Results 11 to 20 of about 20,560 (308)
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 ...
Rottensteiner, David, Ruzhansky, Michael
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On then-dimensional harmonic oscillator [PDF]
Annali di Matematica Pura ed Applicata, 1979 In this paper, various oscillatory properties of solutions of the scalar equation x″+q(t)x=0 are extended to the vector equation u″+Q(t)u=0.
Sui-Sun Cheng
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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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Spiked harmonic oscillators [PDF]
Journal of Mathematical Physics, 2002 A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H=−d2/dx2+Bx2+λ/xα(B>0,λ>0), for arbitrary α>0. A compact topological proof is presented that the set S={ψn} of known exact solutions for α=2 constitutes an orthonormal basis of the Hilbert space L2(0,∞). Closed-form expressions are
Richard L. Hall +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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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, B. +1 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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Enhancement of quantum synchronization via continuous measurement and feedback control
New Journal of Physics, 2021 We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and ...
Yuzuru Kato, Hiroya Nakao
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Foundations, 2023 A brief review of the classical and quantum description of the interaction of electromagnetic radiation with matter based on the model of a harmonic oscillator is presented.
Valery Astapenko, Timur Bergaliyev
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Multipartite Entanglement Generation in a Structured Environment
Entropy, 2020 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
Shijiao Wang +2 more
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