Results 1 to 10 of about 99,463 (71)
On detecting harmonic oscillations [PDF]
Bernoulli, 2015 In this paper, we focus on the following testing problem: assume that we are given observations of a real-valued signal along the grid $0,1,\ldots,N-1$, corrupted by white Gaussian noise. We want to distinguish between two hypotheses: (a) the signal is a nuisance - a linear combination of $d_n$ harmonic oscillations of known frequencies, and (b) signal
Juditsky, Anatoli, +1 more
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On the Inverse to the Harmonic Oscillator [PDF]
Communications in Partial Differential Equations, 2015 Let $b_d$ be the Weyl symbol of the inverse to the harmonic oscillator on $\R^d$. We prove that $b_d$ and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for $b_d$. In the even-dimensional case we characterize $b_d$ in terms of elementary functions. In the analysis we use properties of radial
CAPPIELLO, Marco +2 more
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Relativistic harmonic oscillator [PDF]
Journal of Mathematical Physics, 2005 We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum, its eigenfunctions in “compact form,” i.e., as power series, with expansion coefficients determined by an ...
Zhi-Feng Li +4 more
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A THEOREM ON CYCLIC HARMONIC OSCILLATORS [PDF]
International Journal of Modern Physics A, 2006 It is proven that the energy of a quantum mechanical harmonic oscillator with a generically time-dependent but cyclic frequency, ω(t0) = ω(0), cannot decrease on an average if the system is originally in a stationary state, after the system goes through a full cycle.
KONISHI, KENICHI, PAFFUTI, GIAMPIERO
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Phys. Rev. E 70, 051103 (2004), 2011 We consider the fractional oscillator being a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic ...
arxiv +1 more source
Fourth-order dynamics of the damped harmonic oscillator [PDF]
Nonlinear Dyn 109, 285-301 (2022), 2021 It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary. Two systematic approaches are given for deriving the Pais-Uhlenbeck action from the damped harmonic oscillator ...
arxiv +1 more source
ON RELATIVISTIC HARMONIC OSCILLATOR
Hadronic Journal, 2022 9 LaTeX pages, no ...
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Condition for minimal Harmonic Oscillator Action [PDF]
Am. J. Phys. 85, 633 (2017), 2021 We provide an elementary proof that the action for the physical trajectory of the one-dimensional harmonic oscillator is guaranteed to be a minimum if and only if $\tau < \pi/\omega$, where $\tau$ is the elapsed time and $\omega$ is the oscillator's natural frequency.
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The Harmonic Oscillator on the Heisenberg Group [PDF]
Comptes Rendus. Mathématique, 2020 In this note we present a notion of harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ which forms the natural analogue of the harmonic oscillator on $\mathbb{R}^n$ under a few reasonable assumptions: the harmonic oscillator on $\mathbf{H}_n$ should be a negative sum of squares of operators related to the sub-Laplacian on $\mathbf{H}_n ...
Rottensteiner, David, Ruzhansky, Michael
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ADELIC HARMONIC OSCILLATOR [PDF]
International Journal of Modern Physics A, 1995 Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions.
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