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Journal articles on the topic 'Harmonic oscillators'

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Published: 4 June 2021

Last updated: 29 July 2024

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1

Wang, Shijiao, Xiao San Ma, and Mu-Tian Cheng. "Multipartite Entanglement Generation in a Structured Environment." Entropy 22, no. 2 (February 7, 2020): 191. http://dx.doi.org/10.3390/e22020191.

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In this paper, we investigate the entanglement generation of n-qubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearest-neighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speed-up increase accompanied by some oscillations as non-Markovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.

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2

Dao, Nguyen Van. "Nonlinear oscillators under delay control." Vietnam Journal of Mechanics 21, no. 2 (June 30, 2000): 75–88. http://dx.doi.org/10.15625/0866-7136/9989.

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In this paper, oscillations and stability of nonlinear oscillators with time delay are studied by means of the asymptotic method of nonlinear mechanics. Harmonic, super harmonic, subharmonic and parametric resonances of a Duffing's oscillator are analyzed. Analytical method in combination with a computer is used.

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3

Zaitsev, Valery V., and Alexander V. Karlov. "Quasi-harmonic self-oscillations in discrete time: analysis and synthesis of dynamic systems." Physics of Wave Processes and Radio Systems 24, no. 4 (January 16, 2022): 19–24. http://dx.doi.org/10.18469/1810-3189.2021.24.4.19-24.

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For sampling of time in a differential equation of movement of Thomson type oscillator (generator) it is offered to use a combination of the numerical method of finite differences and an asymptotic method of the slowl-changing amplitudes. The difference approximations of temporal derivatives are selected so that, first, to save conservatism and natural frequency of the linear circuit of self-oscillatory system in the discrete time. Secondly, coincidence of the difference shortened equation for the complex amplitude of self-oscillations in the discrete time with Eulers approximation of the shortened equation for amplitude of self-oscillations in analog system prototype is required. It is shown that realization of such approach allows to create discrete mapping of the van der Pol oscillator and a number of mappings of Thomson type oscillators. The adequacy of discrete models to analog prototypes is confirmed with also numerical experiment.

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4

Pingak, Redi Kristian, Albert Zicko Johannes, Minsyahril Bukit, and Zakarias Seba Ngara. "Quantum Anharmonic Oscillators: A Truncated Matrix Approach." POSITRON 11, no. 1 (October 15, 2021): 9. http://dx.doi.org/10.26418/positron.v11i1.44369.

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This study aims at implementing a truncated matrix approach based on harmonic oscillator eigenfunctions to calculate energy eigenvalues of anharmonic oscillators containing quadratic, quartic, sextic, octic, and decic anharmonicities. The accuracy of the matrix method is also tested. Using this method, the wave functions of the anharmonic oscillators were written as a linear combination of some finite number of harmonic oscillator basis states. Results showed that calculation with 100 basis states generated accurate energies of oscillators with relatively small coupling constants, with computation time less than 1 minute. Including more basis states could result in more correct digits. For instance, using 300 harmonic oscillator basis states in a simple Mathematica code in about 8 minutes, highly accurate energies of the oscillators were obtained for relatively small coupling constants, with up to 15 correct digits. Reasonable accuracy was also found for much larger coupling constants with at least three correct digits for some low lying energies of the oscillators reported in this study. Some of our results contained more correct digits than other results reported in the literature.

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5

Irac-Astaud, Michèle, and Guy Rideau. "Bargmann Representations for Deformed Harmonic Oscillators." Reviews in Mathematical Physics 10, no. 08 (November 1998): 1061–78. http://dx.doi.org/10.1142/s0129055x98000343.

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Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators a, a†, N and the unity 1 such as [a,N]=a,[a†,N]=-a†,a†a=ψ(N) and aa†=ψ(N+1). We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the eigenstates of a (or a†). We give various examples, in particular we consider functions ψ that are linear combinations of qN, q-N and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations.

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6

Kovacic, Ivana, Matthew Cartmell, and Miodrag Zukovic. "Mixed-mode dynamics of certain bistable oscillators: behavioural mapping, approximations for motion and links with van der Pol oscillators." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (December 2015): 20150638. http://dx.doi.org/10.1098/rspa.2015.0638.

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This study is concerned with a new generalized mathematical model for single degree-of-freedom bistable oscillators with harmonic excitation of low-frequency, linear viscous damping and a restoring force that contains a negative linear term and a positive nonlinear term which is a power-form function of the generalized coordinate. Comprehensive numerical mapping of the range of bifurcatory behaviour shows that such non-autonomous systems can experience mixed-mode oscillations, including bursting oscillations (fast flow oscillations around the outer curves of a slow flow), and relaxation oscillations like a classical (autonomous) van der Pol oscillator. After studying the global system dynamics the focus of the investigations is on cubic oscillators of this type. Approximate techniques are presented to quantify their response, i.e. to determine approximations for both the slow and fast flows. In addition, a clear analogy between the behaviour of two archetypical oscillators—the non-autonomous bistable oscillator operating at low frequency and the strongly damped autonomous van der Pol oscillator—is established for the first time.

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7

Kühn, M. R., and E. M. Biebl. "First harmonic injection locking of 24-GHz-oscillators." Advances in Radio Science 1 (May 5, 2003): 197–200. http://dx.doi.org/10.5194/ars-1-197-2003.

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Abstract. An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz) is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.

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8

Dattoli, G., A. Torre, S. Lorenzutta, and G. Maino. "Coupled harmonic oscillators, generalized harmonic-oscillator eigenstates and coherent states." Il Nuovo Cimento B Series 11 111, no. 7 (July 1996): 811–23. http://dx.doi.org/10.1007/bf02749013.

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9

Cahaya, Adam Badra. "Radial wave function of 2D and 3D quantum harmonic oscillator." Al-Fiziya: Journal of Materials Science, Geophysics, Instrumentation and Theoretical Physics 5, no. 2 (June 4, 2023): 95–100. http://dx.doi.org/10.15408/fiziya.v5i2.26172.

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One dimensional quantum harmonic oscillator is well studied in elementary textbooks of quantum mechanics. The wave function of one-dimensional oscillator harmonic can be written in term of Hermite polynomial. Due to the symmetry of the spring energy, the wave functions of two-dimensional and three-dimensional harmonic oscillators can be written as products of the one-dimensional case. Because of that, the wave functions of two- and three-dimensional cases are focused on cartesian coordinates. In this article, we utilize polar and spherical coordinates to describe the wave function of two- and three-dimensional harmonic oscillators, respectively. The radial part of the wave functions can be written in term of associated Laguerre polynomials.

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10

Setiawan, Iwan, Mayasari Katrina Hutagalung, Nurhasanah Nurhasanah, and Dedy Hamdani. "Introduction to Quantum Harmonic Oscillator Material Using Discussion Method for Students of SMAN 5 Bengkulu City." DIKDIMAS : Jurnal Pengabdian Kepada Masyarakat 2, no. 1 (April 30, 2023): 165–69. http://dx.doi.org/10.58723/dikdimas.v2i1.94.

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The knowledge of the student about harmonic oscillators is quite limited. The purpose of this PPM is to 1) increase the knowledge of Bengkulu City 5 SMAN students about Quantum Harmonic Oscillators and their application in everyday life 2) improve the skills of Bengkulu City 5 High School students in calculating Quantum Harmonic Oscillators using the fast-forward method to accelerate quantum dynamics adiabatic. PPM was carried out at SMAN 5 Bengkulu City, especially in class 12 IPA 5 on October 24, 2022. The research method was carried out in three stages. The first stage is preparation. The second stage is the presentation of quantum harmonic oscillator material using research instruments in the form of power points, the third stage is research evaluation.

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11

Drs, Jakub, Michael Müller, Firas Trawi, Norbert Modsching, Valentin J. Wittwer, and Thomas Südmeyer. "Ultrafast thin-disk laser oscillators as driving sources for high harmonic generation." EPJ Web of Conferences 287 (2023): 08007. http://dx.doi.org/10.1051/epjconf/202328708007.

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Thin-disk laser oscillators can nowadays reach few tens of femtosecond pulses at gigawatt-level intracavity powers and megahertz-repetition rates becoming increasingly more powerful sources for intra-oscillator high harmonic generation (HHG). Currently, we can generate high harmonics in neon reaching photon energies of 70 eV, which we expect to increase toward 100 eV in the near future. In parallel, the achievable average and peak output powers of these oscillators in the range of 100 W and 100 MW, respectively, make these sources very promising to drive HHG in single-pass configuration after nonlinear pulse compression. Starting from transform-limited 30 to 50-fs soliton output soliton pulses of TDL oscillators, we will likely see these lasers approaching a single-cycle regime becoming highly attractive sources for attosecond science.

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12

Popov, I. P. "MATHEMATICAL MODELING OF A MULTI-INERT OSCILLATORY MECHANISM." Bulletin of the South Ural State University series "Mechanical Engineering Industry" 20, no. 1 (2020): 22–29. http://dx.doi.org/10.14529/engin200103.

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It is noted that the free harmonic vibrations of a classical pendulum are due to the mutual conversion of the kinetic energy of the load intothe potential energy of the spring. Oscillators with a different nature of energy exchange have been developed, for example, by converting the kinetic energy of a load into the energy of a magnetic field of a solenoid or the energy of an electric field of a capacitor. All these oscillatory systems and the like were a prerequisite for the creation of a biinert oscillator,in which the acceleration of one load occurs due to the braking of another, i. e. only kinetic energies are exchanged. The aim of the work is mathematical modeling of a multi-inert oscillatory mechanism. The main research methods in the framework of this work are methods of mathematical modeling and analysis. The methods used make it possible to obtain a reliable description of the studied objects. Inthe proposed multi-inert oscillator, inert bodies of mass m each carry out harmonic oscillations due to the mutual exchange of kinetic energy. The potential energy of the springs is not requiredfor this. Body vibrationsare free. A feature of a multi-inert oscillator is that the frequency of itsfree oscillations is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self-neutralization of mechanical reactive (inertial) power. n-gon, formed by inert bodies, carries out complex motion – orbital rotation around the center of coordinates and spin rotation around its axis passing through the center of the n-gon. Moreover, each load performs linear harmonic oscillations along its guide. With the arrangement of the guiding weights not in the form of a star, but in parallel to each other, the angles between the corresponding cranks must be 360/n degrees.

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13

Dudinetc, I. V., and V. I. Man’ko. "Quantum correlations for two coupled oscillators interacting with two heat baths." Canadian Journal of Physics 98, no. 4 (April 2020): 327–31. http://dx.doi.org/10.1139/cjp-2019-0067.

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We study a system of two coupled oscillators (A oscillators), each of which linearly interact with their own heat bath consisting of a set of independent harmonic oscillators (B oscillators). The initial state of the A oscillator is taken to be coherent while the B oscillator is in a thermal state. We analyze the time-dependent state of the A oscillator, which is a two-mode Gaussian state. By making use of Simon’s separability criterion, we show that this state is separable for all times. We consider the equilibrium state of the A oscillator in detail and calculate its Wigner function.

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14

Manevitch, L. I., A. S. Kovaleva, and E. L. Manevitch. "Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators." Mathematical Problems in Engineering 2010 (2010): 1–24. http://dx.doi.org/10.1155/2010/760479.

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We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories (LPTs). The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation. As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators. We demonstrate the reduction of the equations of motion to an equation of a single oscillator. It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT. Damped beating and the convergence to rest in a system with dissipation are demonstrated.

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15

BIZZARRI, FEDERICO, DANIELE LINARO, BART OLDEMAN, and MARCO STORACE. "HARMONIC ANALYSIS OF OSCILLATORS THROUGH STANDARD NUMERICAL CONTINUATION TOOLS." International Journal of Bifurcation and Chaos 20, no. 12 (December 2010): 4029–37. http://dx.doi.org/10.1142/s0218127410028161.

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In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard continuation package — without modification — such as AUTO, which we used. Our technique works for any kind of oscillator, including electronic, mechanical and biochemical systems. We provide two case studies. The first study concerns itself with the autonomous electronic oscillator known as the Colpitts oscillator, and the second one with a nonlinear damped oscillator, a nonautonomous mechanical oscillator. As shown in the case studies, the proposed technique can aid both the analysis and the design of the oscillators, by following curves for which a certain constraint, related to harmonic analysis, is fulfilled.

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16

Hall, Richard L., Nasser Saad, and Attila B. von Keviczky. "Spiked harmonic oscillators." Journal of Mathematical Physics 43, no. 1 (January 2002): 94–112. http://dx.doi.org/10.1063/1.1418247.

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17

Znojil, Miloslav. "−symmetric harmonic oscillators." Physics Letters A 259, no. 3-4 (August 1999): 220–23. http://dx.doi.org/10.1016/s0375-9601(99)00429-6.

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18

Calogero, F., and V. I. Inozemtsev. "Nonlinear harmonic oscillators." Journal of Physics A: Mathematical and General 35, no. 48 (November 19, 2002): 10365–75. http://dx.doi.org/10.1088/0305-4470/35/48/310.

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19

MICKENS, RONALD E. "GENERALIZED HARMONIC OSCILLATORS." Journal of Sound and Vibration 236, no. 4 (September 2000): 730–32. http://dx.doi.org/10.1006/jsvi.2000.2989.

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20

CHOI, JEONG-RYEOL. "UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR." Modern Physics Letters B 17, no. 26 (November 10, 2003): 1365–76. http://dx.doi.org/10.1142/s021798490300644x.

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Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

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21

Salas-Castro, Pablo, Finees Delgado-Aranda, Edgar Tristán-Hernández, Roberto C. Martínez-Montejano, J. S. Murguía, and Isaac Campos-Cantón. "Application of dynamical system theory in LC harmonic oscillator circuits: A complement tool to the Barkhausen criterion." International Journal of Electrical Engineering & Education 55, no. 3 (April 16, 2018): 258–72. http://dx.doi.org/10.1177/0020720918770140.

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There are different types of electronic oscillators that have a wide variety of applications in areas such as computing, audio, communication, among others. One of these is the harmonic oscillators that generate an output sinusoidal signal. Due to the advantages of these, this paper proposes a methodology based on an analysis based on the dynamical system theory. This provides undergraduates a useful tool for a better understanding of the harmonic oscillators in order to design and implement accurately this kind of circuits. This tool complements the widely recognized Barkhausen criterion, which is a mathematical condition that must be satisfied by linear feedback oscillators. The analysis based on the dynamical system theory consists of obtaining a state matrix and its eigenvalues from the mathematical model of the oscillator circuits. The eigenvalues are adjusted to get an oscillator system, thus from this way, a set of conditions are derived. These conditions are complementary to those obtained by the Barkhausen criterion.

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22

GANGOPADHYAY, DEBASHIS. "ON CANONICAL q-TRANSFORMATIONS WITH TWO q-OSCILLATORS." Modern Physics Letters A 06, no. 31 (October 10, 1991): 2909–16. http://dx.doi.org/10.1142/s0217732391003390.

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23

Bernal-Casas, D., and J. M. Oller. "Information-Theoretic Models for Physical Observables." Entropy 25, no. 10 (October 14, 2023): 1448. http://dx.doi.org/10.3390/e25101448.

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This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space of a smooth statistical manifold of normal probability distributions. Following this approach, we study the stationary states with the time-independent Schrödinger’s equation to discover that the information could be represented and distributed over a set of quantum harmonic oscillators, one for each independent source of data, whose coordinate for each oscillator is a parameter of the smooth statistical manifold to estimate. We observe that the estimator’s variance equals the energy levels of the quantum harmonic oscillator, proving that the estimator’s variance is definitively quantized, being the minimum variance at the minimum energy level of the oscillator. Interestingly, we demonstrate that quantum harmonic oscillators reach the Cramér–Rao lower bound on the estimator’s variance at the lowest energy level. In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. Interestingly, the opposite is also true, as the prior is constant. Altogether, these results suggest that we can break the sources of information into little elements: quantum harmonic oscillators, with the square modulus of the collective mode at the lowest energy representing the most likely reality, supporting A. Zeilinger’s recent statement that the world is not broken into physical but informational parts.

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24

Boujo, E., and N. Noiray. "Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160894. http://dx.doi.org/10.1098/rspa.2016.0894.

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We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator’s damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker–Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations—for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker–Planck equation is solved to compute Kramers–Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.

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25

Kim, Y. S., and Marilyn E. Noz. "Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators." Journal of Optics B: Quantum and Semiclassical Optics 7, no. 12 (November 4, 2005): S458—S467. http://dx.doi.org/10.1088/1464-4266/7/12/005.

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26

ŁAWRYNOWICZ, JULIAN, and AGNIESZKA NIEMCZYNOWICZ. "LATTICE DYNAMICS IN RELATION TO CHAOS IN ZWANZIG-TYPE CHAINS." International Journal of Bifurcation and Chaos 23, no. 11 (November 2013): 1350183. http://dx.doi.org/10.1142/s0218127413501836.

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The Zwanzig's procedure (1960) for the description of the system of coupled harmonic oscillators is applied to the chain of interacting oscillations in order to find the adsorption power function, which is then determined by two terms: (i) the classical term proportional to the radio-frequency function squared and (ii) the additional term linear with respect to the radio-frequency magnetic field amplitude. From the physical point of view the first term is usually considered in oscillator effect. The second term found in the present paper via Zwanzig's procedure seems to be induced by fluctuations due to stochastic distributions of the oscillatory precession phases. It reflects well the chaos as described in a fractal approach of the first author (2012, paper joint with M. Nowak-Kȩpczyk and O. Suzuki).

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27

JIN, Y. H., S. P. KOU, J. Q. LIANG, and B. Z. LI. "DEVIATION OF COHERENT STATE CAUSED BY DISSIPATION." Modern Physics Letters B 14, no. 07n08 (April 10, 2000): 267–75. http://dx.doi.org/10.1142/s0217984900000379.

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The time evolution of a coherent state was studied in the dissipative system, a harmonic oscillator coupling with a bath of harmonic oscillators with Ohmic spectral density. We define a deviation of uncertainty relation versus the squeezed coherent state as [Formula: see text]. It is found that for the case of η ≪ ω0, namely, the weak dissipation, Δ oscillates with a small amplitude. The system is in a squeezed coherent state essentially and the dissipation only leads to a small deviation. For both strong (η ≫ ω0) and critical (η ~ ω0) dissipations, Δ is divergent with respect to t and the coherence of state is destroyed.

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Li, Bo, and Peng Wang. "Multiscale Quantum Harmonic Oscillator Algorithm With Multi-Harmonic Oscillators for Numerical Optimization." IEEE Access 7 (2019): 51159–70. http://dx.doi.org/10.1109/access.2019.2909102.

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29

ALGIN, A., M. ARIK, and N. M. ATAKISHIYEV. "SU(d)-INVARIANT MULTIDIMENSIONAL q-OSCILLATORS WITH BOSONIC DEGENERACY." Modern Physics Letters A 15, no. 19 (June 21, 2000): 1237–42. http://dx.doi.org/10.1142/s0217732300001535.

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Multidimensional two-parameter (q1, q2)-oscillators are of two kinds: one is invariant under the (ordinary) Lie group SU (d), whereas the other is invariant under the quantum group SU q(d) where q = q1/q2. It is shown that the q1 = q2 limit of both of these two-parameter oscillators coincide and give the q-deformed Newton oscillator which can be derived from the standard quantum harmonic oscillator Newton equation. The bosonic degeneracies of the excited levels of these oscillators are different for q1 ≠ q2, but coincide in the q1 = q2 limit.

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30

Klauder, John R. "A Valid Quantization of a Half-Harmonic Oscillator Field Theory." Axioms 11, no. 8 (July 24, 2022): 360. http://dx.doi.org/10.3390/axioms11080360.

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The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of more realistic field theory models.

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31

Biswas, B. N., P. Pal, and D. Mondal. "A Look at Harmonic Oscillations in Gunn Oscillators." IETE Journal of Research 36, no. 2 (March 1990): 114–18. http://dx.doi.org/10.1080/03772063.1990.11436867.

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32

SAIGO, HAYATO. "A NEW LOOK AT THE ARCSINE LAW AND "QUANTUM-CLASSICAL CORRESPONDENCE"." Infinite Dimensional Analysis, Quantum Probability and Related Topics 15, no. 03 (September 2012): 1250021. http://dx.doi.org/10.1142/s021902571250021x.

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We prove that the arcsine law as the time-averaged distribution for classical harmonic oscillators emerges from the distributions for quantum harmonic oscillators in terms of noncommutative algebraic probability. This is nothing but a simple and rigorous realization of "Quantum-Classical Correspondence" for harmonic oscillators.

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HARWOOD, LUKE, PAUL WARR, and MARK BEACH. "DEVELOPMENT OF CHAOTIC OSCILLATORS FROM THE DAMPED HARMONIC OSCILLATOR." International Journal of Bifurcation and Chaos 23, no. 11 (November 2013): 1330037. http://dx.doi.org/10.1142/s0218127413300371.

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Using the damped harmonic oscillator equations as a mathematical template, several novel chaotic oscillators are developed with an emphasis on mathematical simplicity and ease of electronic circuit implementation. These chaotic systems offer an intuitive introduction to chaos theory, enabling comparison of mathematical and computational analyses with experimental results.

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34

Volkov, Yevgeny. "Forced oscillation modes in a birhythmic system of two coupled relaxation oscillators near Andronoy - Hopf bifurcation." Izvestiya VUZ. Applied Nonlinear Dynamics 12, no. 6 (June 15, 2005): 60–78. http://dx.doi.org/10.18500/0869-6632-2004-12-6-60-78.

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A system of two identical relaxation oscillators of the FitzZHugh-Nagumo type with the parameters chosen in the vicinity of a bifurcation of limit cycle emergence was examined for the dynamic modes arising in the presence of a weak harmonic signal applied to both elements. Slow variable exchange between them gives rise to three stable limit cycles called in-phase, anti-phase, and extremely asymmetrical, in which only one of the oscillators generates spikes. In this study, we show that slow variable exchange also causes this system to respond to weak harmonic forcing in a manner quite different from what is known in the classical dynamics of forced oscillations. In addition to the expected synchronization tongues generated by interaction of the signal with the in-phase attractor, we observed at least three other consequences of the coexistence of different solutions: (i) there appeared broad bands of synchronization of the signal with the anti-phase solution at high frequencies multiple to the frequency of the anti-phase oscillations, whereas the base synchronization frequency band became much narrower; (ii) signal period ranges were found in which the limit cycles were such that several spikes were produced over the complete period and each oscillator was characterized with the same set of discrete

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35

Cintra, Daniel, and Pierre Argoul. "Nonlinear argumental oscillators: A few examples of modulation via spatial position." Journal of Vibration and Control 23, no. 18 (January 22, 2016): 2888–911. http://dx.doi.org/10.1177/1077546315623888.

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Under certain conditions, an oscillator can enter a stable regime when submitted to an external harmonic force whose frequency is far from the natural frequency of the oscillator. This may happen when the external force acts on the oscillator in a way which depends on the oscillator's spatial position. This phenomenon is called “argumental oscillation”. In this paper, six argumental oscillators are described and modeled, and experimental results are given and compared to numerical simulations based on the models. A polar Van der Pol representation, with embedded time indications, is used to allow a precise comparison. The pendulums are modeled as Duffing oscillators. The six models are based on various pendulums excited by spatially localized magnetic-field sources consisting of wire coils. Each pendulum receives the excitation via a steel element, or a permanent magnet, fitted at the tip of the pendulum's rod. The spatial localization induces another nonlinearity besides the Duffing nonlinearity. A control system allowing a real-time Van der Pol representation of the motion is presented. Attractors are brought out from experimental results.

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Moran, James, and Véronique Hussin. "Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators." Quantum Reports 1, no. 2 (November 15, 2019): 260–70. http://dx.doi.org/10.3390/quantum1020023.

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In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the S U ( 2 ) coherent states, where these are then used as the basis of expansion for Schrödinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.

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Xia, Guanghan. "Quantum Harmonic Oscillators in One and Two Dimensions." Highlights in Science, Engineering and Technology 64 (August 21, 2023): 213–20. http://dx.doi.org/10.54097/hset.v64i.11282.

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The Schrödinger equation is a significant achievement on the development of quantum mechanics. By solving the Schrödinger equation, the fundamental behaviors and properties of a microscopic particle can be found in one- to three-dimensions. The article focuses on the derivations of quantum harmonic oscillators in one dimension by solving second order-differential equation. The wave functions, probability densities under different energy levels are presented. The results can be used to estimate different forms of continuous potential experienced by an oscillator. By calculating the uncertainty relation of the oscillator under one specific excited state, the general relation can be confirmed. Based on the output, by splitting the variables, the two-dimensional harmonic oscillator can also be derived. The degenerate energy levels are presented as . Numerical simulations are made to visualize those results and suggests the relation of energy levels and number of maxima of the probability densities.

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Wang, Chengen, and Keegan J. Moore. "Breaking reciprocity to realize extreme energy isolation in coupled oscillators." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A42. http://dx.doi.org/10.1121/10.0010595.

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This research investigates the isolation achieved by breaking the reciprocity of between two coupled oscillators. The two oscillators have equal mass and the first one is linearly grounded and called the linear oscillator (LO). The second oscillator is nonlinearly coupled to the LO and is termed the nonlinear oscillator (NO). By breaking dynamical reciprocity using asymmetry and nonlinearity, the LO–NO system is shown to exhibit regimes of extreme energy isolation in only one of the oscillators as well as regimes where energy is exchanged between them. These regimes are shown to arise under both impulsive and harmonic excitation. The resulting system is governed by two nonlinear normal modes (NNMs), which can interact with each other under internal resonance of different ratios. Under different loading scenarios, different energy isolations are illustrated. This research starts with analytical study using numerical simulations that assess how energy distributes in the structure under varying loads. The analytical predictions are validated experimentally for both impulsive and harmonic excitations. The results of this research demonstrate that there remains much to learn about energy transfer in general and the breaking of dynamic reciprocity may lead to new types of acoustic and vibrational metamaterials.

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Laszuk, Dawid, Jose O. Cadenas, and Slawomir J. Nasuto. "KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem." Advances in Data Science and Adaptive Analysis 10, no. 02 (April 2018): 1840002. http://dx.doi.org/10.1142/s2424922x18400028.

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Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals.

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TURBINER, ALEXANDER. "CANONICAL DISCRETIZATION I: DISCRETE FACES OF (AN)HARMONIC OSCILLATOR." International Journal of Modern Physics A 16, no. 09 (April 10, 2001): 1579–603. http://dx.doi.org/10.1142/s0217751x01003299.

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A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and the quasiexactly-solvable anharmonic oscillators are found. They can be viewed as a translation-covariant discretization of the (an)harmonic oscillator preserving isospectrality. The notion of the q-deformation of the canonical equivalence leading to a dilatation-covariant discretization preserving polynomiality of eigenfunctions is also presented.

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LAWANDE, S. V., and Q. V. LAWANDE. "PATH INTEGRAL DERIVATION OF AN EXACT MASTER EQUATION." Modern Physics Letters B 09, no. 02 (January 20, 1995): 87–94. http://dx.doi.org/10.1142/s0217984995000097.

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The Feynman propagator in coherent states representation is obtained for a system of a single harmonic oscillator coupled to a reservoir of N oscillators. Using this propagator, an exact master equation is obtained for the evolution of the reduced density matrix for the open system of the oscillator.

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Rottensteiner, David, and Michael Ruzhansky. "Harmonic and anharmonic oscillators on the Heisenberg group." Journal of Mathematical Physics 63, no. 11 (November 1, 2022): 111509. http://dx.doi.org/10.1063/5.0106068.

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In this article, we present a notion of the harmonic oscillator on the Heisenberg group H n, which, under a few reasonable assumptions, forms the natural analog of a harmonic oscillator on [Formula: see text]: a negative sum of squares of operators on H n, which is essentially self-adjoint on L2(H n) with purely discrete spectrum and whose eigenvectors are Schwartz functions forming an orthonormal basis of L2(H n). The differential operator in question is determined by the Dynin–Folland group—a stratified nilpotent Lie group—and its generic unitary irreducible representations, which naturally act on L2(H n). As in the Euclidean case, our notion of harmonic oscillator on H n extends to a whole class of so-called anharmonic oscillators, which involve left-invariant derivatives and polynomial potentials of order greater or equal 2. These operators, which enjoy similar properties as the harmonic oscillator, are in one-to-one correspondence with positive Rockland operators on the Dynin–Folland group. The latter part of this article is concerned with spectral multipliers. We obtain useful L p- L q-estimates for a large class of spectral multipliers of the sub-Laplacian [Formula: see text] and, in fact, of generic Rockland operators on graded groups. As a by-product, we obtain explicit hypoelliptic heat semigroup estimates and recover the continuous Sobolev embeddings on graded groups, provided 1 < p ≤ 2 ≤ q < ∞.

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Kananizadeh, Rouzbeh, and Omeed Momeni. "Second-Harmonic Power Generation Limits in Harmonic Oscillators." IEEE Journal of Solid-State Circuits 53, no. 11 (November 2018): 3217–31. http://dx.doi.org/10.1109/jssc.2018.2868283.

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Fomin, Anton, Tatjana Vadivasova, Olga Sosnovtseva, and Vadim Anishchenko. "External phase synchronization of chaotic oscillators chain." Izvestiya VUZ. Applied Nonlinear Dynamics 8, no. 4 (2000): 103–12. http://dx.doi.org/10.18500/0869-6632-2000-8-4-103-112.

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External synchronization of a chain of chaotic Rossler oscillators with unidirectoral coupling is studied numerically. Synchronizing harmonic signal is applied to the first oscillator of chain. The region of synchronization is obtained on the plane of parameters «external frequency - coupling». Pecularities of dynamical regimes of the chain in this region are analized.

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BOTELHO, LUIZ C. L. "QUANTUM BROWNIAN MOTIONS AND NAVIER–STOKES WEAKLY TURBULENCE — A PATH INTEGRAL STUDY." International Journal of Modern Physics B 19, no. 25 (October 10, 2005): 3799–823. http://dx.doi.org/10.1142/s0217979205032292.

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In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier–Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.

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Wu, Jing, Anthony J. Brady, and Quntao Zhuang. "Optimal encoding of oscillators into more oscillators." Quantum 7 (August 16, 2023): 1082. http://dx.doi.org/10.22331/q-2023-08-16-1082.

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Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also extend the applicability of error correction to continuous-variable states ubiquitous in quantum sensing and communication. In this work, we derive the optimal oscillator-to-oscillator codes among the general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal encoding to minimize the geometric mean error can be constructed from GKP-TMS codes with an optimized GKP lattice and TMS gains. For single-mode data and ancilla, this optimal code design problem can be efficiently solved, and we further provide numerical evidence that a hexagonal GKP lattice is optimal and strictly better than the previously adopted square lattice. For the multimode case, general GKP lattice optimization is challenging. In the two-mode data and ancilla case, we identify the D4 lattice—a 4-dimensional dense-packing lattice—to be superior to a product of lower dimensional lattices. As a by-product, the code reduction allows us to prove a universal no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on Gaussian encoding, even when the ancilla are not GKP states.

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47

Meyer, Kenneth R. "The Geometry of Harmonic Oscillators." American Mathematical Monthly 97, no. 6 (June 1990): 457. http://dx.doi.org/10.2307/2323828.

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48

Fay, Temple H. "Harmonic Oscillators with Periodic Forcing." College Mathematics Journal 28, no. 2 (March 1997): 98. http://dx.doi.org/10.2307/2687432.

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Kim, Hyeong-Chan, and Youngone Lee. "Nonadiabaticity of quantum harmonic oscillators." Physics Letters A 430 (April 2022): 127974. http://dx.doi.org/10.1016/j.physleta.2022.127974.

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Sprott, J. C., and W. G. Hoover. "Harmonic Oscillators with Nonlinear Damping." International Journal of Bifurcation and Chaos 27, no. 11 (October 2017): 1730037. http://dx.doi.org/10.1142/s0218127417300373.

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Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

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