficiently high, it does not allow spatial modes to form and the population of oscillators behaves like a mean-field system. Estimating the relaxation timescale of the longest spatial mode and comparing it with systems with long-range coupling, we reveal how mobility effectively extends the interaction range.
Susceptibility of large populations of coupled oscillators
NASA Astrophysics Data System (ADS)
Daido, Hiroaki
2015-01-01
It is an important and interesting problem to elucidate how the degree of phase order in a large population of coupled oscillators responds to a synchronizing periodic force from the outside. Here this problem is studied analytically as well as numerically by introducing the concept of susceptibility for globally coupled phase oscillators with either nonrandom or random interactions. It is shown that the susceptibility diverges at the critical point in the nonrandom case with Widom's equality satisfied, while it exhibits a cusp in the most random case.
Synchronization of weakly coupled canard oscillators
NASA Astrophysics Data System (ADS)
Köksal Ersöz, Elif; Desroches, Mathieu; Krupa, Martin
2017-06-01
Synchronization has been studied extensively in the context of weakly coupled oscillators using the so-called phase response curve (PRC) which measures how a change of the phase of an oscillator is affected by a small perturbation. This approach was based upon the work of Malkin, and it has been extended to relaxation oscillators. Namely, synchronization conditions were established under the weak coupling assumption, leading to a criterion for the existence of synchronous solutions of weakly coupled relaxation oscillators. Previous analysis relies on the fact that the slow nullcline does not intersect the fast nullcline near one of its fold points, where canard solutions can arise. In the present study we use numerical continuation techniques to solve the adjoint equations and we show that synchronization properties of canard cycles are different than those of classical relaxation cycles. In particular, we highlight a new special role of the maximal canard in separating two distinct synchronization regimes: the Hopf regime and the relaxation regime. Phase plane analysis of slow-fast oscillators undergoing a canard explosion provides an explanation for this change of synchronization properties across the maximal canard.
Spatial analysis of harmonic oscillation of gypsy moth outbreak intensity.
Haynes, Kyle J; Liebhold, Andrew M; Johnson, Derek M
2009-03-01
Outbreaks of many forest-defoliating insects are synchronous over broad geographic areas and occur with a period of approximately 10 years. Within the range of the gypsy moth in North America, however, there is considerable geographic heterogeneity in strength of periodicity and the frequency of outbreaks. Furthermore, gypsy moth outbreaks exhibit two significant periodicities: a dominant period of 8-10 years and a subdominant period of 4-5 years. In this study, we used a simulation model and spatially referenced time series of outbreak intensity data from the Northeastern United States to show that the bimodal periodicity in the intensity of gypsy moth outbreaks is largely a result of harmonic oscillations in gypsy moth abundance at and above a 4 km(2) scale of resolution. We also used geographically weighted regression models to explore the effects of gypsy moth host-tree abundance on the periodicity of gypsy moths. We found that the strength of 5-year cycles increased relative to the strength of 10-year cycles with increasing host tree abundance. We suggest that this pattern emerges because high host-tree availability enhances the growth rates of gypsy moth populations.
Calorimetric measurement of work for a driven harmonic oscillator.
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Calorimetric measurement of work for a driven harmonic oscillator
NASA Astrophysics Data System (ADS)
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Acceleration effect of coupled oscillator systems
NASA Astrophysics Data System (ADS)
Aonishi, Toru; Kurata, Koji; Okada, Masato
2002-04-01
We have developed a curved isochron clock (CIC) by modifying the radial isochron clock to provide a clean example of the acceleration (deceleration) effect. By analyzing a two-body system of coupled CICs, we determined that an unbalanced mutual interaction caused by curved isochron sets is the minimum mechanism needed for generating the acceleration (deceleration) effect in coupled oscillator systems. From this we can see that the Sakaguchi and Kuramoto (SK) model, which is a class of nonfrustrated mean field model, has an acceleration (deceleration) effect mechanism. To study frustrated coupled oscillator systems, we extended the SK model to two oscillator associative memory models, one with symmetric and the other with asymmetric dilution of coupling, which also have the minimum mechanism of the acceleration (deceleration) effect. We theoretically found that the Onsager reaction term (ORT), which is unique to frustrated systems, plays an important role in the acceleration (deceleration) effect. These two models are ideal for evaluating the effect of the ORT because, with the exception of the ORT, they have the same order parameter equations. We found that the two models have identical macroscopic properties, except for the acceleration effect caused by the ORT. By comparing the results of the two models, we can extract the effect of the ORT from only the rotation speeds of the oscillators.
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.
Purity and decoherence in the theory of a damped harmonic oscillator
NASA Astrophysics Data System (ADS)
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.
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.
Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.
Viñales, A D; Wang, K G; Despósito, M A
2009-07-01
The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
NASA Technical Reports Server (NTRS)
Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.
Mode coupling in solar spicule oscillations
NASA Astrophysics Data System (ADS)
Fazel, Zahra
2016-01-01
In a real medium which has oscillations, the perturbations can cause an energy transfer between different modes. A perturbation, which is interpreted as an interaction between the modes, is inferred to be mode coupling. The mode coupling process in an inhomogeneous medium such as solar spicules may lead to the coupling of kink waves to local Alfvén waves. This coupling occurs in practically any conditions when there is smooth variation in density in the radial direction. This process is seen as the decay of transverse kink waves in the medium. To study the damping of kink waves due to mode coupling, a 2.5-dimensional numerical simulation of the initial wave is considered in spicules. The initial perturbation is assumed to be in a plane perpendicular to the spicule axis. The considered kink wave is a standing wave which shows an exponential damping in the inhomogeneous layer after the mode coupling occurs.
Dynamics of weakly coupled parametrically forced oscillators.
Salgado Sánchez, P; Porter, J; Tinao, I; Laverón-Simavilla, A
2016-08-01
The dynamics of two weakly coupled parametric oscillators are studied in the neighborhood of the primary subharmonic instability. The nature of both primary and secondary instabilities depends in a critical way on the permutation symmetries, if any, that remain after coupling is considered, and this depends on the relative phases of the parametric forcing terms. Detailed bifurcation sets, revealing a complex series of transitions organized in part by Bogdanov-Takens points, are calculated for representative sets of parameters. In the particular case of out-of-phase forcing the predictions of the coupled oscillator model are compared with direct numerical simulations and with recent experiments on modulated cross waves. Both the initial Hopf bifurcation and the subsequent saddle-node heteroclinic bifurcation are confirmed.
Braenzel, J.; Schnürer, M.; Steinke, S.; Priebe, G.; Sandner, W.; Andreev, A.; Platonov, K.
2013-08-15
Theoretical and experimental investigations of the dynamics of a relativistically oscillating plasma slab reveal spectral line splitting in laser driven harmonic spectra, leading to double harmonic series. Both series are well characterized with harmonics arising by two fundamental frequencies. While a relativistic oscillation of the critical density drives the harmonic emission, the splitting is a result of an additional acceleration during the laser pulse duration. In comparison with the oscillatory movement, this acceleration is rather weak and can be described by a plasma shock wave driven by the pressure of light. We introduce particle in cell simulations and an analytical model explaining the harmonic line splitting. The derived analytical formula gives direct access between the splitting in the harmonic spectrum and the acceleration of the plasma surface.
Complex behavior in coupled bromate oscillators.
Chen, Yu; Wang, Jichang
2005-05-05
In this study, coupled bromate-oscillators constructed by adding 1,4-cyclohexanedione (1,4-CHD) to the ferroin-catalyzed Belousov-Zhabotinsky reaction are investigated in a batch reactor under anaerobic conditions. Various complex behaviors such as sequential oscillations and bursting phenomena are observed. At low concentrations of ferroin or malonic acid (MA), the development of sequential oscillations is found to depend on the ratio of [1,4-CHD]/[ferroin] and [1,4-CHD]/[MA] rather than their absolute concentrations. As the concentration of MA or ferroin was increased gradually, however, the minimum 1,4-CHD concentration required to induce complex oscillations reaches a plateau. Perturbations by light illustrate that the first oscillatory window is governed by the ferroin-MA-BZ mechanism, whereas the 1,4-CHD-bromate oscillator plays a prominent role during the non-oscillatory evolution and the second oscillatory window. Our conclusion is further supported by numerical simulations in which sequential oscillations observed in experiments are qualitatively reproduced by a modified FKN mechanism.
Restoration of oscillation from conjugate-coupling-induced amplitude death
NASA Astrophysics Data System (ADS)
Zhao, Nannan; Sun, Zhongkui; Yang, Xiaoli; Xu, Wei
2017-05-01
Maintaining oscillation is essential for practical applications in various natural and artificial systems, thus, restoring rhythmic oscillation from amplitude death (AD) always plays an important role in the real world. In this paper recovery of oscillation has been investigated in Stuart-Landau oscillators with conjugate coupling topologies. Two asymmetry coupling strategies have been firstly employed and utilized in the coupled Stuart-Landau oscillators by introducing asymmetry factors in the coupling topology. It has been found that, via adjusting the asymmetry factors, the AD regions shrink evidently in the parameter plane, recovering the oscillation rhythmicity efficiently in the coupled identical oscillators or nonidentical oscillators. Therefore it provides a candidate to eliminate the AD state and evoke rhythmic oscillation in coupled Stuart-Landau oscillators.
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.
Brownian motion of a harmonic oscillator in a noninertial reference frame.
Jiménez-Aquino, J I; Romero-Bastida, M
2013-08-01
The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.
NASA Astrophysics Data System (ADS)
Gia Vinh, Ngo; Van Ngu, Man; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Dung, Nguyen Thi; Viet, Nguyen Ai
2017-06-01
In our previous article, the connections between q-deformed harmonic oscillator and the two types of asymmetric (Morse-like) and symmetric (inverse square cosine form) potentials have been investigated. The use of these relations in an inverse way to investigate the properties of q-deformed harmonic oscillators has been proposed. In this work, we explore the possibility of using this approach to study some real physical systems, such as diatomic molecules, phonon, etc.
Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator
Fernandez Guasti, M.; Moya-Cessa, H.
2003-06-01
The correspondence between classical and quantum invariants is established. The Ermakov-Lewis quantum invariant of the time-dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time-dependent harmonic-oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.
Locally and globally coupled oscillators in muscle.
Sato, Katsuhiko; Kuramoto, Yoshiki; Ohtaki, Masako; Shimamoto, Yuta; Ishiwata, Shin'ichi
2013-09-06
At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.
Locally and Globally Coupled Oscillators in Muscle
NASA Astrophysics Data System (ADS)
Sato, Katsuhiko; Kuramoto, Yoshiki; Ohtaki, Masako; Shimamoto, Yuta; Ishiwata, Shin'ichi
2013-09-01
At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.
Discrete Excitation Spectrum of a Classical Harmonic Oscillator in Zero-Point Radiation
NASA Astrophysics Data System (ADS)
Huang, Wayne Cheng-Wei; Batelaan, Herman
2015-03-01
We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.
Study of continuous variable entanglement in multipartite harmonic oscillator systems
NASA Astrophysics Data System (ADS)
Landau, Mayer Amitai
In this thesis we investigate the entanglement of Schrodinger cat states that derive from harmonic oscillator models. In order to extend the finite dimensional framework of entanglement to the infinite dimensional case we consider only initial conditions that have some type of symmetry. Systems with symmetry usually have fewer important parameters. In our case, symmetry allows us to discard the bulk of the Hilbert space as irrelevant to our particular entanglement problem. We are then left with an effectively finite dimensional Hilbert space, and the developed entanglement framework can therefore be followed. The dimension we derive for the reduced Hilbert space in each subsystem is equal to the number of coherent states in the Schrodinger cat superposition. We investigate the entanglement vs. time of our Schrodinger cat state for closed and open systems. For closed systems, we place no limit on the number of coherently summed linearly independent coherent states. So the dimension of our effective Hilbert space can be quite high. We also place no restriction on the number of subsystems (or parties). Consequently, we use the entanglement measure developed by Barnum, Knill, Ortiz, and Viola (BKOV). This is the only measure to our knowledge that has no restriction on the dimension of the Hilbert space or the number of subsystems. We also place no constraint on the magnitude of our coherent states. The coherent value may be quite large, or quite small. We find that the entanglement of the Schrodinger cat state has nontrivial dependence on the above mentioned three variables. That is, the entanglement is a non-separable function of the values of the coherent states, the number of coherent states in the superposition, and the number of partitions of the Hilbert space. For open systems, we model the reservoir as a harmonic oscillator zero temperature bath. Due to the interactions with the bath the Schrodinger cat state becomes a mixed density matrix. To investigate the
Pagel, D; Alvermann, A; Fehske, H
2013-01-01
We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.
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
Synchronization in Networks of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Showalter, Kenneth; Tinsley, Mark; Nkomo, Simbarashe; Ke, Hua
2014-03-01
We have studied networks of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on networks with different topologies and modes of coupling. We describe experimental and modeling studies of chimera and phase-cluster states and their relation to other synchronization states. Networks of integrate-and-fire oscillators are also studied in which sustained coordinated activity is exhibited. Individual nodes display incoherent firing events; however, a dominant frequency within the collective signal is exhibited. The introduction of spike-timing-dependent plasticity allows the network to evolve and leads to a stable unimodal link-weight distribution. M. R. Tinsley et al., Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev. Lett. 110, 244102 (2013); H. Ke et al., in preparation.
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.
NASA Astrophysics Data System (ADS)
Gaiko, Nick V.; van Horssen, Wim T.
2016-11-01
In this paper, the free transverse vibrations of a vertically moving string with a harmonically time-varying length are studied. The string length variations are assumed to be small. By using the multiple-timescales perturbation method in conjunction with a Fourier series approach, we determine the resonance frequencies and derive the non-secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations. This system describes the long time behavior of the amplitudes of the oscillations. Then, the eigenvalues of the obtained system are studied by the Galerkin truncation method, and applicability of this method is discussed. Apart from this, the dynamic stability of the solution is investigated by an energy analysis. Additionally, resonance detuning is considered.
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…
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…
Image hiding based on time-averaged fringes produced by non-harmonic oscillations
NASA Astrophysics Data System (ADS)
Ragulskis, M.; Aleksa, A.; Navickas, Z.
2009-12-01
Image hiding based on time-averaged fringes produced by non-harmonic oscillations is presented in this paper. The secret image is embedded into the background moiré grating. Phase matching and initial stochastic phase deflection algorithms are used to encrypt the image. The decoding of the image is completely visual. The secret embedded image appears when the encrypted image is oscillated according to a predefined law of motion. No secret is leaked when the encrypted image is oscillated harmonically. Numerical experiments are used to illustrate the functionality of the method.
Calculation of the convex roof for an open entangled harmonic oscillator system
Landau, Mayer A.; Stroud, C. R. Jr.
2010-05-15
We explicitly calculate the time dependence of entanglement via the convex roof extension for a system of noninteracting harmonic oscillators. These oscillators interact only indirectly with each other by way of a zero-temperature bath. The initial state of the oscillators is taken to be that of an entangled Schroedinger-cat state. This type of initial condition leads to superexponential decay of the entanglement when the initial state has the same symmetry as the interaction Hamiltonian.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of...expressed in terms of a Bessel series, and the sums of many such series are known or can be developed. The method is illustrated for five different... Bessel series, work-energy theorem, nonlinear oscillator, pendulum. 1 Introduction Nonlinear oscillators are ubiquitous in physical and engineering
Nicu, Valentin Paul
2016-08-03
Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.
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.
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.
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.
Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks
NASA Astrophysics Data System (ADS)
Velichko, Andrey; Belyaev, Maksim; Putrolaynen, Vadim; Pergament, Alexander; Perminov, Valentin
2017-01-01
In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.
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.
Harmonic trap resonance enhanced synthetic atomic spin-orbit coupling.
Wu, Ling-Na; Luo, Xin-Yu; Xu, Zhi-Fang; Ueda, Masahito; Wang, Ruquan; You, L
2017-04-27
Spin-orbit coupling (SOC) plays an essential role in many exotic and interesting phenomena in condensed matter physics. In neutral-atom-based quantum simulations, synthetic SOC constitutes a key enabling element. The strength of SOC realized so far is limited by various reasons or constraints. This work reports tunable SOC synthesized with a gradient magnetic field (GMF) for atoms in a harmonic trap. Nearly ten-fold enhancement is observed when the GMF is modulated near the harmonic-trap resonance in comparison with the free-space situation. A theory is developed that well explains the experimental results. Our work offers a clear physical insight into and analytical understanding of how to tune the strength of atomic SOC synthesized with GMF using harmonic trap resonance.
Harmonic trap resonance enhanced synthetic atomic spin-orbit coupling
Wu, Ling-Na; Luo, Xin-Yu; Xu, Zhi-Fang; Ueda, Masahito; Wang, Ruquan; You, L.
2017-01-01
Spin-orbit coupling (SOC) plays an essential role in many exotic and interesting phenomena in condensed matter physics. In neutral-atom-based quantum simulations, synthetic SOC constitutes a key enabling element. The strength of SOC realized so far is limited by various reasons or constraints. This work reports tunable SOC synthesized with a gradient magnetic field (GMF) for atoms in a harmonic trap. Nearly ten-fold enhancement is observed when the GMF is modulated near the harmonic-trap resonance in comparison with the free-space situation. A theory is developed that well explains the experimental results. Our work offers a clear physical insight into and analytical understanding of how to tune the strength of atomic SOC synthesized with GMF using harmonic trap resonance. PMID:28447670
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.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Plyushchay, Mikhail S.
2016-11-01
Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp (1 |2 ) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.
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
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
Sugawara-Tanabe, Kazuko
2011-05-06
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 {delta} and {gamma}. The special cases with tan {gamma} = 1/{radical}(3)({gamma} = 30 deg.) and {radical}(3)/5({gamma}{approx}19 deg.) are discussed.
Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Ren, Zhong-Zhou; Ju, Guo-Xing; Guo, Xiao-Yong
2012-03-01
The time evolution of a time-dependent inverted harmonic oscillator (TDIHO) of arbitrary dimensions is investigated. Using the algebraic method, we obtain the exact orthogonal basis of solutions of a TDIHO in which the dimensionality d and angular momentum l appear as parameters, and also discuss its properties. With the wavepacket as the initial state, the general expressions of sojourn time of a TDIHO are given. The method is also applied to the inverted Caldirola-Kanai harmonic oscillator. The results show that the sojourn time appears as an increasing function of the dissipation parameter in arbitrary dimensions, but a decreasing function of the dimensionality.
Planck scale corrections to the harmonic oscillator, coherent, and squeezed states
NASA Astrophysics Data System (ADS)
Bosso, Pasquale; Das, Saurya; Mann, Robert B.
2017-09-01
The generalized uncertainty principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of quantum gravity. It consists of a modified commutator between the position and momentum. In this work, we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent, and squeezed states in quantum mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.
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.
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-off intermittency in coupled chaotic thermoacoustic oscillations
NASA Astrophysics Data System (ADS)
Delage, Rémi; Takayama, Yusuke; Biwa, Tetsushi
2017-04-01
This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size.
On-off intermittency in coupled chaotic thermoacoustic oscillations.
Delage, Rémi; Takayama, Yusuke; Biwa, Tetsushi
2017-04-01
This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size.
On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator
Dubois, Daniel M.
2008-10-17
A fundamental mathematical formalism related to the Quantum Potential factor, Q, is presented in this paper. The Schroedinger equation can be transformed to two equations depending on a group velocity and a density of presence of the particle. A factor, in these equations, was called ''Quantum Potential'' by D. Bohm and B. Hiley. In 1999, I demonstrated that this Quantum Potential, Q, can be split in two Quantum Potentials, Q{sub 1}, and Q{sub 2}, for which the relation, Q=Q{sub 1}+Q{sub 2}, holds. These two Quantum Potentials depend on a fundamental new variable, what I called a phase velocity, u, directly related to the probability density of presence of the wave-particle, given by the modulus of the wave function. This paper gives some further developments for explaining the Quantum Potential for oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator. It is shown that the two Quantum Potentials play a central role in the interpretation of quantum mechanics. A breakthrough in the formalism of the Quantum Mechanics could be provoked by the physical properties of these Quantum Potentials. The probability density of presence of the oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator is directly depending on the ratio Q{sub 2}/Q{sub 1} of the two Quantum Potentials. In the general case, the energy of these Gaussian wave packets is not constant, but is oscillating. The energy is given by the sum of the kinetic energy, T, the potential energy, V, and the two Quantum Potentials: E=T+V+Q{sub 1}+Q{sub 2}. For some conditions, given in the paper, the energy can be a constant. The first remarkable result is the fact that the first Quantum Potential, Q{sub 1}, is related to the ground state energy, E{sub 0}, of the Quantum Harmonic Oscillator: Q{sub 1}=h-bar {omega}/2=E{sub 0}. The second result is related to the property of the second Quantum Potential, Q{sub 2}, which plays the role of an anti-potential, Q{sub 2}=-V(x), where V is
NASA Astrophysics Data System (ADS)
Mandal, Swapan
2017-03-01
The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.
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.
Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood's machine
NASA Astrophysics Data System (ADS)
Pecori, Barbara; Torzo, Giacomo; Sconza, Andrea
1999-03-01
We describe how the Atwood's machine, interfaced to a personal computer through a rotary encoder, is suited for investigating harmonic and anharmonic oscillations, exploiting the buoyancy force acting on a body immersed in water. We report experimental studies of oscillators produced by driving forces of the type F=-kxn with n=1,2,3, and F=-k sgn(x). Finally we suggest how this apparatus can be used for showing to the students a macroscopic model of interatomic forces.
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.
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.
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.
Synchronization in arrays of coupled self-induced friction oscillators
NASA Astrophysics Data System (ADS)
Marszal, Michał; Saha, Ashesh; Jankowski, Krzysztof; Stefański, Andrzej
2016-11-01
We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.
Behavior of orbits of two coupled oscillators
Greene, J.M.
1984-06-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This is a very general theory, and applies to many equivalent systems. A typical problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. It is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert MacKay's thesis, for which this is an advertisement.
Constructing quantum logic gates using q-deformed harmonic oscillator algebras
NASA Astrophysics Data System (ADS)
Altintas, Azmi Ali; Ozaydin, Fatih; Yesilyurt, Can; Bugu, Sinan; Arik, Metin
2014-04-01
We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.
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.
Note on the Time-Dependent Damped and Forced Harmonic Oscillator.
ERIC Educational Resources Information Center
Leach, P. G. L.
1978-01-01
A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)
Morales, J.; Ovando, G.; Pena, J. J.
2010-12-23
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space
NASA Astrophysics Data System (ADS)
Das, Saurya; Robbins, Matthew P. G.; Walton, Mark A.
2016-01-01
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
Note on the Time-Dependent Damped and Forced Harmonic Oscillator.
ERIC Educational Resources Information Center
Leach, P. G. L.
1978-01-01
A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
ERIC Educational Resources Information Center
Fay, Temple H.
2002-01-01
This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…
NASA Astrophysics Data System (ADS)
Döntgen, M.
2016-09-01
Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙ H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.
Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations.
Bader, Philipp; Blanes, Sergio
2011-04-01
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using fast Fourier transforms. Splitting the system into the quantum harmonic-oscillator problem and the remaining part allows us to get higher accuracies in many cases, but it requires us to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build methods that combine the advantages of using Fourier methods while solving the time-dependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).
Damped harmonic oscillator model for analyzing the dynamic characteristics of STM system
NASA Astrophysics Data System (ADS)
Liu, A. P.; Yao, X. X.; Wang, X.; Yang, D. X.; Zhang, X. M.
2015-09-01
Recognizing and distinguishing the dynamic characteristics of scanning tunneling microscopy (STM) system is fatal for studying STM image. In this paper, a method for analyzing system’s characteristics by using a damped harmonic oscillator model is presented. The model is driven by random force and all of its properties are described by damping and periodic. For the general solution of such harmonic oscillator’s Langevin equation is deduced and the auto-correlation function (ACF) is obtained for fitting curve. It is shown that damping and periodic property of the two curves have a good agreement by comparing the fitting curve with the auto-correlation curve of time series dates which are acquired by STM. It could be concluded that the damped harmonic oscillator model and auto-correlation method are feasible for analyzing the dynamic characteristics of STM system.
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.
Coupled Oscillators System in the True Slime Mold
NASA Astrophysics Data System (ADS)
Takamatsu, A.; Fujii, T.; Endo, I.
The Plasmodium of true slime mold, Physarum polycephalum, which shows various oscillatory phenomena, can be regarded as a coupled nonlinear oscillators system. The partial bodies of the Plasmodium are interconnected by microscale tubes, whose dimension can be related to the coupling strength between the plasmodial oscillators. Investigation on the collective behavior of the oscillators under the condition that the configuration of the tube structure can be manipulated gives significant information on the characteristics of the Plasmodium from the viewpoint of nonlinear dynamics. In this study, we propose a living coupled oscillators system. Using a microfabricated structure, we patterned the geometry and the dimensions of the microscale tube structure of the Plasmodium. As the first step, the Plasmodium was grown in the microstructure for coupled two oscillators system that has two wells (oscillator part) and a microchannel (coupling part). We investigated the oscillation bahavior by monitoring the thickness oscillation of Plasmodium in the strucutre with various width (W) and length (L) of microchannel. We found that there are various types of oscillation bahavior, such as anti-phase and in-phase oscillations depending on the channel dimension W and L. The present method is suitable for further studies of the network of the Plasmodium as a collective nonlinear oscillators system.
Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
Saha, Anirban; Gangopadhyay, Sunandan; Saha, Swarup
2011-01-15
We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GWs) in the long-wavelength and low-velocity limit. Following the prescription in Saha and Gangopadhyay [Phys. Lett. B 681, 96 (2009)] we quantize the system. The Hamiltonian of the system is solved by using standard algebraic iterative methods. The solution shows signatures of the coordinate noncommutativity via alterations in the oscillation frequency of the harmonic oscillator system from its commutative counterpart. Moreover, it is found that the response of the harmonic oscillator to periodic GWs, when their frequencies match, will oscillate with a time scale imposed by the noncommutative parameter. We expect this noncommutative signature to show up as some noise source in the GW detection experiments since the recent phenomenological upper bounds set on the spatial noncommutative parameter imply a length scale comparable to the length variations due to the passage of gravitational waves, detectable in the present-day GW detectors.
NASA Astrophysics Data System (ADS)
Vignat, C.; Lamberti, P. W.
2009-10-01
Recently, Cariñena, 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.
NASA Astrophysics Data System (ADS)
Qin, Jie; Ning, Lijuan
2017-08-01
This paper addresses the entropy evolution of a damped harmonic oscillator driven by quasimonochromatic noise (QMN). Due to QMN is distinct from white noise, so this paper studied the effect of QMN noise on the upper bound of time derivative of entropy for a damped harmonic oscillator. Through the comparison of probability density function (PDF) and the upper bound for the time derivative of entropy, we find that the entropy evolution is also a useful tool to describe the system dynamic behavior. Then we discuss the interplay of the parameters of QMN, damping constant, the frequency of oscillator and external periodic force and their effects on the upper bound for the rate of entropy change. Finally, some beneficial conclusions are obtained.
Silvestrelli, Pier Luigi
2013-08-07
We present a new scheme to include the van der Waals (vdW) interactions in approximated Density Functional Theory (DFT) by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique. With respect to the recently developed DFT/vdW-WF2 method, also based on Wannier Functions, the new approach is more general, being no longer restricted to the case of well separated interacting fragments. Moreover, it includes higher than pairwise energy contributions, coming from the dipole-dipole coupling among quantum oscillators. The method is successfully applied to the popular S22 molecular database, and also to extended systems, namely graphite and H2 adsorbed on the Cu(111) metal surface (in this case metal screening effects are taken into account). The results are also compared with those obtained by other vdW-corrected DFT schemes.
NASA Astrophysics Data System (ADS)
Gautam, Kumar; Chauhan, Garv; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet
2015-09-01
This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiation- perturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O( e) and perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to , and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0, T]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.
Amplitude death in coupled robust-chaos oscillators
NASA Astrophysics Data System (ADS)
Palazzi, M. J.; Cosenza, M. G.
2014-12-01
We investigate the synchronization behavior of a system of globally coupled, continuous-time oscillators possessing robust chaos. The local dynamics corresponds to the Shimizu-Morioka model where the occurrence of robust chaos in a region of its parameter space has been recently discovered. We show that the global coupling can drive the oscillators to synchronization into a fixed point created by the coupling, resulting in amplitude death in the system. The existence of robust chaos allows to introduce heterogeneity in the local parameters, while guaranteeing the functioning of all the oscillators in a chaotic mode. In this case, the system reaches a state of oscillation death, with coexisting clusters of oscillators in different steady states. The phenomena of amplitude death or oscillation death in coupled robust-chaos flows could be employed as mechanisms for stabilization and control in systems that require reliable operation under chaos.
Quorum Sensing and Synchronization in Populations of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Taylor, Annette F.; Tinsley, Mark R.; Showalter, Kenneth
2013-12-01
Experiments and simulations of populations of coupled chemical oscillators, consisting of catalytic particles suspended in solution, provide insights into density-dependent dynamics displayed by many cellular organisms. Gradual synchronization transitions, the "switching on" of activity above a threshold number of oscillators (quorum sensing) and the formation of synchronized groups (clusters) of oscillators have been characterized. Collective behavior is driven by the response of the oscillators to chemicals emitted into the surrounding solution.
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.
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…
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…
Whitfield, Troy W; Martyna, Glenn J
2007-02-21
In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose "pseudoelectrons" are harmonically bound to their respective "pseudonuclei," is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.
Gluing Bifurcations in Coupled Spin Torque Nano-Oscillators
2013-01-01
REPORT Gluing bifurcations in coupled spin torque nano -oscillators 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: Over the past few years it has been...shown, through theory and experiments, that the AC current produced by spin torque nano -oscillators (STNO), coupled in an array, can lead to feedback...Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Nano -oscillators, symmetry, bifurcations Katherine
Dynamics of a network of phase oscillators with plastic couplings
Nekorkin, V. I.; Kasatkin, D. V.
2016-06-08
The processes of synchronization and phase cluster formation are investigated in a complex network of dynamically coupled phase oscillators. Coupling weights evolve dynamically depending on the phase relations between the oscillators. It is shown that the network exhibits several types of behavior: the globally synchronized state, two-cluster and multi-cluster states, different synchronous states with a fixed phase relationship between the oscillators and chaotic desynchronized state.
Entangling Qubits in a One-Dimensional Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Owen, Edmund; Dean, Matthew; Barnes, Crispin
2012-02-01
We present a method for generating entanglement between qubits associated with a pair of particles interacting in a one-dimensional harmonic potential. By considering the effect of the interaction on the energy spectrum of the system, we show that, under certain approximations, a ``power-of-SWAP" operation is performed on the initial two-qubit quantum state without requiring any time-dependent control. Initialization errors and deviations from our approximation are shown to have a negligible effect on the final state. Using a GPU-accelerated iteration scheme to find numerical solutions to the two-particle time-dependent Schr"odinger equation, we demonstrate that it is possible to generate maximally entangled Bell states between the two qubits with high fidelity for a range of possible interaction potentials.
Fidler, Andrew F; Engel, Gregory S
2013-10-03
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.
Bifurcation analysis of a non-linear hysteretic oscillator under harmonic excitation
NASA Astrophysics Data System (ADS)
Il Chang, Seo
2004-09-01
The steady state oscillations of a system incorporating a non-linear hysteretic damper are studied analytically by applying a perturbation technique. The hysteretic damper of the system subject to harmonic resonant force is modelled by combining a Maxwell's model and Kelvin-Voigt's model in series. The non-linearity is imposed by replacing a spring element by a cubic-non-linear spring. The response of the system is described by two coupled second order differential equations including a non-linear constitutive equation. Proper rescaling of the variables and parameters of the equations of motion leads to a set of weakly non-linear equations of motion to which the method of averaging is applied. The bifurcation analysis of the reduced four-dimensional amplitude- and phase-equations of motion shows typical non-linear behaviors including saddle-node and Hopf bifurcations and separate solution branch. By the stability analysis, the saddle-node and Hopf bifurcation sets are obtained in parameter spaces. The software package AUTO is used to numerically study the bifurcation sets and limit cycle solutions bifurcating from the Hopf bifurcation points. It is shown that the limit cycle responses of the averaged system exist over broad parameter ranges.
Amplitude death of identical oscillators in networks with direct coupling
NASA Astrophysics Data System (ADS)
Illing, Lucas
2016-08-01
It is known that amplitude death can occur in networks of coupled identical oscillators if they interact via diffusive time-delayed coupling links. Here we consider networks of oscillators that interact via direct time-delayed coupling links. It is shown analytically that amplitude death is impossible for directly coupled Stuart-Landau oscillators, in contradistinction to the case of diffusive coupling. We demonstrate that amplitude death in the strict sense does become possible in directly coupled networks if the node dynamics is governed by second-order delay differential equations. Finally, we analyze in detail directly coupled nodes whose dynamics are described by first-order delay differential equations and find that, while amplitude death in the strict sense is impossible, other interesting oscillation quenching scenarios exist.
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
Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System
Jolma, Ingunn W.; Ni, Xiao Yu; Rensing, Ludger; Ruoff, Peter
2010-01-01
Abstract Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks. PMID:20197027
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
Spin-orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Malomed, Boris A.; Skryabin, Dmitry V.
2017-08-01
We consider a model of the exciton-polariton condensate based on a system of two Gross-Pitaevskii equations coupled by the second-order differential operator, which represents the spin-orbit coupling in the system. Also included are the linear gain, effective diffusion, nonlinear loss, and the standard harmonic-oscillator trapping potential, as well as the Zeeman splitting. By means of combined analytical and numerical methods, we identify stable two-dimensional modes supported by the nonlinear system. In the absence of the Zeeman splitting, these are mixed modes, which combine zero and nonzero vorticities in each of the two spinor components, and vortex-antivortex complexes. We have also found a range of parameters where the mixed-mode and vortex-antivortex states coexist and are stable. Sufficiently strong Zeeman splitting creates stable semi-vortex states, with vorticities 0 in one component and 2 in the other.
Non-Heisenberg states of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Dechoum, K.; França, H. M.
1995-11-01
The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0) within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h' with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h'>0. The exact solutions for which h'
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.
Spectra of delay-coupled heterogeneous noisy nonlinear oscillators
NASA Astrophysics Data System (ADS)
Vüllings, Andrea; Schöll, Eckehard; Lindner, Benjamin
2014-02-01
Nonlinear oscillators that are subject to noise and delayed interaction have been used to describe a number of dynamical phenomena in Physics and beyond. Here we study the spectral statistics (power and cross-spectral densities) of a small number of noisy nonlinear oscillators and derive analytical approximations for these spectra. In our paper, individual oscillators are described by the normal form of a supercritical or subcritical Hopf bifurcation supplemented by Gaussian white noise. Oscillators can be distinguished from each other by their frequency, bifurcation parameter, and noise intensity. Extending previous results from the literature, we first calculate in linear response theory the power spectral density and response function of the single oscillator in both super- and subcritical parameter regime and test them against numerical simulations. For small heterogeneous groups of oscillators (N = 2 or 3), which are coupled by a delayed linear term, we use a linear response ansatz to derive approximations for the power and cross-spectral densities of the oscillators within this small network. These approximations are confirmed by comparison with extensive numerical simulations. Using the theory we relate the peaks in the spectra of the homogeneous system (identical oscillators) to periodic solutions of the deterministic (noiseless) system. For two delay-coupled subcritical Hopf oscillators, we show that the coupling can enhance the coherence resonance effect, which is known to occur for the single subcritical oscillator. In the case of heterogeneous oscillators, we find that the delay-induced characteristic profile of the spectra is conserved for moderate frequency detuning.
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-01-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis. PMID:28378760
Basin stability measure of different steady states in coupled oscillators.
Rakshit, Sarbendu; Bera, Bidesh K; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-05
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
Basin stability measure of different steady states in coupled oscillators
NASA Astrophysics Data System (ADS)
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
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.
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.
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
NASA Astrophysics Data System (ADS)
Mahdifar, A.; Roknizadeh, R.; Naderi, M. H.
2006-06-01
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
Harmonically pumped femtosecond optical parametric oscillator with multi-gigahertz repetition rate.
Tian, Wenlong; Wang, Zhaohua; Zhu, Jiangfeng; Wei, Zhiyi
2016-12-26
We report a multi-gigahertz (GHz) repetition-rate femtosecond MgO:PPLN optical parametric oscillator (OPO) harmonically pumped by a 75.6 MHz Kerr-lens mode-locked Yb:KGW laser. By fractionally increasing the OPO cavity length, we obtained OPO operation up to the 493rd harmonic of the pump laser repetition rate, corresponding to a repetition rate as high as 37.3 GHz. Using a 1.5% output coupler, we are able to extract signal pulses with up to 260 mW average power at the 102nd harmonic (7.7 GHz) and 90 mW at the 493rd harmonic (37.3 GHz) under 2 W pump power. The measured relative standard deviations of the fundamental and the 102nd harmonic signal power were recorded to be 0.5% and 2.1%, respectively. The signal pulse durations at different harmonics were measured in the range of 160-230 fs.
Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath.
Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M
2017-06-02
Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an 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 the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. 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.
Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath
NASA Astrophysics Data System (ADS)
Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M.
2017-06-01
Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an 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 the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. 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.
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.
Form of the effective interaction in harmonic-oscillator-based effective theory
NASA Astrophysics Data System (ADS)
Haxton, W. C.
2008-03-01
I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in leading order (LO) through next-to-next-to-next-to-leading order (NLO3). Because the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion, free of operator mixing and corresponding to a systematic expansion in nodal quantum numbers, is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds a simple and rather surprising result, that the interplay of QT and QV is governed by a single parameter κ, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy ℏω. Once the functional dependence on κ is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8ℏω. At NLO3 various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV, at 8ℏω. Channel-by-channel variations in convergence rates are similar to those found in effective field theory approaches. The state dependence of the effective interaction has been a troubling problem in nuclear physics and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on κ. Thus there exists a simple, Hermitian Heff that can be use
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.
Study of the harmonic oscillation on EAST by an eight-channel Doppler Backscattering (DBS) system
NASA Astrophysics Data System (ADS)
Zhou, C.; Liu, A. D.; Wang, M. Y.; Hu, J. Q.; Zhang, J.; Li, H.; Lan, T.; Xie, J. L.; Liu, W. D.; Yu, C. X.; Doyle, E. J.; University of California, Los Angeles Collaboration; University of Science; Technology of China Team
2016-10-01
The eight-channel DBS system has been installed for turbulence measurements in such plasmas. The frequency range is 55 to 75 GHz, covering the entire H-mode pedestal, with a turbulence wavenumber range of 4-12/cm. A harmonic oscillation has been observed by DBS on EAST during ELMy-free H mode. The fundamental frequency of the coherent oscillation is 12-20 kHz and 2nd-8th harmonic are observed, and the radial coverage is from the edge to rho 0.85. Work supported by the Natural Science Foundation of China (NSFC) under 11475173, 11505184, National Magnetic Confinement Fusion Energy Development Program of China under 2013GB106002 and 2014GB109002, and DOE Grants DE- SC0010424 and DE-SC0010469.
Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions
NASA Astrophysics Data System (ADS)
Ferkous, N.; Boudjedaa, T.
2017-03-01
We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods. Supported by the Algerian Ministry of Higher Education and Scientific Research under the CNEPRU project No. D01720140001
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
NASA Technical Reports Server (NTRS)
Szebehely, V.; Bond, V.
1983-01-01
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.
Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise
NASA Astrophysics Data System (ADS)
Jara, Milton; Komorowski, Tomasz; Olla, Stefano
2015-10-01
We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126-1142, 2014).
NASA Astrophysics Data System (ADS)
Hamerly, Ryan; Marandi, Alireza; Jankowski, Marc; Fejer, M. M.; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-12-01
We develop reduced models that describe half-harmonic generation in a synchronously pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simultonlike sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs nondegenerate operation, and stability are derived and compared to numerical and experimental results.
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.
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.
Dynamics of SU(1,1) coherent states for the damped harmonic oscillator
Choi, Jeong Ryeol; Yeon, Kyu Hwang
2009-05-15
Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.
The mutual synchronization of coupled delayed feedback klystron oscillators
NASA Astrophysics Data System (ADS)
Emel'yanov, V. V.; Emelianova, Yu. P.; Ryskin, N. M.
2016-08-01
We report on the results of a numerical investigation of the synchronization of two coupled klystron oscillators with an external feedback circuit. Simulation has been carried out using the particle-in-cell method. We have also considered the results of a numerical analysis of an amplifier klystron and an isolated klystron oscillator, which make it possible to choose the optimal values of parameters of coupled klystrons. The structure of the synchronization domain for various parameters has been analyzed. The possibility of increasing the total output power with an appropriate choice of parameter of coupling between the oscillators has been revealed.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear transient waves in coupled phase oscillators with inertia
NASA Astrophysics Data System (ADS)
Jörg, David J.
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Statistics of Lyapunov exponent spectrum in randomly coupled Kuramoto oscillators.
Patra, Soumen K; Ghosh, Anandamohan
2016-03-01
Characterization of spatiotemporal dynamics of coupled oscillatory systems can be done by computing the Lyapunov exponents. We study the spatiotemporal dynamics of randomly coupled network of Kuramoto oscillators and find that the spectral statistics obtained from the Lyapunov exponent spectrum show interesting sensitivity to the coupling matrix. Our results indicate that in the weak coupling limit the gap distribution of the Lyapunov spectrum is Poissonian, while in the limit of strong coupling the gap distribution shows level repulsion. Moreover, the oscillators settle to an inhomogeneous oscillatory state, and it is also possible to infer the random network properties from the Lyapunov exponent spectrum.
Two families of super-harmonic resonances in a time-delayed nonlinear oscillator
NASA Astrophysics Data System (ADS)
Ji, J. C.
2015-08-01
Two stable bifurcating periodic solutions are numerically found to coexist in a time-delayed nonlinear oscillator by using different initial conditions, after the trivial equilibrium loses its stability via two-to-one resonant Hopf bifurcations. These two coexisting solutions have different amplitudes and frequency components with one having the frequencies of Hopf bifurcations while the other containing different frequencies from those of Hopf bifurcations. The dynamic interaction of the periodic excitation and the two coexisting solutions can induce two families of super-harmonic resonances, when the forcing frequency is approximately at half the lower frequency component of the stable bifurcating solutions. It is found that the forced response under two families of super-harmonic resonances exhibits qualitatively different dynamic behaviour. In addition, one family of super-harmonic resonances may suddenly disappear when the excitation magnitude reaches a certain value and then the forced response becomes non-resonant response. The other family of super-harmonic resonances can be established by adjusting the forcing frequency accordingly. Time trajectories, phase portraits, frequency spectra, basin of attraction and bifurcation diagrams are given to characterise the different dynamic behaviours of the time-delayed nonlinear oscillator.
NASA Astrophysics Data System (ADS)
Han, Wenchen; Cheng, Hongyan; Dai, Qionglin; Li, Haihong; Ju, Ping; Yang, Junzhong
2016-10-01
In this work, we investigate the dynamics in a ring of identical Stuart-Landau oscillators with conjugate coupling systematically. We analyze the stability of the amplitude death and find the stability independent of the number of oscillators. When the amplitude death state is unstable, a large number of states such as homogeneous oscillation death, heterogeneous oscillation death, homogeneous oscillation, and wave propagations are found and they may coexist. We also find that all of these states are related to the unstable spatial modes to the amplitude death state.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
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.
Brownian motion of a classical harmonic oscillator in a magnetic field.
Jiménez-Aquino, J I; Velasco, R M; Uribe, F J
2008-05-01
In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.
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.
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 true chemical clock: Serially coupled chlorite iodide oscillators
NASA Astrophysics Data System (ADS)
Long, David A.; Chodroff, Leah; O'Neal, Tim M.; Hemkin, Sheryl
2007-10-01
A set of serially coupled flow reactors are modeled which contain chlorite-iodide oscillators. By independently varying the reactor flow rates it is possible to produce oscillatory systems with differing periods where the ratio of the period of oscillation between reactors is always an integer value. This system was thoroughly examined and utilized to produce a 'true' chemical clock whose three reactors oscillate with a frequency of minutes, hours, and days.
Experimental study on three chemical oscillators coupled with time delay
NASA Astrophysics Data System (ADS)
Nishiyama, Nobuaki; Eto, Kaori
1994-05-01
A new experimental system of coupled chemical oscillators is presented. Three cation-exchange beads loaded with ferroin are spatially distributed in triangular forms and immersed in the Belousov-Zabotinsky reaction mixture. The cation-exchange beads were in no contact with each other. The cation-exchange bead was used as a chemical oscillator. Spontaneous switching between two out-of-phase oscillation was observed.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
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 [Formula: see text] 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.
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.
Collective Dipole Oscillations of a Spin-Orbit Coupled Bose-Einstein Condensate
NASA Astrophysics Data System (ADS)
Zhang, Jin-Yi; Ji, Si-Cong; Chen, Zhu; Zhang, Long; Du, Zhi-Dong; Yan, Bo; Pan, Ge-Sheng; Zhao, Bo; Deng, You-Jin; Zhai, Hui; Chen, Shuai; Pan, Jian-Wei
2012-09-01
In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region as a function of spin-orbit coupling parameters as well as the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility—a static physical quantity—can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.
NASA Astrophysics Data System (ADS)
Venkatesh, P. R.; Venkatesan, A.; Lakshmanan, M.
2017-08-01
We have used a system of globally coupled double-well Duffing oscillators under an enhanced resonance condition to design and implement Dual Input Multiple Output (DIMO) logic gates. In order to enhance the resonance, the first oscillator in the globally coupled system alone is excited by two forces out of which one acts as a driving force and the other will be either sub-harmonic or super-harmonic in nature. We report that for an appropriate coupling strength, the second force coherently drives and enhances not only the amplitude of the weak first force to all the coupled systems but also drives and propagates the digital signals if any given to the first system. We then numerically confirm the propagation of any digital signal or square wave without any attenuation under an enhanced resonance condition for an amplitude greater than a threshold value. Further, we extend this idea for computing various logical operations and succeed in designing theoretically DIMO logic gates such as AND/NAND, OR/NOR gates with globally coupled systems.
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…
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…
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
2016-04-15
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.
Revoking amplitude and oscillation deaths by low-pass filter in coupled oscillators
NASA Astrophysics Data System (ADS)
Zou, Wei; Zhan, Meng; Kurths, Jürgen
2017-06-01
When in an ensemble of oscillatory units the interaction occurs through a diffusion-like manner, the intrinsic oscillations can be quenched through two structurally different scenarios: amplitude death (AD) and oscillation death (OD). Unveiling the underlying principles of stable rhythmic activity against AD and OD is a challenging issue of substantial practical significance. Here, by developing a low-pass filter (LPF) to track the output signals of the local system in the coupling, we show that it can revoke both AD and OD, and even the AD to OD transition, thereby giving rise to oscillations in coupled nonlinear oscillators under diverse death scenarios. The effectiveness of the local LPF is proven to be valid in an arbitrary network of coupled oscillators with distributed propagation delays. The constructive role of the local LPF in revoking deaths provides a potential dynamic mechanism of sustaining a reliable rhythmicity in real-world systems.
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
NASA Astrophysics Data System (ADS)
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-12-01
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
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
NASA Astrophysics Data System (ADS)
Rhén, Christin; Isacsson, Andreas
2017-09-01
By numerical integration, we study the relaxation dynamics of degenerate harmonic oscillator modes dispersively coupled to particle positions. Depending on whether the effective inertial potential induced by the oscillators keeps the particles confined or if the particle trajectories traverse the system, the local oscillator energy dissipation rate changes drastically. The inertial trapping, release, and retrapping of particles result in a characteristic stepwise relaxation process, with alternating regions of fast and slow dissipation. To demonstrate this phenomenon we consider first a one-dimensional minimal prototype model which displays these characteristics. We then treat the effect of dispersive interaction in a model corresponding to an adsorbate diffusing on a circular membrane interacting with its three lowest vibrational modes. In the latter model, stepwise relaxation appears only in the presence of thermal noise, which also causes a slow-in-time stochastic precession of the mixing angle between the degenerate eigenmodes.
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.
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.
Coupling between ion-acoustic waves and neutrino oscillations.
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2017-01-01
The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a nonrelativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernova parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.
Coupling between ion-acoustic waves and neutrino oscillations
NASA Astrophysics Data System (ADS)
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2017-01-01
The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a nonrelativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernova parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.
Weak chimeras in minimal networks of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Ashwin, Peter; Burylko, Oleksandr
2015-01-01
We suggest a definition for a type of chimera state that appears in networks of indistinguishable phase oscillators. Defining a "weak chimera" as a type of invariant set showing partial frequency synchronization, we show that this means they cannot appear in phase oscillator networks that are either globally coupled or too small. We exhibit various networks of four, six, and ten indistinguishable oscillators, where weak chimeras exist with various dynamics and stabilities. We examine the role of Kuramoto-Sakaguchi coupling in giving degenerate (neutrally stable) families of weak chimera states in these example networks.
The vertical oscillations of coupled magnets
NASA Astrophysics Data System (ADS)
Kewei, Li; Jiahuang, Lin; Yang, Kang Zi; Liang, Samuel Yee Wei; Wong Say Juan, Jeremias
2011-07-01
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
Energetics of synchronization in coupled oscillators rotating on circular trajectories
NASA Astrophysics Data System (ADS)
Izumida, Yuki; Kori, Hiroshi; Seifert, Udo
2016-11-01
We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.
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.
Heatwole, Eric; Prezhdo, Oleg V
2007-05-28
A conceptually simple approximation to quantum mechanics, quantized Hamilton dynamics (QHD) includes zero-point energy, tunneling, dephasing, and other important quantum effects in a classical-like description. The hierarchy of coupled differential equations describing the time evolution of observables in QHD can be mapped in the second order onto a classical system with double the dimensionality of the original system. While QHD excels at dynamics with a single initial condition, the correct method for generating thermal initial conditions in QHD remains an open question. Using the coherent state representation of thermodynamics of the harmonic oscillator (HO) [Schnack, Europhys. Lett. 45, 647 (1999)], we develop canonical averaging for the second order QHD [Prezhdo, J. Chem. Phys. 117, 2995 (2002)]. The methodology is exact for the free particle and HO, and shows good agreement with quantum results for a variety of quartic potentials.
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 Harmonic Bases for Longitudinal Characterization of Brain Networks
Hwang, Seong Jae; Adluru, Nagesh; Collins, Maxwell D.; Ravi, Sathya N.; Bendlin, Barbara B.; Johnson, Sterling C.; Singh, Vikas
2016-01-01
There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection. The scientific interest is in characterizing the evolution of these graphs over time or from healthy individuals to diseased. We pose this important question in terms of the Laplacian of the connectivity graphs derived from various longitudinal or disease time points — quantifying its progression is then expressed in terms of coupling the harmonic bases of a full set of Laplacians. We derive a coupled system of generalized eigenvalue problems (and corresponding numerical optimization schemes) whose solution helps characterize the full life cycle of brain connectivity evolution in a given dataset. Finally, we show a set of results on a diffusion MR imaging dataset of middle aged people at risk for Alzheimer’s disease (AD), who are cognitively healthy. In such asymptomatic adults, we find that a framework for characterizing brain connectivity evolution provides the ability to predict cognitive scores for individual subjects, and for estimating the progression of participant’s brain connectivity into the future. PMID:27812274
Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks.
Hwang, Seong Jae; Adluru, Nagesh; Collins, Maxwell D; Ravi, Sathya N; Bendlin, Barbara B; Johnson, Sterling C; Singh, Vikas
2016-01-01
There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection. The scientific interest is in characterizing the evolution of these graphs over time or from healthy individuals to diseased. We pose this important question in terms of the Laplacian of the connectivity graphs derived from various longitudinal or disease time points - quantifying its progression is then expressed in terms of coupling the harmonic bases of a full set of Laplacians. We derive a coupled system of generalized eigenvalue problems (and corresponding numerical optimization schemes) whose solution helps characterize the full life cycle of brain connectivity evolution in a given dataset. Finally, we show a set of results on a diffusion MR imaging dataset of middle aged people at risk for Alzheimer's disease (AD), who are cognitively healthy. In such asymptomatic adults, we find that a framework for characterizing brain connectivity evolution provides the ability to predict cognitive scores for individual subjects, and for estimating the progression of participant's brain connectivity into the future.
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.
Probing Phase Coupling Between Two Spin-Torque Nano-Oscillators with an External Source
NASA Astrophysics Data System (ADS)
Li, Yi; de Milly, Xavier; Abreu Araujo, Flavio; Klein, Olivier; Cros, Vincent; Grollier, Julie; de Loubens, Grégoire
2017-06-01
Phase coupling between auto-oscillators is central for achieving coherent responses such as synchronization. Here we present an experimental approach to probe it in the case of two dipolarly coupled spin-torque vortex nano-oscillators using an external microwave field. By phase locking one oscillator to the external source, we observe frequency pulling on the second oscillator. From coupled phase equations we show analytically that this frequency pulling results from concerted actions of oscillator-oscillator and source-oscillator couplings. The analysis allows us to determine the strength and phase shift of coupling between two oscillators, yielding important information for the implementation of large interacting oscillator networks.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
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
Santos, Marcelo França
2005-07-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state.
Amplitude death induced by fractional derivatives in nonlinear coupled oscillators
NASA Astrophysics Data System (ADS)
Liu, Q. X.; Liu, J. K.; Chen, Y. M.
2017-07-01
This paper presents a study on amplitude death in nonlinear coupled oscillators containing fractional derivatives. Analytical criterion for amplitude death region is obtained by eigenvalue analysis and verified by numerical results. It is found that amplitude death regions can be enlarged to a large extent by fractional derivatives. For this reason, amplitude death can be detected in fractional Stuart-Landau systems with weak coupling strength and low frequency, whereas it never appears in integer-order systems. Interestingly, the widening of amplitude death region induced by fractional derivative is shared by a variety of oscillators with different types of coupling mechanisms. An interpretation for the underlying mechanism of this phenomenon is briefly addressed, based on which we further suggest a coupling organization leading to amplitude death only in fractional oscillators.
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.
Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise
NASA Astrophysics Data System (ADS)
Zhong, Suchuan; Yang, Jianqiang; Zhang, Lu; Ma, Hong; Luo, Maokang
2017-02-01
The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.
RESONANT HARMONIC GENERATION AND NONLINEAR OPTICS.
OSCILLATORS, *QUANTUM THEORY, *OPTICS, HARMONIC GENERATORS, OSCILLATORS, HARMONIC GENERATORS, OSCILLATORS, HARMONIC GENERATORS, NONLINEAR SYSTEMS, QUARTZ, TOURMALINE , ZINC COMPOUNDS, OXIDES, HYDRATES, NIOBATES, TENSOR ANALYSIS.
Beam splitter coupled CDSE optical parametric oscillator
Levinos, Nicholas J.; Arnold, George P.
1980-01-01
An optical parametric oscillator is disclosed in which the resonant radiation is separated from the pump and output radiation so that it can be manipulated without interfering with them. Thus, for example, very narrow band output may readily be achieved by passing the resonant radiation through a line narrowing device which does not in itself interfere with either the pump radiation or the output radiation.
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.
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-01-01
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129
Comment on 'Wave functions of a time-dependent harmonic oscillator in a static magnetic field'
Maamache, M.; Bounames, A.; Ferkous, N.
2006-01-15
We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant I(t) they derived does not satisfy the Liouville-Von Neuman equation. (ii) They found that the eigenvalues of I(t) are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schroedinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
NASA Technical Reports Server (NTRS)
Kazansky, A. K.; Ostrovsky, Valentin N.
1995-01-01
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
NASA Astrophysics Data System (ADS)
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
2016-10-01
Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential.
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-12-06
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
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.
Bohr Hamiltonian with an energy dependent γ-unstable harmonic oscillator potential
NASA Astrophysics Data System (ADS)
Budaca, Radu
2017-01-01
A new exactly solvable collective solution is realized by inducing a linear energy dependence in the γ-unstable harmonic oscillator potential of the Bohr Hamiltonian and taking the asymptotic limit of the slope parameter. The model preserves the degeneracy features of the U(5) dynamical symmetry but with an expanded energy spectrum and with damped B(E2) rates. The phenomenological interpretation of the model is investigated in comparison to the spherical vibrator collective conditions by means of particular features of the corresponding ground state. Three experimental candidates for the new parameter free model are identified and extensively confronted with the theoretical predictions.
An Agile Beam Transmit Array Using Coupled Oscillator Phase Control
NASA Technical Reports Server (NTRS)
Pogorzelski, Ronald S.; Scaramastra, Rocco P.; Huang, John; Beckon, Robert J.; Petree, Steve M.; Chavez, Cosme
1993-01-01
A few years ago York and colleagues suggested that injection locking of voltage controlled oscillators could be used to implement beam steering in a phased array [I]. The scheme makes use of the fact that when an oscillator is injection locked to an external signal, the phase difference between the output of the oscillator and the injection signal is governed by the difference between the injection frequency and the free running frequency of the oscillator (the frequency to which the oscillator is tuned). Thus, if voltage controlled oscillators (VCOs) are used, this phase difference is controlled by an applied voltage. Now, if a set of such oscillators are coupled to nearest neighbors, they can be made to mutually injection lock and oscillate as an ensemble. If they are all tuned to the same frequency, they will all oscillate in phase. Thus, if the outputs are connected to radiating elements forming a linear array, the antenna will radiate normal to the line of elements. Scanning is accomplished by antisymmetrically detuning the end oscillators in the array by application of a pair of appropriate voltages to their tuning ports. This results in a linear phase progression across the array which is just the phasing required to scan the beam. The scan angle is determined by the degree of detuning. We have constructed a seven element one dimensional agile beam array at S-band based on the above principle. Although, a few such arrays have been built in the past, this array possesses two unique features. First, the VCO MMICs have buffer amplifiers which isolate the output from the tuning circuit, and second, the oscillators are weakly coupled to each other at their resonant circuits rather than their outputs. This results in a convenient isolation between the oscillator array design and the radiating aperture design. An important parameter in the design is the so called coupling phase which determines the phase shift of the signals passing from one oscillator to its
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators.
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-03-10
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.
The sojourn time of the inverted harmonic oscillator on the noncommutative plane
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Ren, Zhong-Zhou; Ju, Guo-Xing; Long, Chao-Yun
2011-10-01
The sojourn time of the Gaussian wavepacket that is stationed at the center of the inverted harmonic oscillator is investigated on the noncommutative plane in detail. In ordinary commutative space quantum mechanics, the sojourn time of the Gaussian wavepacket is always a monotonically decreasing function of the curvature parameter ω of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of ω with a minimum at an inflection point ω0. Furthermore, if ω is larger than a certain critical value the sojourn time will become infinity. Thus, the ordinary intuitive physical picture about the relation between the sojourn time and the shape of the inverted oscillator potential is changed when the spatial noncommutativity is considered.
NASA Astrophysics Data System (ADS)
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
Ultra-light and strong: The massless harmonic oscillator and its singular path integral
NASA Astrophysics Data System (ADS)
Modanese, Giovanni
2017-09-01
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes completely de-localized in the limit m → 0. The harmonic oscillator thus ceases to be a useful microscopic physical model in the limit m → 0, but its Feynman path integral has interesting singularities which make it a prototype of other systems exhibiting a “quantum runaway” from the classical configurations near the minimum of the action. The probability density of the coherent runaway modes can be obtained as the solution of a Fokker-Planck equation associated to the condition S = Smin. This technique can be applied also to other systems, notably to a dimensional reduction of the Einstein-Hilbert action.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
A time-discrete harmonic oscillator model of human car-following
NASA Astrophysics Data System (ADS)
Wagner, P.
2011-12-01
A time-discrete stochastic harmonic oscillator is presented as a model of human car-following behaviour. This describes especially the non-continuous control of a human driver - acceleration changes from time to time at so called action-points and is kept constant in between. Analytical results can be derived which allow to classify the different types of motion possible within this approach. These results show that with weaker control by the human, unstable behaviour of the oscillator becomes more likely. This is in line with common understanding about the causes of accidents. Finally, since even the stochastic behaviour of this model is in parts analytically tractable, the width of the speed-difference and distance fluctuations can be expressed as function of the model's parameter. This allows a fresh view on empirical car-following data and the identification of parameters from real data in the context of the theory presented here.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-01-01
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962
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.
Irregular behaviors of two chemical oscillators with a diffusion coupling
NASA Astrophysics Data System (ADS)
Miyakawa, Kenji; Okabe, Tadao; Sakamoto, Fumitaka
1997-02-01
Dynamic behaviors of two chemical oscillators coupled with a time delay were investigated at the border between regions of 1:1 and 2:1 entrainment. Chemical oscillators were realized by immersing cation exchange beads loaded with the ferroin catalyst in the Belousov-Zabotinskii reaction solution. On decreasing the distance d between two oscillators, subharmonic entrainment at commensurate frequency ratios such as 2:1, 3:2, and 4:3 occurred in that order. When d was further decreased, an irregular behavior was observed in the slower oscillator near the coupling region of 1:1. The time series for these states were characterized in terms of their power spectra, reconstructed attractors, and the largest Lyapunov exponent to confirm the feature of chaos.
NASA Astrophysics Data System (ADS)
Yu, Da-ren; Wei, Li-qiu; Ding, Yong-jie; Han, Ke; Yan, Guo-jun; Qi, Feng-yan
2007-11-01
In order to study the physical mechanism of an oscillation newly discovered by the Harbin Institute of Technology Plasma Propulsion Lab (HPPL) in the range of hundreds of kHz to several MHz, Hall thrusters with different magnetic coils are studied by changing one of the following three parameters: discharge voltage, anode flow and coil current, directly measuring the coil current and measuring plasma oscillations related to coil current oscillation with the Langmuir probe. Experimental results indicated that in the discharge process of a Hall thruster the broadband turbulence of the Hall current causes an unstable spatial magnetic field and this field causes the magnetic circuit to resonate as an equivalent high level resistance-inductance-capacitance (RLC) network. As the response of the network, the oscillation of the coil current has a large oscillating component at the natural frequencies of the network. Also, the oscillation of coil current has an effect on the discharge process at the same time, so that they reach a self-consistent equilibrium state. As a result of such a coupling, both coil current and the discharge current exhibit their oscillating component at the natural frequencies of the magnetic circuit. It is therefore concluded that the newly discovered oscillation is caused by the coupling between the magnetic circuit and the discharge circuit.
Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators.
Ashwin, Peter; Borresen, Jon
2004-08-01
We study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators. These slow oscillations are due to the appearance of structurally stable heteroclinic connections between cluster states in the noise-free dynamics. In the presence of low levels of noise they give rise to long periods of residence near cluster states interspersed with sudden transitions between them. Moreover, these transitions may occur between cluster states of the same symmetry, or between cluster states with conjugate symmetries given by some rearrangement of the oscillators. We consider the system of coupled phase oscillators studied by Hansel et al. [Phys. Rev. E 48, 3470 (1993)] in which one can observe slow, noise-driven oscillations that occur between two families of two cluster periodic states; in the noise-free case there is a robust attracting heteroclinic cycle connecting these families. The two families consist of symmetric images of two inequivalent periodic orbits that have the same symmetry. For N=5 oscillators, one of the periodic orbits has one unstable direction and the other has two unstable directions. Examining the behavior on the unstable manifold for the two unstable directions, we observe that the dimensionality of the manifold can give rise to switching between conjugate symmetry orbits. By applying small perturbations to the system we can easily steer it between a number of different marginally stable attractors. Finally, we show that similar behavior occurs in a system of phase-energy oscillators that are a natural extension of the phase model to two dimensional oscillators. We suggest that switching between conjugate symmetries is a very efficient method of encoding information into a globally coupled system of oscillators and may therefore be a good and simple model for the neural encoding of information.
Solvable model for chimera states of coupled oscillators.
Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A
2008-08-22
Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators
NASA Astrophysics Data System (ADS)
Guin, A.; Dandapathak, M.; Sarkar, S.; Sarkar, B. C.
2017-01-01
We have studied the dynamics of two bilaterally-coupled non-oscillatory Rayleigh-Duffing oscillators (RDOs). With the increase of coupling factor (CF) between RDOs, birth of periodic oscillations observed. For increased values of CF, dynamics becomes chaotic through a quasi-periodicroute but for even higher CF, synchronized stable periodic oscillations in RDOs are found. Taking direct and anti-diffusive coupling cases into consideration, we derive conditions for periodic bifurcation in parameter space analytically and verified them through numerical solution of system equations. Numerical simulation is also used to predict system states in two parameter space involving CF and linear damping parameter of RDOs. It indicates non-oscillatory, periodic, quasi-periodic and chaotic zones of system dynamics. Qualitative explanation of the simulated dynamics is given using homoclinic perturbation theory. Hardware experiment is performed on analog circuits simulating RDO model and obtained results confirm the predictions regarding birth of periodic oscillation and other features of system dynamics. Experimental results examining onset of oscillations in two under-biased bi-laterally coupled X-band Gunn oscillators (which are modelled as RDOs) is presented in support of the analysis.
Link weight evolution in a network of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Ke, Hua; Tinsley, Mark R.; Steele, Aaron; Wang, Fang; Showalter, Kenneth
2014-05-01
Link weight evolution is studied in a network of coupled chemical oscillators. Oscillators are perturbed by adjustments in imposed light intensity based on excitatory or inhibitory links to other oscillators undergoing excitation. Experimental and modeling studies demonstrate that the network is capable of producing sustained coordinated activity. The individual nodes of the network exhibit incoherent firing events; however, a dominant frequency can be discerned within the collective signal by Fourier analysis. The introduction of spike-timing-dependent plasticity yields a network that evolves to a stable unimodal link weight distribution.
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
2017-04-01
In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ < α ≤ 2) or non-integer (α^{*} ≠ α, - ∞ < α < 3) SF quantum number. We note that the potentials (V^{{(pl^{ * } )}}-SFPs and V^{{(α^{*} )}}-MSFPs), and forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.
Wang, Zhengxin; Duan, Zhisheng; Cao, Jinde
2012-03-01
This paper aims to investigate the synchronization problem of coupled dynamical networks with nonidentical Duffing-type oscillators without or with coupling delays. Different from cluster synchronization of nonidentical dynamical networks in the previous literature, this paper focuses on the problem of complete synchronization, which is more challenging than cluster synchronization. By applying an impulsive controller, some sufficient criteria are obtained for complete synchronization of the coupled dynamical networks of nonidentical oscillators. Furthermore, numerical simulations are given to verify the theoretical results.
Dynamical regimes of four oscillators with excitatory pulse coupling.
Safonov, Dmitry A; Klinshov, Vladimir V; Vanag, Vladimir K
2017-05-17
The dynamical regimes of four almost identical oscillators with pulsatile excitatory coupling have been studied theoretically with two models: a kinetic model of the Belousov-Zhabotinsky reaction and a phase-reduced model. Unidirectional coupling on a ring and all-to-all coupling have been considered. The time delay τ between the moments of a spike in one oscillator and a pulse perturbation of the other(s) plays a crucial role in the emergence of the dynamical modes, which are classified as regular, complex, and OS (oscillation-suppression)-modes. The regular modes, in which each oscillator gives only one spike during the period T, consist of the modes in which the period T is linearly dependent on τ and modes in which T is almost independent of τ. The τ-dependent and τ-independent modes alternate if τ increases. A unique sequence of modes observed at growing τ is the same for all types of connectivity and even for both excitatory and inhibitory coupling. For unidirectional coupling, the analytical dependence of T on τ is found for all regular modes. Multirhythmicity is observed at large values of the coupling strength Cex. The effect of small frequency dispersion (within a few percents) on the stability of the regular modes has been studied. Unusual modes like bursting or heteroclinic switching are found in narrow regions of the Cex-τ plane between the regular modes.
Control of coupled oscillator networks with application to microgrid technologies
Skardal, Per Sebastian; Arenas, Alex
2015-01-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions—a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself. PMID:26601231
Enhancing the stability of the synchronization of multivariable coupled oscillators
NASA Astrophysics Data System (ADS)
Sevilla-Escoboza, R.; Gutiérrez, R.; Huerta-Cuellar, G.; Boccaletti, S.; Gómez-Gardeñes, J.; Arenas, A.; Buldú, J. M.
2015-09-01
Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.
Control of coupled oscillator networks with application to microgrid technologies.
Skardal, Per Sebastian; Arenas, Alex
2015-08-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Clustering and phase synchronization in populations of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Cascallares, Guadalupe; Gleiser, Pablo M.
2015-10-01
In many species daily rhythms are endogenously generated by groups of coupled neurons that play the role of a circadian pacemaker. The adaptation of the circadian clock to environmental and seasonal changes has been proposed to be regulated by a dual oscillator system. In order to gain insight into this model, we analyzed the synchronization properties of two fully coupled groups of Kuramoto oscillators. Each group has an internal coupling parameter and the interaction between the two groups can be controlled by two parameters allowing for symmetric or non-symmetric coupling. We show that even for such a simple model counterintuitive behaviours take place, such as a global decrease in synchrony when the coupling between the groups is increased. Through a detailed analysis of the local synchronization processes we explain this behaviour.
Dynamics of phase oscillators with generalized frequency-weighted coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Gao, Jian; Xiang, Hairong; Jia, Wenjing; Guan, Shuguang; Zheng, Zhigang
2016-12-01
Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.
Chimera states in purely local delay-coupled oscillators.
Bera, Bidesh K; Ghosh, Dibakar
2016-05-01
We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.
Chimera states in purely local delay-coupled oscillators
NASA Astrophysics Data System (ADS)
Bera, Bidesh K.; Ghosh, Dibakar
2016-05-01
We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Plyushchay, Mikhail S.
2017-07-01
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.
NASA Astrophysics Data System (ADS)
Wang, Zhiguo; Liang, Zhenguo
2017-04-01
In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of the perturbation in [24] are weakened from polynomial decay to logarithmic decay. As a consequence, we can apply it to 1D quantum harmonic oscillators and prove the reducibility of the linear harmonic oscillator, T=-\\frac{{{\\text{d}}2}}{\\text{d}{{x}2}}+{{x}2} , on {{L}2}≤ft({R}\\right) perturbed by the quasi-periodic in the time potential V(x,ω t;ω ) with logarithmic decay. This proves the pure-point nature of the spectrum of the Floquet operator K, where K:=-i∑k=1nωk∂∂θk-d2dx2+x2+ɛV(x,θω) is defined on {{L}2}≤ft({R}\\right)\\otimes {{L}2}≤ft({{{T}}n}\\right) , and the potential V(x,θ ;ω ) has logarithmic decay as well as its gradient in ω.
Solving a fuzzy initial value problem of a harmonic oscillator model
NASA Astrophysics Data System (ADS)
Karim, M. A.; Gunawan, A. Y.; Apri, M.; Sidarto, K. A.
2017-03-01
Modeling in systems biology is often faced with challenges in terms of measurement uncertainty. This is possibly either due to limitations of available data, environmental or demographic changes. One of typical behavior that commonly appears in the systems biology is a periodic behavior. Since uncertainties would get involved into the systems, the change of solution behavior of the periodic system should be taken into account. To get insight into this issue, in this work a simple mathematical model describing periodic behavior, i.e. a harmonic oscillator model, is considered by assuming its initial value has uncertainty in terms of fuzzy number. The system is known as Fuzzy Initial Value Problems. Some methods to determine the solutions are discussed. First, solutions are examined using two types of fuzzy differentials, namely Hukuhara Differential (HD) and Generalized Hukuhara Differential (GHD). Application of fuzzy arithmetic leads that each type of HD and GHD are formed into α-cut deterministic systems, and then are solved by the Runge-Kutta method. The HD type produces a solution with increasing uncertainty starting from the initial condition. While, GHD type produces an oscillatory solution but only until a certain time and above it the uncertainty becomes monotonic increasing. Solutions of both types certainly do not provide the accuracy for harmonic oscillator model during its evolution. Therefore, we propose the third method, so called Fuzzy Differential Inclusions (FDI), to attack the problem. Using this method, we obtain oscillatory solutions during its evolution.
Persistent chimera states in nonlocally coupled phase oscillators
NASA Astrophysics Data System (ADS)
Suda, Yusuke; Okuda, Koji
2015-12-01
Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state.
Low dimensional behavior of large systems of globally coupled oscillators
NASA Astrophysics Data System (ADS)
Ott, Edward; Antonsen, Thomas M.
2008-09-01
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.
Phase space path integral approach to harmonic oscillator with a time-dependent force constant
NASA Astrophysics Data System (ADS)
Janakiraman, Deepika; Sebastian, K. L.
2015-09-01
The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, mω2(t) , has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Lévy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form ω2(t) =λ2(t) - dλ(t)/dt, where λ(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Lévy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction.
Coupled, Active Oscillators and Lizard Otoacoustic Emissions
NASA Astrophysics Data System (ADS)
Bergevin, Christopher; Velenovsky, David S.; Bonine, Kevin E.
2011-11-01
The present study empirically explores the relationship between spontaneous otoacoustic emissions (SOAEs) and stimulus-frequency emissions (SFOAEs) in lizards, an ideal group for such research given their relatively simple inner ear (e.g., lack of basilar membrane traveling waves), diverse morphology across species/families (e.g., tectorial membrane structure) and robust emissions. In a nutshell, our results indicate that SFOAEs evoked using low-level tones are intimately related to underlying SOAE activity, and appear to represent the entrained response of active oscillators closely tuned to the probe frequency. The data described here indicate several essential features that are desirable to capture in theoretical models for auditory transduction in lizards, and potentially represent generic properties at work in many different classes of "active" ears.
NASA Astrophysics Data System (ADS)
Nori, Franco; Ashhab, Sahel
2011-03-01
We consider a system composed of a two-level system (i.e. a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. We explore the possibility of preparing nonclassical states in this system, especially in the ground state of the combined system. The nonclassical states that we consider include squeezed states, Schrodinger-cat states and entangled states. We also analyze the nature of the change in the ground state as the coupling strength is increased, going from a separable ground state in the absence of coupling to a highly entangled ground state in the case of very strong coupling. Reference: S. Ashhab and F. Nori, Phys. Rev. A 81, 042311 (2010). We thank support from DARPA, AFOSR, NSA, LPS, ARO, NSF, MEXT, JSPS, FIRST, and JST.
Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D
NASA Astrophysics Data System (ADS)
Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.
2015-10-01
Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
Phase-lag synchronization in networks of coupled chemical oscillators.
Totz, Jan F; Snari, Razan; Yengi, Desmond; Tinsley, Mark R; Engel, Harald; Showalter, Kenneth
2015-08-01
Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-04-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems--e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects of finite sampling rate and sampling time for these models as well. ©2011 American Physical Society
Coupling among three chemical oscillators: Synchronization, phase death, and frustration
NASA Astrophysics Data System (ADS)
Yoshimoto, Minoru; Yoshikawa, Kenichi; Mori, Yoshihito
1993-02-01
Various modes in three coupled chemical oscillators in a triangular arrangement were observed. As a well-defined nonlinear oscillator, the Belousov-Zhabotinsky reaction was studied in a continuous-flow stirred tank reactor (CSTR). Coupling among CSTR's was performed by mass exchange. The coupling strength was quantitatively controlled by changing the flow rate of reacting solutions among the three CSTR's using peristaltic pumps between each pair of the reactors. As a key parameter to control the model of coupling, we changed the symmetry of the interaction between the oscillators. In the case of the symmetric coupling, a quasiperiodic state or a biperiodic mode, an all-death mode and two kinds of synchronized modes appeared, depending on the coupling strength. On the other hand, under the asymmetric coupling, a quasiperiodic state or a biperiodic mode, an all death mode and four kinds of synchronized modes appeared. Those modes have been discussed in relation to the idea of ``frustration'' in the Ising spin system, where the three-phase mode appears as a transition from the Ising spin system to the XY spin system.
Dynamics of learning in coupled oscillators tutored with delayed reinforcements
NASA Astrophysics Data System (ADS)
Trevisan, M. A.; Bouzat, S.; Samengo, I.; Mindlin, G. B.
2005-07-01
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.
Dynamics of learning in coupled oscillators tutored with delayed reinforcements.
Trevisan, M A; Bouzat, S; Samengo, I; Mindlin, G B
2005-07-01
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.
NASA Astrophysics Data System (ADS)
Proskurkin, I. S.; Vanag, V. K.
2015-02-01
Resonance regimes of two frequency different chemical oscillators coupled via pulsed inhibitory coupling with time delay τ have been studied theoretically and experimentally. The Belousov-Zhabotinsky reaction is used as a chemical oscillator. Regions of the 1: 1, 2: 3, 1: 2, 2: 5, and 1: 3 resonances, as well as complex oscillations and a regime in which one oscillator is suppressed have been found in the parameter plane "the ratio between the T 2/ T 1-τ." For the 1: 2 resonance, a sharp transition from one synchronized regime (called "0/0.5") to the other one (called "0.2/0.7") has been found. This transition (reminiscent to the transition between in-phase and anti-phase oscillations in case of the 1: 1 resonance) is controlled by time delay τ and the coupling strength.
A generalized harmonic balance method for forced non-linear oscillations: the subharmonic cases
NASA Astrophysics Data System (ADS)
Wu, J. J.
1992-12-01
This paper summarizes and extends results in two previous papers, published in conference proceedings, on a variant of the generalized harmonic balance method (GHB) and its application to obtain subharmonic solutions of forced non-linear oscillation problems. This method was introduced as an alternative to the method of multiple scales, and it essentially consists of two parts. First, the part of the multiple scales method used to reduce the problem to a set of differential equations is used to express the solution as a sum of terms of various harmonics with unknown, time dependent coefficients. Second, the form of solution so obtained is substituted into the original equation and the coefficients of each harmonic are set to zero. Key equations of approximations for a subharmonic case are derived for the cases of both "small" damping and excitations, and "Large" damping and excitations, which are shown to be identical, in the intended order of approximation, to those obtained by Nayfeh using the method of multiple scales. Detailed numerical formulations, including the derivation of the initial conditions, are presented, as well as some numerical results for the frequency-response relations and the time evolution of various harmonic components. Excellent agreement is demonstrated between results by GHB and by integrating the original differential equation directly. The improved efficiency in obtaining numerical solutions using GHB as compared with integrating the original differential equation is demonstrated also. For the case of large damping and excitations and for non-trivial solutions, it is noted that there exists a threshold value of the force beyond which no subharmonic excitations are possible.
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators.
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators
NASA Astrophysics Data System (ADS)
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures Th and Tc(
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.
Driben, R; Konotop, V V; Malomed, B A; Meier, T
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators
NASA Astrophysics Data System (ADS)
Driben, R.; Konotop, V. V.; Malomed, B. A.; Meier, T.
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3 +3 harmonic-oscillator p -wave eigenfunctions with orbital and magnetic quantum numbers l =1 and m =1 , 0, -1 . The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l =1 .
NASA Technical Reports Server (NTRS)
Defacio, B.; Vannevel, Alan; Brander, O.
1993-01-01
A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
NASA Astrophysics Data System (ADS)
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
2005-11-01
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.
Coupling of radial and nonradial oscillations of relativistic stars: Gauge-invariant formalism
NASA Astrophysics Data System (ADS)
Passamonti, Andrea; Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F.
2005-01-01
Linear perturbation theory is appropriate to describe small oscillations of stars, while a mild nonlinearity is still tractable perturbatively but requires one to consider mode coupling, i.e., to take into account second order effects. It is natural to start to look at this problem by considering the coupling between linear radial and nonradial modes. A radial pulsation may be thought of as an important component of an overall mildly nonlinear oscillation, e.g., of a protoneutron star. Radial pulsations of spherical compact objects do not per se emit gravitational waves but, if the coupling between the existing first order radial and nonradial modes is efficient in driving and possibly amplifying the nonradial oscillations, one may expect the appearance of nonlinear harmonics, and gravitational radiation could then be produced to a significant level. More in general, mode coupling typically leads to an interesting phenomenology, thus it is worth investigating in the context of star perturbations. In this paper we develop the relativistic formalism to study the coupling of radial and nonradial first order perturbations of a compact spherical star. From a mathematical point of view, it is convenient to treat the two sets of perturbations as separately parametrized, using a 2-parameter perturbative expansion of the metric, the energy-momentum tensor and Einstein equations in which λ is associated with the radial modes, ɛ with the nonradial perturbations, and the λɛ terms describe the coupling. This approach provides a well-defined framework to consider the gauge dependence of perturbations, allowing us to use ɛ order gauge-invariant nonradial variables on the static background and to define new second order λɛ gauge-invariant variables representing the result of the nonlinear coupling. We present the evolution and constraint equations for our variables outlining the setup for numerical computations, and briefly discuss the surface boundary conditions in terms
Experimental Evidence on Intermittent Lag Synchronization in Coupled Chua's Oscillators
NASA Astrophysics Data System (ADS)
Roy, P. K.; Dana, S. K.
2003-08-01
Phase synchronization (PS) in coupled chaotic oscillators has been investigated numerically in Lorenz, Rossler models and also experimentally in cardiorespiratory systems by many researchers. In non-identical oscillators, which is a reality, complete synchronization (CS) of amplitude and phase is difficult to arrive at. Lag synchronization (LS) is an intermediate step between complete (CS) and PS. PS shows promises in communication, in the context of pulse position modulation, in homoclinic chaotic systems. As has been observed earlier by others in numerical experiments that there is an intermittent region between PS and LS. This intermediate region is defined as the intermittent lag synchronization (ILS). Experimental evidence on both PS and ILS using two coupled Chua's oscillator (non-identical) is reported here.
Internal wave--vorticity coupling for an oscillating disk
NASA Astrophysics Data System (ADS)
Voisin, Bruno; Joubaud, Sylvain; Dauxois, Thierry
2011-11-01
In a density-stratified fluid, viscosity couples internal waves with vertical vorticity. So far this coupling used to be neglected in analytical studies and only the viscous attenuation and spreading of the waves was taken into account, except in a very recent study of the oscillations of a horizontal circular disk. We investigate the relations between the previous analytical approaches of the disk, considering either inviscid or viscous propagation of the waves and either free- or no-slip conditions at the disk, and compare their output with an original approach based on the boundary integral method. In particular, the role of the Stokes number is clarified. The analytical predictions are compared with contact measurements for vertical oscillations and with original PIV measurements and visualizations for both vertical and horizontal oscillations. Supported by grant PIWO of the ANR (France).
Raman-Suppressing Coupling for Optical Parametric Oscillator
NASA Technical Reports Server (NTRS)
Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Rubiola, Enrico
2007-01-01
A Raman-scattering-suppressing input/ output coupling scheme has been devised for a whispering-gallery-mode optical resonator that is used as a four-wave-mixing device to effect an all-optical parametric oscillator. Raman scattering is undesired in such a device because (1) it is a nonlinear process that competes with the desired nonlinear four-wave conversion process involved in optical parametric oscillation and (2) as such, it reduces the power of the desired oscillation and contributes to output noise. The essence of the present input/output coupling scheme is to reduce output loading of the desired resonator modes while increasing output loading of the undesired ones.
String-Coupled Pendulum Oscillators: Theory and Experiment.
ERIC Educational Resources Information Center
Moloney, Michael J.
1978-01-01
A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)
Dynamics of finite-size networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Buice, Michael; Chow, Carson
2010-03-01
Mean field models of coupled oscillators do not adequately capture the dynamics of large but finite size networks. For example, the incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model. We also demonstrate this approach with a system of pulse coupled theta neurons and describe the stability of the population activity.
Golden Ratio in a Coupled-Oscillator Problem
ERIC Educational Resources Information Center
Moorman, Crystal M.; Goff, John Eric
2007-01-01
The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.
Dynamics of globally coupled oscillators: Progress and perspectives
NASA Astrophysics Data System (ADS)
Pikovsky, Arkady; Rosenblum, Michael
2015-09-01
In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.
String-Coupled Pendulum Oscillators: Theory and Experiment.
ERIC Educational Resources Information Center
Moloney, Michael J.
1978-01-01
A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)
Synchronizing large number of nonidentical oscillators with small coupling
NASA Astrophysics Data System (ADS)
Wu, Ye; Xiao, Jinghua; Hu, Gang; Zhan, Meng
2012-02-01
The topic of synchronization of oscillators has attracted great and persistent interest, and all previous conclusions and intuitions have convinced that large coupling is required for synchronizing a large number of coupled nonidentical oscillators. Here the influences of different spatial frequency distributions on the efficiency of frequency synchronization are investigated by studying arrays of coupled oscillators with diverse natural frequency distributions. A universal log-normal distribution of critical coupling strength Kc for synchronization irrespective of the initial natural frequency is found. In particular, a physical quantity "roughness"R of spatial frequency configuration is defined, and it is found that the efficiency of synchronization increases monotonously with R. For large R we can reach full synchronization of arrays with a large number of oscillators at finite Kc. Two typical kinds of synchronization, the "multiple-clustering" one and the "single-center-clustering" one, are identified for small and large R's, respectively. The mechanism of the latter type is the key reason for synchronizing long arrays with finite Kc.
Golden Ratio in a Coupled-Oscillator Problem
ERIC Educational Resources Information Center
Moorman, Crystal M.; Goff, John Eric
2007-01-01
The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.
Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers.
Sei, Norihiro; Ogawa, Hiroshi; Okuda, Shuichi
2017-09-01
The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions.
Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers
Ogawa, Hiroshi; Okuda, Shuichi
2017-01-01
The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions. PMID:28862612
Wu, Wei; Chen, Tianping
2009-12-01
Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.
Cold atoms coupled with mechanical oscillators
NASA Astrophysics Data System (ADS)
Valencia, Jose; Montoya, Cris; Ranjit, Gambhir; Geraci, Andrew; Eardley, Matt; Kitching, John
2015-05-01
Mechanical resonators can be used to probe and manipulate atomic spins with nanometer spatial resolution and single-spin sensitivity, ultimately enabling new approaches in neutral-atom quantum computation, quantum simulation, or precision sensing. We describe our experiment that manipulates the spin of trapped, cold Rb atoms using magnetic material on a cantilever. Cold atoms can also be used as a coolant for mechanical resonators: we estimate that ground state cooling of an optically trapped nano-sphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle.
Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator
Martens, Craig C.
2013-07-14
In this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a two-state quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a well-defined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the off-diagonal density matrix element of the quantum system are derived in the second-order cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in many-body quantum systems.
Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator.
Martens, Craig C
2013-07-14
In this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a two-state quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a well-defined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the off-diagonal density matrix element of the quantum system are derived in the second-order cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in many-body quantum systems.
Casimir friction force and energy dissipation for moving harmonic oscillators. II
NASA Astrophysics Data System (ADS)
Høye, J. S.; Brevik, I.
2011-01-01
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)]). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is finite at finite temperatures, whereas in the case of two oscillators moving with constant relative velocity the force becomes zero at zero temperature, due to slowly varying coupling.
Revised calculation of four-particle harmonic-oscillator transformation brackets matrix
NASA Astrophysics Data System (ADS)
Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.
2013-02-01
In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C. T.; Schouten, Alfred C.
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15–35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback. PMID:27999537
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion.
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C T; Schouten, Alfred C
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15-35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.
Three People Can Synchronize as Coupled Oscillators during Sports Activities
Yokoyama, Keiko; Yamamoto, Yuji
2011-01-01
We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R) in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA) in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter. PMID:21998570
Three people can synchronize as coupled oscillators during sports activities.
Yokoyama, Keiko; Yamamoto, Yuji
2011-10-01
We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R) in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA) in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter.
Speech encoding by coupled cortical theta and gamma oscillations
Hyafil, Alexandre; Fontolan, Lorenzo; Kabdebon, Claire; Gutkin, Boris; Giraud, Anne-Lise
2015-01-01
Many environmental stimuli present a quasi-rhythmic structure at different timescales that the brain needs to decompose and integrate. Cortical oscillations have been proposed as instruments of sensory de-multiplexing, i.e., the parallel processing of different frequency streams in sensory signals. Yet their causal role in such a process has never been demonstrated. Here, we used a neural microcircuit model to address whether coupled theta–gamma oscillations, as observed in human auditory cortex, could underpin the multiscale sensory analysis of speech. We show that, in continuous speech, theta oscillations can flexibly track the syllabic rhythm and temporally organize the phoneme-level response of gamma neurons into a code that enables syllable identification. The tracking of slow speech fluctuations by theta oscillations, and its coupling to gamma-spiking activity both appeared as critical features for accurate speech encoding. These results demonstrate that cortical oscillations can be a key instrument of speech de-multiplexing, parsing, and encoding. DOI: http://dx.doi.org/10.7554/eLife.06213.001 PMID:26023831
Lozano-Soldevilla, Diego; ter Huurne, Niels; Oostenveld, Robert
2016-01-01
Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (>40 Hz) occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC). However, the CFC patterns might be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 or 1.5 mg of lorazepam (LZP; GABAergic enhancer) in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM), we were able to demonstrate that posterior alpha (8–12 Hz) phase was coupled to beta-low gamma band (20–45 Hz) amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh) values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD). Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs. Furthermore, we
Coherence of mechanical oscillators mediated by coupling to different baths
NASA Astrophysics Data System (ADS)
Boyanovsky, Daniel; Jasnow, David
2017-07-01
We study the nonequilibrium dynamics of two mechanical oscillators with general linear couplings to two uncorrelated thermal baths at temperatures T1 and T2, respectively. We obtain the complete solution of the Heisenberg-Langevin equations, which reveal a coherent mixing among the normal modes of the oscillators as a consequence of their off-diagonal couplings to the baths. Unique renormalization aspects resulting from this mixing are discussed. Diagonal and off-diagonal (coherence) correlation functions are obtained analytically in the case of strictly Ohmic baths with different couplings in the strong- and weak-coupling regimes. An asymptotic nonequilibrium stationary state emerges for which we obtain the complete expressions for the correlations and coherence. Remarkably, the coherence survives in the high-temperature, classical limit for T1≠T2 . This is a consequence of the coherence being determined by the difference of the bath correlation functions. In the case of vanishing detuning between the oscillator normal modes both coupling to one and the same bath, the coherence retains memory of the initial conditions at long times. An out-of-equilibrium setup with small detuning and large | T1-T2| produces nonvanishing steady-state coherence in the high-temperature limit of the baths.
ERIC Educational Resources Information Center
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
ERIC Educational Resources Information Center
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
NASA Astrophysics Data System (ADS)
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
The quantum fidelity for the time-periodic singular harmonic oscillator
NASA Astrophysics Data System (ADS)
Combescure, Monique
2006-03-01
In this paper we perform an exact study of "quantum fidelity" (also called Loschmidt echo) for the time-periodic quantum harmonic oscillator of the following Hamiltonian: Ĥg(t)≔(P2/2)+f(t)(Q2/2)+(g2/Q2), when compared with the quantum evolution induced by Ĥ0(t) (g=0), in the case where f is a T-periodic function and g a real constant. The reference (initial) state is taken to be an arbitrary "generalized coherent state" in the sense of Perelomov. We show that, starting with a quadratic decrease in time in the neighborhood of t =0, this quantum fidelity may recur to its initial value 1 at an infinite sequence of times tk. We discuss the result when the classical motion induced by Hamiltonian Ĥ0(t) is assumed to be stable versus unstable.
Energy distribution of the quantum harmonic oscillator under random time-dependent perturbations.
Garnier, J
1999-10-01
This paper investigates the evolution of a quantum particle in a harmonic oscillator driven by time-dependent forces. The perturbations are small, but they act long enough so that we can solve the problem in the asymptotic framework corresponding to a perturbation amplitude that tends to zero and a perturbation duration that tends to infinity. We describe the effective evolution equation of the state vector, which reads as a stochastic partial differential equation. We exhibit a closed-form equation for the transition probabilities, which can be interpreted in terms of a jump process. Using standard probability tools, we are then able to compute explicitly the probabilities for observing the different energy eigenstates and give the exact statistical distribution of the energy of the particle.
Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator.
Carvalho, A R R; de Matos Filho, R L; Davidovich, L
2004-08-01
We discuss the roles of the macroscopic limit and different system-environment interactions in a quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the classical case to purely dissipative or purely diffusive behavior, a situation that can be implemented in ion trap experiments. In the dissipative case, we derive an expression for the time at which quantum and classical predictions become different (breaking time) and show that complete quantum-classical correspondence is not possible in the chaotic regime. For the diffusive environment we estimate the minimum value of the diffusion coefficient necessary to retrieve the classical limit and also show numerical evidence that, for diffusion below this threshold, the breaking time behaves, essentially, like that in the case of a system without a reservoir.
Structure of the harmonic oscillator in the space of n-particle Glauber correlators
NASA Astrophysics Data System (ADS)
Zubizarreta Casalengua, E.; López Carreño, J. C.; del Valle, E.; Laussy, F. P.
2017-06-01
We map the Hilbert space of the quantum harmonic oscillator to the space of Glauber's nth-order intensity correlators, in effect showing "the correlations between the correlators" for a random sampling of the quantum states. In particular, we show how the popular g(2) function is correlated to the mean population and how a recurrent criterion to identify single-particle states or emitters, namely, g ( 2 ) < 1 / 2 , actually identifies states with at most two particles on average. Our charting of the Hilbert space allows us to capture its structure in a simpler and physically more intuitive way that can be used to classify quantum sources by surveying which territory they can access.
Alternative descriptions of wave and particle aspects of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Schuch, Dieter
1993-01-01
The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.
NASA Astrophysics Data System (ADS)
Marengo, Edwin A.; Khodja, Mohamed R.
2006-09-01
The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.
LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator
NASA Astrophysics Data System (ADS)
Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen
2006-09-01
Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.
Some properties of an infinite family of deformations of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Quesne, Christiane
2010-12-01
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians Hk on the plane, depending on a positive real parameter k. Two algebraic extensions of Hk are described. The first one, based on the elements of the dihedral group D2k and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of Hk for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of Hk of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
NASA Astrophysics Data System (ADS)
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.