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  • Qubit... (Color online.) Contour plots of the normalized decay rate γ(τ)/γ0 of the qubit only in the cavity bath, versus the time interval τ between successive measurements, and the central frequency ωcav of the cavity mode. (a) The width of the cavity frequency is λ=10−4Δ, and accordingly the cavity quality factor Q=104. (b) The width of the cavity frequency λ=5×10−3Δ, corresponding to the cavity quality factor Q=2×103. The region 1⩽γ(τ)/γ0⩽1.05 is shown as light magenta. The QZE region corresponds to γ(τ)/γ01. Evidently, a transition from the QZE to the AZE is observed by varying the central frequency of the cavity mode at finite τ (τ>0.6Δ−1 when Q=104, and τ>2.6Δ−1 when Q=2×103). ... (Color online.) Time dependence of the probability for the qubit at its excited state. In the resonant case, the parameters are ωcav=Δ=100g and τ=0.1g−1. In the detuning case, the cavity mode frequency is varied to ωcav=80g. Note that the successive measurements slow down the decay rate of excited state in the resonant case, which is the QZE. While in the detuning case, the measurements speed up the qubit decay rate, which is the AZE. ... The normalized effective decay rate γ(τ)/γ0 of the qubit for two quality factors Q when τ=5Δ−1, in the presence of both the cavity bath and the low-frequency qubitʼs intrinsic bath. ... (Color online.) (a) Sketch of a qubit with the spontaneous dissipation rate γ coupled to a cavity with the loss rate κ via a coupling strength g. (b) and (c) schematically show the bath density spectrum of the qubit environment: (b) the Ohmic qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid), (c) the low-frequency qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid). ... (Color online.) (a) Superconducting circuit model of a frequency-tunable transmission line resonator, which is archived by changing the boundary condition, coupled with a qubit. (b) Superconducting circuit model (1) of the effective tunable inductors, which are consisted of a series array of SQUIDs (2).
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  • The period of oscillation T0 in a QR as a function of the transverse and longitudinal effective confinement lengths of the QR lp and lv. ... The period of oscillation T0 in a QR as a function of the electron–phonon coupling strength α and the Coulomb bound potential β. ... Qubit... The period of oscillation T0 in a QR as a function of the ellipsoid aspect ratio e′ and the electron–phonon coupling strength α.
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  • The phase of the oscillator after action of a linearly-chirped pulsed force as a function of the chirp strength. In this case Ω0=4, σ=5. ... The amplitude of a harmonic oscillator after the action of a pulsed force with a Gaussian envelope and a linear chirp in dependence on the chirp strength, ΔΩ. In this case Ω0=5 and σ=5, 10, and 20; A=1 in all figures. ... The amplitude of the oscillator after the action of a force with an asymmetrical Gaussian envelope, σ1=5, Ω0=5, σ2=10 and 20. ... The amplitude of the oscillator vs. ΔΩ in the case of a periodical chirp in the force. The parameters of the force are: Ω0=5, σ=20, b=4. ... Classical oscillator... Frequency chirp
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  • Microwave spectroscopy of a one-electron double dot. (a) Charge occupancy of the left dot, M, as a function of ε for several microwave frequencies. (b) One-half of the resonance peak splitting as a function of f for several values of VT. Solid lines are best fits to the experimental data using the theory outlined in the text. Inset: Two-level system energy level diagram. (c) Amplitude of the resonance, expressed as Mmax(τ)/Mmax(τ=5ns), as a function of chopped cw period, τ, with f=19GHz. Theory gives a best fit T1=16ns (solid line, see text). Inset: Single photon peak shown in a plot of M as a function of ε for τ=5ns and 1μs. (d) Power dependence of the resonance for f=24GHz. Widths are used to extract the ensemble-averaged charge dephasing time T2*. At higher microwave powers multiple photon processes occur. Curves are offset by 0.3 for clarity. ... Rabi oscillation... Spin qubit... Charge qubit
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  • Adaptive frequency oscillator... The left plot of this figure represents the evolution of ω(t) when the adaptive Hopf oscillator is coupled to the z variable of the Lorenz attractor. The right plot represents the z variable of the Lorenz attractor. We clearly see that the adaptive Hopf oscillators can correctly learn the pseudo-frequency of the Lorenz attractor. See the text for more details. ... Plots of the frequency of the oscillations of the Van der Pol oscillator according to ω. Here α=50. There are two plots, for the dotted line the oscillator is not coupled and for the plain line the oscillator is coupled to F=sin30t. The strength of coupling is ϵ=2. We clearly see basins of phase-locking, the main one for frequency of oscillations 30. The other major basins appear each 30n (dotted horizontal lines). We also notice small entrainment basins for some frequencies of the form 30pq. For a more detailed discussion of these results refer to the text. ... We show the adaptation of the Van der Pol oscillator to the frequencies of various input signals: (a) a simple sinusoidal input (F=sin(40t)), (b) a sinusoidal input with uniformly distributed noise (F=sin(40t)+uniform noise in [−0.5,0.5]), (c) a square input (F=square(40t)) and (d) a sawtooth input (F=sawtooth(40t)). For each experiment, we set ϵ=0.7 and α=100 and we show three plots. The right one shows the evolution of ω(t). The upper left graph is a plot of the oscillations, x, of the system, at the beginning of the learning. The lower graph shows the oscillations at the end of learning. In both graphs, we also plotted the input signal (dashed). In each experiment, ω converges to ω≃49.4, which corresponds to oscillations with a frequency of 40 rad s−1 like the input and thus the oscillator correctly adapts its frequency to the frequency of the input. ... Frequency spectra of the Van der Pol oscillator, both plotted with ω=10. The left figure is an oscillator with α=10 and on the right the nonlinearity is higher, α=50. On the y-axis we plotted the square root of the power intensity, in order to be able to see smaller frequency components. ... This figure shows the convergence of ω for several initial frequencies. The Van der Pol oscillator is perturbed by F=sin(30t), with coupling ϵ=0.7, α=50. We clearly see that the convergence directly depends on the initial conditions and as expected the different kinds of convergence correspond to the several entrainment basins of Fig. 7.
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  • Dominant frequencies of 10mm nozzle. ... Condensation regime map by Cho et al. [1] (C–chugging, TC—transitional region from chugging to CO, CO—condensation oscillation, SC—stable condensation, BCO—bubble condensation oscillation, IOC—interfacial oscillation condensation). ... Condensation oscillation... Frequencies at different test conditions—250kgm−2s−1. ... Frequency... Prediction accuracy of simultaneous equations for oscillation frequency. ... Frequencies at different test conditions—300kgm−2s−1.
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  • Frequency modulation... Frequency modulated Ca2+ oscillations. (A) A computer generated (in silico) oscillating wave with the parameters: period (T), frequency (f), full duration half maximum (FDHM), and duty cycle is depicted. (B) Oscillating wave frequency modulated by agonist concentration. (C) Oscillating wave frequency modulated by the different agonists X, Y, and Z. Three single cell Ca2+ recordings of a Fluo-4/AM-loaded neuroblastoma cell (D), HeLa cell (E), and cardiac cell (F) with the parameters T, f, FDHM, and duty cycle stated. Scale bars are 100s. ... Frequency decoders and host cells. Illustration showing the frequencies and periods that modulate the different frequency decoders and host cells. ... Frequency decoding
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  • Spatial frequencies distributions... Ragged oscillation death... The phase synchronization domains (areas enclosed by the red lines) and the OD regions (black areas) in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8}, (b) G={1,4,3,6,2,8,5,7}, and (c) G={1,2,3,6,8,4,7,5}. N=8. The ragged OD sates are clear in (b) and (c) within a certain interval of δω indicated by two vertical dashed lines. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The bifurcation diagram and the largest Lyapunov exponent λ of the coupled Rossler oscillators versus the coupling strength ε with the same spatial arrangement of natural frequencies as in Fig. 1(a)–(c), respectively for δω=0.58. The bifurcation diagram is realized by the soft of XPPAUT [33] where the black dots are fixed points and the red dots are the maximum and minimum values of x1 for the stable periodic solution while the blue dots means the max/min values of x1 for the unstable periodical states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The critical curves of OD domain from analysis in N coupled Landau–Stuart oscillators for different N’s: (a) N=2, (b) N=3, and (c)–(e) N=4 for G={1,2,3,4},G={1,2,4,3}, and G={1,3,2,4}, respectively. The ragged OD domain is clear in (d). The numerical results with points within the domains perfectly verify the analytical results. ... The OD regions in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}, (b) G={26,16,25,18,5,14,10,4,6,7,21,12,23,8,1,15,9,29,28,11,2,20,27,30,3,13,17,22,24,19}, and (c) G={19,22,18,13,10,28,7,15,17,8,30,12,26,11,20,9,27,21,25,6,29,1,23,5,3,24,16,14,4,2}. N=30. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. ... Coupled nonidentical oscillators
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  • Driven qubit
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  • Summary of resonance frequencies found in all 10 babies (1 and 2 represents first and second run, respectively) ... A screen from our phase analysis program, showing phase analysis performed at four points of the respiratory cycle: top of breath, mid-inspiration, mid-expiration and bottom of breath. Corresponding points from the driving trace and the mouth pressure trace are matched and the phase difference calculated. In this case, the phase difference at the top of breath is 0° at an oscillating frequency of 20 Hz. ... high-frequency oscillation
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