Topic
Parametric oscillator
About: Parametric oscillator is a research topic. Over the lifetime, 5836 publications have been published within this topic receiving 95631 citations. The topic is also known as: Parametric excitation.
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TL;DR: In this article, a simplified form of Simon's separability criterion for two-mode Gaussian states is given for systems whose unitary evolution is governed by arbitrary time-dependent quadratic Hamiltonians, and the separability dynamics is completely described in terms of the determinant of the cross-covariance matrix.
Abstract: We give a simplified form of Simon's separability criterion for two-mode Gaussian states, showing that for systems whose unitary evolution is governed by arbitrary time-dependent quadratic Hamiltonians, the separability dynamics is completely described in terms of the determinant of the cross-covariance matrix. As concrete examples, we consider the evolution of the 'inverse negativity coefficient' (which gives a quantitative estimation of the 'degree of entanglement') for two initially uncoupled modes (each being in a squeezed thermal state) in the cases of parametric converter, parametric amplifier and for a cavity whose boundary oscillates in resonance with two field modes.
53 citations
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TL;DR: In this paper, an autoparametric system, composed of a nonlinear mechanical oscillator with an attached damped pendulum, around the principal resonance region is investigated, and approximate analytical solutions of the model are determined on the basis of the Harmonic Balance Method (HBM).
53 citations
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TL;DR: In this article, the authors describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belongs to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime.
Abstract: We describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belongs to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime. We identify a distinct spectral PT anti-symmetry associated with optical parametric interaction, and show that pump-controlled symmetry breaking can facilitate spectrally selective mode amplification in analogy with PT lasers. We also establish a connection between the breaking of spectral and spatial mode symmetries, revealing the potential to implement unconventional regimes of spatial light switching through ultrafast control of PT breaking by pump pulses.
53 citations
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01 Nov 1994
TL;DR: In this paper, the parametric resonances in a stationary classical annular disc when excited by a rotating mass-spring-damper system together with a frictional follower load are analyzed.
Abstract: This paper is concerned with the parametric resonances in a stationary classical annular disc when excited by a rotating mass-spring-damper system together with a frictional follower load. An analysis by the method of multiple scales is performed to reveal the existence of instabilities associated with subcritical parametric resonances, and other instabilities of the backward waves in modes with nodal diameters. The latter are shown to be driven by friction and not to be dependent upon the rotational speed. A state-space analysis, with truncated modes, is used to investigate the effect of varying the friction, stiffness, mass and damping prameters in a series of simulated problems. The results obtained from the state-space eigenvalue method tend to support the conclusions of the multiple scales analysis.
53 citations
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TL;DR: In this paper, the Van der Pol's oscillator was used to investigate a non-linearity in the damping term, and the results from the analysis were compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods.
Abstract: This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge–Kutta) methods.
53 citations