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Journal articles on the topic 'Classical oscillator'

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Author: Grafiati

Published: 25 May 2024

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1

Li, Minggen, and Jingdong Bao. "Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems." Entropy 22, no. 8 (July 30, 2020): 839. http://dx.doi.org/10.3390/e22080839.

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We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency wd, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on wd, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with wd decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.

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2

Adhikari, Sondipon. "Qualitative dynamic characteristics of a non-viscously damped oscillator." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2059 (June 16, 2005): 2269–88. http://dx.doi.org/10.1098/rspa.2005.1485.

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This paper considers the linear dynamics of a single-degree-of-freedom non-viscously damped oscillator. It is assumed that the non-viscous damping force depends on the history of velocity via a convolution integral over an exponentially decaying kernel function. Classical qualitative dynamic properties known for viscously damped oscillators have been generalized to such non-viscously damped oscillators. The following questions of fundamental interest have been addressed: (i) under what conditions can a non-viscously damped oscillator sustain oscillatory motions? (ii) how does the natural frequency of a non-viscously damped oscillator compare with that of an equivalent undamped oscillator? and (iii) how does the decay rate compare with that of an equivalent viscously damped oscillator? Introducing two non-dimensional factors, namely, the viscous damping factor and the non-viscous damping factor, we provide answers to these questions. Wherever possible, attempts are made to relate the new results with equivalent classical results for a viscously damped oscillator.

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3

Wang, Wei-Ping. "Binary-Oscillator Networks: Bridging a Gap between Experimental and Abstract Modeling of Neural Networks." Neural Computation 8, no. 2 (February 15, 1996): 319–39. http://dx.doi.org/10.1162/neco.1996.8.2.319.

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This paper proposes a simplified oscillator model, called binary-oscillator, and develops a class of neural network models having binary-oscillators as basic units. The binary-oscillator has a binary dynamic variable v = ±1 modeling the “membrane potential” of a neuron, and due to the presence of a “slow current” (as in a classical relaxation-oscillator) it can oscillate between two states. The purpose of the simplification is to enable abstract algorithmic study on the dynamics of oscillator networks. A binary-oscillator network is formally analogous to a system of stochastic binary spins (atomic magnets) in statistical mechanics.

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4

Khan, Kamran-ul-Haq, and Suhaib Masroor. "Numerical simulation along with the experimental work for an underdamped oscillator using fourth order Runge–Kutta method. An undergraduate experiment." Physics Education 58, no. 6 (August 31, 2023): 065006. http://dx.doi.org/10.1088/1361-6552/acede4.

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Abstract Experiments based on oscillatory motion are an essential part of the curricula for students of physics and engineering in their undergraduate studies, such as the determination of spring constant for a well-known classical oscillator i.e., spring-mass system. Moreover, it is important for students to understand the physics of damped oscillators because, in real-world scenarios, a system involving oscillations cannot be completely analysed without understanding conditions of damped oscillations i.e., underdamped, overdamped, and critical damped. In this work, we design a computational physics lab for the simulation of the underdamped oscillator using an Excel spreadsheet by employing 4th order Runge–Kutta method. Further, we construct a simple experimental setup to observe the damped oscillation and obtaindata for the underdamped system. Final analysis was based on comparison between the experimental data and the numerically estimated data.

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5

da Costa, Bruno G., Ignacio S. Gomez, and Biswanath Rath. "Exact solution and coherent states of an asymmetric oscillator with position-dependent mass." Journal of Mathematical Physics 64, no. 1 (January 1, 2023): 012102. http://dx.doi.org/10.1063/5.0094564.

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We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space ( x, p) to a deformed one ( x γ, Π γ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

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6

Frolov, Andrei V., and Valeri P. Frolov. "Classical Mechanics with Inequality Constraints and Gravity Models with Limiting Curvature." Universe 9, no. 6 (June 10, 2023): 284. http://dx.doi.org/10.3390/universe9060284.

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In this paper, we discuss mechanical systems with inequality constraints Φ(q,q˙,...)≤0. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate this approach, we consider a harmonic oscillator in the model with limiting velocity. We compare the behavior of such an oscillator with the behavior of a relativistic oscillator and demonstrate that when the amplitude of the oscillator is large, the properties of both types of oscillators are quite similar. We also discuss inequality constraints, which contain higher derivatives. At the end of the paper, we briefly discuss possible applications of the developed approach to gravity models with limiting curvature.

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7

POPOV, I. P. "MULTI–INERT OSCILLATORY MECHANISM." Fundamental and Applied Problems of Engineering and Technology 2 (2020): 19–25. http://dx.doi.org/10.33979/2073-7408-2020-340-2-19-25.

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A mechanical oscillatory system with homogeneous elements, namely, with n massive loads (multi– inert oscillator), is considered. The possibility of the appearance of free harmonic oscillations of loads in such a system is shown. Unlike the classical spring pendulum, the oscillations of which are due to the mutual conversion of the kinetic energy of the load into the potential energy of the spring, in a multi–inert oscillator, the oscillations are due to the mutual conversion of only the kinetic energies of the goods. In this case, the acceleration of some loads occurs due to the braking of others. A feature of the multi–inert oscillator is that its free oscillation frequency 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 in oscillatory systems.

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8

NEŠKOVIĆ, P. V., and B. V. UROŠEVIĆ. "QUANTUM OSCILLATORS: APPLICATIONS IN STATISTICAL MECHANICS." International Journal of Modern Physics A 07, no. 14 (June 10, 1992): 3379–88. http://dx.doi.org/10.1142/s0217751x92001496.

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We consider a canonical ensemble of q oscillators. Using classical realization for q oscillator algebra,17 we calculate, for a small real q, the partition function and thermodynamic potentials F, E and S. We show that F reaches the minimum and E and S the maximum (as functions of the deformation parameter q) when q = 1 (for the classical oscillator). We argue about possible far-reaching consequences of this fact. As an application we obtain a first quantum correction to Planck's black body radiation law. We introduce the slightly deformed oscillator (SDO) model, which provides us with a significant amount of information about the system. When q = 1, our results are shown to coincide with classical results.

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9

Murakami, Shintaro, Okuto Ikeda, Yusuke Hirukawa, and Toshiharu Saiki. "Investigation of Eigenmode-Based Coupled Oscillator Solver Applied to Ising Spin Problems." Symmetry 13, no. 9 (September 19, 2021): 1745. http://dx.doi.org/10.3390/sym13091745.

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We evaluate a coupled oscillator solver by applying it to square lattice (N × N) Ising spin problems for N values up to 50. The Ising problems are converted to a classical coupled oscillator model that includes both positive (ferromagnetic-like) and negative (antiferromagnetic-like) coupling between neighboring oscillators (i.e., they are reduced to eigenmode problems). A map of the oscillation amplitudes of lower-frequency eigenmodes enables us to visualize oscillator clusters with a low frustration density (unfrustrated clusters). We found that frustration tends to localize at the boundary between unfrustrated clusters due to the symmetric and asymmetric nature of the eigenmodes. This allows us to reduce frustration simply by flipping the sign of the amplitude of oscillators around which frustrated couplings are highly localized. For problems with N = 20 to 50, the best solutions with an accuracy of 96% (with respect to the exact ground state) can be obtained by simply checking the lowest ~N/2 candidate eigenmodes.

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10

Kordahl, David. "Complementarity and entanglement in a simple model of inelastic scattering." American Journal of Physics 91, no. 10 (October 1, 2023): 796–804. http://dx.doi.org/10.1119/5.0141389.

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A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three different conceptual approaches, with both analytical and numerical techniques discussed for each. In a purely classical approach, the final amplitude of the oscillator can be found directly from the initial conditions. In a partially quantum approach, with a classical beam and a quantum oscillator, the final magnitude of the quantum-mechanical amplitude for the oscillator's first excited state is directly proportional to the oscillator's classical amplitude of vibration. Nearly the same first-order transition probabilities emerge in the partially and fully quantum approaches, but conceptual differences emerge. The two-particle scattering wavefunction clarifies these differences and allows the consequences of quantum entanglement to be explored.

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11

Rosu, H. C., O. Cornejo-Pérez, and P. Chen. "Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator." EPL (Europhysics Letters) 100, no. 6 (December 1, 2012): 60006. http://dx.doi.org/10.1209/0295-5075/100/60006.

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12

Powles, J. G., A. Dornford-Smith, and W. A. B. Evans. "Classical, microscopic, liquid Poisson oscillator." Physical Review Letters 66, no. 9 (March 4, 1991): 1177–80. http://dx.doi.org/10.1103/physrevlett.66.1177.

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13

Choi, Jeong Ryeol. "Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems." Axioms 10, no. 3 (July 10, 2021): 153. http://dx.doi.org/10.3390/axioms10030153.

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Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. We focus on two particular cases; one is a linearly mass-accreting oscillator and the other is an exponentially mass-accreting one. It is confirmed that the quantum energy is in agreement with the classical one in the limit ℏ→0. We showed that not only the classical but also the quantum energy oscillates with time. It is carefully analyzed why the energy oscillates with time, and a reasonable explanation for that outcome is given.

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14

Simaciu, Ion, Zoltan Borsos, Gheorghe Dumitrescu, and Viorel Drafta. "Gravitational Interaction Mediated by Classical Zero Point Field." BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică 68, no. 3 (September 1, 2022): 23–37. http://dx.doi.org/10.2478/bipmf-2022-0012.

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Abstract By modeling the particle as a two-dimensional oscillator with the natural angular frequency equal to the Zitterbewegung frequency, the expression of the gravitational force between two particles is obtained. Gravitational force is the effect of the absorption-scattering of the CZPF background by the oscillators. The connection between the gravitational and the electrostatic interaction is obtained.

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15

Radovancevic, Darko, and Ljubisa Nesic. "Kantowski-Sachs minisuperspace cosmological model on noncommutative space." Facta universitatis - series: Physics, Chemistry and Technology 14, no. 1 (2016): 21–26. http://dx.doi.org/10.2298/fupct1601021r.

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A vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model is considered. In a classical case, Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model is formulated also on noncommutative space.

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16

MAN'KO, V. I., G. MARMO, S. SOLIMENO, and F. ZACCARIA. "PHYSICAL NONLINEAR ASPECTS OF CLASSICAL AND QUANTUM q-OSCILLATORS." International Journal of Modern Physics A 08, no. 20 (August 10, 1993): 3577–97. http://dx.doi.org/10.1142/s0217751x93001454.

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The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce nonlinearity. Guided by this idea, we considered q fields, the partition function, and compute a consequence on the specific heat and second order correlation function of the q-oscillator which may serve for experimental checks for the nonlinearity.

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17

Gershenzon, Igor, Geva Arwas, Sagie Gadasi, Chene Tradonsky, Asher Friesem, Oren Raz, and Nir Davidson. "Exact mapping between a laser network loss rate and the classical XY Hamiltonian by laser loss control." Nanophotonics 9, no. 13 (June 25, 2020): 4117–26. http://dx.doi.org/10.1515/nanoph-2020-0137.

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AbstractRecently, there has been growing interest in the utilization of physical systems as heuristic optimizers for classical spin Hamiltonians. A prominent approach employs gain-dissipative optical oscillator networks for this purpose. Unfortunately, these systems inherently suffer from an inexact mapping between the oscillator network loss rate and the spin Hamiltonian due to additional degrees of freedom present in the system such as oscillation amplitude. In this work, we theoretically analyze and experimentally demonstrate a scheme for the alleviation of this difficulty. The scheme involves control over the laser oscillator amplitude through modification of individual laser oscillator loss. We demonstrate this approach in a laser network classical XY model simulator based on a digital degenerate cavity laser. We prove that for each XY model energy minimum there corresponds a unique set of laser loss values that leads to a network state with identical oscillation amplitudes and to phase values that coincide with the XY model minimum. We experimentally demonstrate an eight fold improvement in the deviation from the minimal XY energy by employing our proposed solution scheme.

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18

SISTO, RENATA, and ARTURO MOLETI. "ON THE SENSITIVITY OF GRAVITATIONAL WAVE RESONANT BAR DETECTORS." International Journal of Modern Physics D 13, no. 04 (April 2004): 625–39. http://dx.doi.org/10.1142/s021827180400475x.

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Different theoretical estimates of the sensitivity of gravitational wave resonant bar detectors, which have been published in the last decades, are reviewed and discussed. The "classical" cross-section estimate is obtained considering the bar as a classical or quantum oscillator, whose initial thermal state is that of a single oscillator driven by a single external stochastic force. Other theoretical studies computed a much larger cross-section, using a variety of quantum-mechanical arguments. The review of the existing literature shows that there is no well established model for the response of a resonant detector to gravitational waves. The resonant, yet random, nature of the Brownian thermal motion may justify considering the bar response at the fundamental longitudinal eigenfrequency as that of a large number of effective quantum mechanical oscillators. Assuming this hypothesis, quantum coherence effects, as first suggested by Weber, lead to a much larger cross-section than that "classically" predicted. The reduction of this amplification due to thermal noise itself is also computed.

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19

YANG, SHI-PING, YAN LI, HONG CHANG, GANG TIAN, and GUO-YONG YUAN. "THE STUDY OF COUPLED OSCILLATORS ON CLASSICAL CHAOS AND QUANTUM CHARACTERISTIC." International Journal of Modern Physics B 20, no. 24 (September 30, 2006): 3465–75. http://dx.doi.org/10.1142/s021797920603562x.

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In this paper, the classical and quantum chaos characteristic of single electronic motion in the double quantum well with external magnetic field are studied. The system can be regarded as the linear coupling of a harmonic oscillator and a Duffing oscillator. The study shows that because of the interaction of two oscillators, the system demonstrates the characteristic of quasi-periodicity, multi-chaos coexisting attractors, chaos, super-chaos, etc., with different energy. Furthermore, as shown in the corresponding analysis of spectrum distribution statistics, the system in most energy fields demonstrates the coexisting of the integrable and non-integrable characteristic, which means that there is a close corresponding relation in classical and quantum behavior.

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20

Karahan, M. M. Fatih, and Mehmet Pakdemirli. "Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators." Zeitschrift für Naturforschung A 72, no. 1 (January 1, 2017): 59–69. http://dx.doi.org/10.1515/zna-2016-0263.

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AbstractStrongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.

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21

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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22

Petrov, S. V. "Classical dynamics of the relativistic oscillator." European Journal of Physics 37, no. 6 (September 20, 2016): 065605. http://dx.doi.org/10.1088/0143-0807/37/6/065605.

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23

Bievre, S. De. "Oscillator eigenstates concentrated on classical trajectories." Journal of Physics A: Mathematical and General 25, no. 11 (June 7, 1992): 3399–418. http://dx.doi.org/10.1088/0305-4470/25/11/039.

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24

Gitterman, M. "Classical harmonic oscillator with multiplicative noise." Physica A: Statistical Mechanics and its Applications 352, no. 2-4 (July 2005): 309–34. http://dx.doi.org/10.1016/j.physa.2005.01.008.

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25

Amore, P., and R. A. Sáenz. "The period of a classical oscillator." Europhysics Letters (EPL) 70, no. 4 (May 2005): 425–31. http://dx.doi.org/10.1209/epl/i2005-10017-3.

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26

Wei-Zhong, He, Xu Liu-Su, and Zou Feng-Wu. "Wavefunction of Coupled Quantum-Classical Oscillator." Chinese Physics Letters 20, no. 5 (April 24, 2003): 600–601. http://dx.doi.org/10.1088/0256-307x/20/5/302.

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27

FRYDRYSZAK, ANDRZEJ. "NILPOTENT CLASSICAL MECHANICS." International Journal of Modern Physics A 22, no. 14n15 (June 20, 2007): 2513–33. http://dx.doi.org/10.1142/s0217751x07036749.

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The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates η. Necessary geometrical notions and elements of generalized differential η-calculus are introduced. The so-called s-geometry, in a special case when it is orthogonally related to a traceless symmetric form, shows some resemblances to the symplectic geometry. As an example of an η-system the nilpotent oscillator is introduced and its supersymmetrization considered. It is shown that the R-symmetry known for the graded superfield oscillator also present here for the supersymmetric η-system. The generalized Poisson bracket for (η, p)-variables satisfies modified Leibniz rule and has nontrivial Jacobiator.

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28

Burban, I. M. "Oscillators in the Framework of Unified (q, α, β, γ, ν)-Deformation and Their Oscillator Algebras." Ukrainian Journal of Physics 57, no. 4 (April 30, 2012): 396. http://dx.doi.org/10.15407/ujpe57.4.396.

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The aim of this paper is to review our results on the description of multiparameter deformed oscillators and their oscillator algebras. We define generalized (q; α, β, γ, ν)-deformed oscillator algebras and study their irreducible representations. The Arik–Coon oscillator with the main relation aa+ – qa+a = 1, where q >1, is embedded in this framework. We have found the connection of this oscillator with the Askey q–1-Hermite polynomials. We construct a family of generalized coherent states associated with these polynomials and give their explicit expression in terms of standard special functions. By means of the solution of the appropriate classical Stieltjes moment problem, we prove the property of (over)completeness of these states.

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29

Li, XiaoFu, Md Raf E Ul Shougat, Tushar Mollik, Robert N. Dean, Aubrey N. Beal, and Edmon Perkins. "Field-programmable analog array (FPAA) based four-state adaptive oscillator for analog frequency analysis." Review of Scientific Instruments 94, no. 3 (March 1, 2023): 035103. http://dx.doi.org/10.1063/5.0129365.

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Adaptive oscillators are a subset of nonlinear oscillators that can learn and encode information in dynamic states. By appending additional states onto a classical Hopf oscillator, a four-state adaptive oscillator is created that can learn both the frequency and amplitude of an external forcing frequency. Analog circuit implementations of nonlinear differential systems are usually achieved by using operational amplifier-based integrator networks, in which redesign procedures of the system topology is time consuming. Here, an analog implementation of a four-state adaptive oscillator is presented for the first time as a field-programmable analog array (FPAA) circuit. The FPAA diagram is described, and the hardware performance is presented. This simple FPAA-based oscillator can be used as an analog frequency analyzer, as its frequency state will evolve to match the external forcing frequency. Notably, this is done without any analog-to-digital conversion or pre-processing, making it an ideal frequency analyzer for low-power and low-memory applications.

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Rath, Biswanath, Pravanjan Mallick, Prachiprava Mohapatra, Jihad Asad, Hussein Shanak, and Rabab Jarrar. "Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study." Open Physics 19, no. 1 (January 1, 2021): 266–76. http://dx.doi.org/10.1515/phys-2021-0024.

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Abstract We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.

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Krok, Kamila A., Artur P. Durajski, and Radosław Szczȩśniak. "The Abraham–Lorentz force and the time evolution of a chaotic system: The case of charged classical and quantum Duffing oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073130. http://dx.doi.org/10.1063/5.0090477.

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This paper proves that the Abraham–Lorentz (AL) force can noticeably modify the trajectories of the charged Duffing oscillators over time. The influence of the reaction force on the oscillator evolution is strongly enhanced if the system is considered at the level of quantum mechanics. For example, the AL force examined within the scope of Newtonian description can change the trajectory of the Duffing oscillator only if it has the mass of an electron. However, we showed that when quantum corrections along with the nondeterministic contributions are taken into account, the reaction force of the electromagnetic field affects noticeably even the oscillator with a mass equal to the mass of the [Formula: see text] ion. The charged Duffing oscillators belong to the class of systems characterized by the chaotic nondeterministic dynamics. In classical terms, the nondeterministic behavior of the discussed systems results from the breaking of the causality principle by the AL force.

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Hab-arrih, Radouan, Ahmed Jellal, Dionisis Stefanatos, and Abdeldjalil Merdaci. "Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators." Quantum Reports 3, no. 4 (October 17, 2021): 684–702. http://dx.doi.org/10.3390/quantum3040043.

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In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

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Marcôndes, David William Cordeiro, Pedro Bertemes-Filho, and Aleksander Sade Paterno. "Current Oscillator Based on Pyragas Model for Electrical Bioimpedance Applications." Electronics 11, no. 17 (August 25, 2022): 2653. http://dx.doi.org/10.3390/electronics11172653.

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Current sources play an essential role in tissue excitation used in bioelectrical impedance spectroscopy. Most investigations use Howland current sources that, despite their practicality and simplified implementation, have operating frequency limitations and dependence on the load impedance due to their narrow output impedance, especially at higher frequencies. The objective of this work is to propose a model for a robust current-controlled sinusoidal oscillator. The oscillator is based on fully analog electronics, which enables controlling the oscillation phase and amplitude by using a voltage reference. The mathematical model is based on Pyragas control application to the classical harmonic oscillator. From the modeling process, an oscillator topology was built based on second-generation current carriers and on transconductance amplifiers. A sinusoidal voltage source having a frequency of 1 MHz and an amplitude of 1Vpp was used as a reference signal to drive the oscillator. The oscillator output current synchronized the oscillations’ phase and amplitude using the reference, regardless of their magnitude before the control signal acted in the circuit at t≈13.5μs. SPICE simulations using ideal components have confirmed the successful operation of the proposed oscillator. This type of oscillator can be implemented in SOIC, then allowing oscillation control interface with logic circuits.

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34

BUSCARINO, ARTURO, LUIGI FORTUNA, MATTIA FRASCA, and GREGORIO SCIUTO. "COUPLED INDUCTORS-BASED CHAOTIC COLPITTS OSCILLATOR." International Journal of Bifurcation and Chaos 21, no. 02 (February 2011): 569–74. http://dx.doi.org/10.1142/s0218127411028611.

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In this paper, a new chaotic circuit is introduced, conceived by considering a Colpitts oscillator with the inclusion of two further elements: a coupled inductor and a variable resistor. The proposed circuit exhibits a rich dynamics that has been experimentally characterized through the bifurcation diagram with respect to the resistor value. The main result that can be derived from the analysis of the new circuit leads to a simple way to control chaos in the chaotic Colpitts oscillator by varying a single external control parameter. The same technique has then been applied to the classical periodic Colpitts oscillator, demonstrating how in this way the oscillation frequency can be controlled.

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35

Giannakis, Dimitrios. "Quantum dynamics of the classical harmonic oscillator." Journal of Mathematical Physics 62, no. 4 (April 1, 2021): 042701. http://dx.doi.org/10.1063/5.0009977.

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36

Kriegsmann, Gregory A. "Bifurcation in Classical Bipolar Transistor Oscillator Circuits." SIAM Journal on Applied Mathematics 49, no. 2 (April 1989): 390–403. http://dx.doi.org/10.1137/0149024.

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37

Case, William B. "The field oscillator approach to classical electrodynamics." American Journal of Physics 68, no. 9 (September 2000): 800–811. http://dx.doi.org/10.1119/1.1302626.

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Knop, W., and W. Lauterborn. "Bifurcation structure of the classical Morse oscillator." Journal of Chemical Physics 93, no. 6 (September 15, 1990): 3950–57. http://dx.doi.org/10.1063/1.458780.

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39

Maamache, Mustapha, and Jeong Ryeol Choi. "Quantum-classical correspondence for the inverted oscillator." Chinese Physics C 41, no. 11 (October 24, 2017): 113106. http://dx.doi.org/10.1088/1674-1137/41/11/113106.

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40

Bliokh, K. Yu. "Generalized geometric phase of a classical oscillator." Journal of Physics A: Mathematical and General 36, no. 6 (January 29, 2003): 1705–10. http://dx.doi.org/10.1088/0305-4470/36/6/313.

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41

Batouli, J., and M. El Baz. "Classical Interpretation of a Deformed Quantum Oscillator." Foundations of Physics 44, no. 2 (January 1, 2014): 105–13. http://dx.doi.org/10.1007/s10701-013-9766-9.

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42

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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43

Haque, B. M. Ikramul, and M. M. Ayub Hossain. "An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure." International Journal of Differential Equations 2021 (December 21, 2021): 1–11. http://dx.doi.org/10.1155/2021/7819209.

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The cube-root truly nonlinear oscillator and the inverse cube-root truly nonlinear oscillator are the most meaningful and classical nonlinear ordinary differential equations on behalf of its various applications in science and engineering. Especially, the oscillators are used widely in the study of elastic force, structural dynamics, and elliptic curve cryptography. In this paper, we have applied modified Mickens extended iteration method to solve the cube-root truly nonlinear oscillator, the inverse cube-root truly nonlinear oscillator, and the equation of pendulum. Comparison is made among iteration method, harmonic balance method, He’s amplitude-frequency formulation, He’s homotopy perturbation method, improved harmonic balance method, and homotopy perturbation method. After comparison, we analyze that modified Mickens extended iteration method is more accurate, effective, easy, and straightforward. Also, the comparison of the obtained analytical solutions with the numerical results represented an extraordinary accuracy. The percentage error for the fourth approximate frequency of cube-root truly nonlinear oscillator is 0.006 and the percentage error for the fourth approximate frequency of inverse cube-root truly nonlinear oscillator is 0.12.

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44

RALPH, J. F., T. P. SPILLER, T. D. CLARK, R. J. PRANCE, and H. PRANCE. "THE NONLINEAR DYNAMICS OF A LINEAR CLASSICAL OSCILLATOR COUPLED TO A MACROSCOPIC QUANTUM OBJECT." International Journal of Modern Physics B 08, no. 19 (August 30, 1994): 2637–51. http://dx.doi.org/10.1142/s0217979294001056.

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In this paper we will discuss a model for the behavior of an rf-SQUID magnetometer, which consists of a macroscopic quantum object which is reactively coupled to a linear classical oscillator. We demonstrate that the coupling between the quantum object and the classical oscillator can lead to manifestly nonlinear behavior in the otherwise linear oscillator; including multi-periodic and chaotic solutions.

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Popov, Igor'. "MECHANICAL OSCILLATOR WITHOUT POTENTIAL ENERGY STORAGE." Transport engineering 2022, no. 12 (December 9, 2022): 13–17. http://dx.doi.org/10.30987/2782-5957-2022-12-13-17.

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In a monoreactive harmonic oscillator, inert elements can make free sinusoidal oscillations, which are accompanied by the transformation of one inert element kinetic energy into the kinetic energy of another inert element. In this condition the energy of the first inert element is zero. At the same time, the energy of the second element has the maximum value. At the next moment of time, the first element acquires acceleration due to the kinetic energy of the second element, the speed of which begins to decrease. In a classical oscillator, free sinusoidal oscillations are accompanied by an exchange of energy between its elements having the opposite reactivity character. In a spring pendulum, the potential energy of an elastic element is transformed into the kinetic energy of an inert element and vice versa. These elements have the opposite character of reactivity. In an electric oscillatory circuit, the energy of the coil magnetic field is transformed into the energy of the condenser electric field and vice versa. These elements also have the opposite character of reactivity. There are also oscillators in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element or the potential energy of an elastic element into the energy of the coil magnetic field or the energy of the capacitor electric field and vice versa. Free sinusoidal oscillations can occur during the mutual transformation of any physical types of energy.This circumstance is the motive to make an oscillator, in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element into the kinetic energy of another inert element. There are no elements with a different reactivity character in such an oscillator. This type of an oscillator is essentially monoreactive.

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Berdichevsky, V., O. O¨zbek, and W. W. Kim. "Thermodynamics of Duffing’s Oscillator." Journal of Applied Mechanics 61, no. 3 (September 1, 1994): 670–75. http://dx.doi.org/10.1115/1.2901512.

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We study the averaged characteristics of the response of Duffing’s oscillator to harmonic excitation. We show that, as in classical thermodynamics, response characteristics are potential functions of excitation characteristics.

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47

Ngamsa Tegnitsap, Joakim Vianney, Merlin Brice Saatsa Tsefack, Elie Bertrand Megam Ngouonkadi, and Hilaire Bertrand Fotsin. "On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator." Physica Scripta 96, no. 12 (December 1, 2021): 125269. http://dx.doi.org/10.1088/1402-4896/ac3ea3.

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Abstract In this work, the dynamic of the triode-based Van der Pol oscillator coupled to a linear circuit is investigated (Triode-based VDPCL oscillator). Towards this end, we present a mathematical model of the triode, chosen from among the many different ones present in literature. The dynamical behavior of the system is investigated using classical tools such as two-parameter Lyapunov exponent, one-parameter bifurcation diagram associated with the graph of largest Lyapunov exponent, phase portraits, and time series. Numerical simulations reveal rather rich and complex phenomena including chaos, transient chaos, the coexistence of solutions, crisis, period-doubling followed by reverse period-doubling sequences (bubbles), and bursting oscillation. The coexistence of attractors is illustrated by the phase portraits and the cross-section of the basin of attraction. Such triode-based nonlinear oscillators can find their applications in many areas where ultra-high frequencies and high powers are demanded (radio, radar detection, satellites communication, etc) since triode can work with these performances and are often used in the aforementioned areas. In contrast to some recent work on triode-based oscillators, LTSPICE simulations, based on real physical consideration of the triode, are carried out in order to validate the theoretical results obtained in this paper as well as the mathematical model adopted for the triode.

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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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DE MARTINO, SALVATORE, SILVIO DE SIENA, and FABRIZIO ILLUMINATI. "A CLASS OF QUANTUM STATES WITH CLASSICAL-LIKE EVOLUTION." Modern Physics Letters B 08, no. 29 (December 20, 1994): 1823–31. http://dx.doi.org/10.1142/s0217984994001734.

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In the framework of the stochastic formulation of quantum mechanics we derive non-stationary states for a class of time-dependent potentials. The wave packets follow a classical motion with constant dispersion. The new states define a possible extension of the harmonic oscillator coherent states. As an explicit application, we study a sestic oscillator potential.

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50

Kitio, Gabin Jeatsa, Cyrille Ainamon, Karthikeyan Rajagopal, Léandre Kamdjeu Kengne, Sifeu Takougang Kingni, and Justin Roger Mboupda Pone. "Four-Scroll Hyperchaotic Attractor in a Five-Dimensional Memristive Wien Bridge Oscillator: Analysis and Digital Electronic Implementation." Mathematical Problems in Engineering 2021 (October 19, 2021): 1–21. http://dx.doi.org/10.1155/2021/4820771.

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An electronic implementation of a novel Wien bridge oscillation with antiparallel diodes is proposed in this paper. As a result, we show by using classical nonlinear dynamic tools like bifurcation diagrams, Lyapunov exponent plots, phase portraits, power density spectra graphs, time series, and basin of attraction that the oscillator transition to chaos is operated by intermittency and interior crisis. Some interesting behaviors are found, namely, multistability, hyperchaos, transient chaos, and bursting oscillations. In comparison with some memristor-based oscillators, the plethora of dynamics found in this circuit with current-voltage (i–v) characteristic of diodes mounted in the antiparallel direction represents a major advance in the knowledge of the behavior of this circuit. A suitable microcontroller based design is built to support the numerical findings as these experimental results are in good agreement.

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