7,812 research outputs found
Statistics of Chaotic Resonances in an Optical Microcavity
Distributions of eigenmodes are widely concerned in both bounded and open
systems. In the realm of chaos, counting resonances can characterize the
underlying dynamics (regular vs. chaotic), and is often instrumental to
identify classical-to-quantum correspondence. Here, we study, both
theoretically and experimentally, the statistics of chaotic resonances in an
optical microcavity with a mixed phase space of both regular and chaotic
dynamics. Information on the number of chaotic modes is extracted by counting
regular modes, which couple to the former via dynamical tunneling. The
experimental data are in agreement with a known semiclassical prediction for
the dependence of the number of chaotic resonances on the number of open
channels, while they deviate significantly from a purely
random-matrix-theory-based treatment, in general. We ascribe this result to the
ballistic decay of the rays, which occurs within Ehrenfest time, and
importantly, within the timescale of transient chaos. The present approach may
provide a general tool for the statistical analysis of chaotic resonances in
open systems.Comment: 5 pages, 5 figures, and a supplemental informatio
local fractional fourier series solutions for nonhomogeneous heat equations arising in fractal heat flow with local fractional derivative
The fractal heat flow within local fractional derivative is investigated. The nonhomogeneous heat equations arising in fractal heat flow are discussed. The local fractional Fourier series solutions for one-dimensional nonhomogeneous heat equations are obtained. The nondifferentiable series solutions are given to show the efficiency and implementation of the present method
Simple scheme for implementing the Deutsch-Jozsa algorithm in thermal cavity
We present a simple scheme to implement the Deutsch-Jozsa algorithm based on
two-atom interaction in a thermal cavity. The photon-number-dependent parts in
the evolution operator are canceled with the strong resonant classical field
added. As a result, our scheme is immune to thermal field, and does not require
the cavity to remain in the vacuum state throughout the procedure. Besides,
large detuning between the atoms and the cavity is not necessary neither,
leading to potential speed up of quantum operation. Finally, we show by
numerical simulation that the proposed scheme is equal to demonstrate the
Deutsch-Jozsa algorithm with high fidelity.Comment: 7 pages, 4 figure
Chaos-assisted two-octave-spanning microcombs
Since its invention, optical frequency comb has revolutionized a broad range of subjects from metrology to spectroscopy. The recent development of microresonator-based frequency combs (microcombs) provides a unique pathway to create frequency comb systems on a chip. Indeed, microcomb-based spectroscopy, ranging, optical synthesizer, telecommunications and astronomical calibrations have been reported recently. Critical to many of the integrated comb systems is the broad coverage of comb spectra. Here, microcombs of more than two-octave span (450 nm to 2,008 nm) is demonstrated through χ^((2)) and χ^((3)) nonlinearities in a deformed silica microcavity. The deformation lifts the circular symmetry and creates chaotic tunneling channels that enable broadband collection of intracavity emission with a single waveguide. Our demonstration introduces a new degree of freedom, cavity deformation, to the microcomb studies, and our microcomb spectral range is useful for applications in optical clock, astronomical calibration and biological imaging
Optimal weighting models based on linear uncertain constraints in intuitionistic fuzzy preference relations
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Although the classic exponential-smoothing models and grey prediction models have been widely used in time series forecasting, this paper shows that they are susceptible to fluctu- ations in samples. A new fractional bidirectional weakening buffer operator for time series prediction is proposed in this paper. This new operator can effectively reduce the negative impact of unavoidable sample fluctuations. It overcomes limitations of existing weakening buffer operators, and permits better control of fluctuations from the entire sample period. Due to its good performance in improving stability of the series smoothness, the new op- erator can better capture the real developing trend in raw data and improve forecast accu- racy. The paper then proposes a novel methodology that combines the new bidirectional weakening buffer operator and the classic grey prediction model. Through a number of case studies, this method is compared with several classic models, such as the exponential smoothing model and the autoregressive integrated moving average model, etc. Values of three error measures show that the new method outperforms other methods, especially when there are data fluctuations near the forecasting horizon. The relative advantages of the new method on small sample predictions are further investigated. Results demonstrate that model based on the proposed fractional bidirectional weakening buffer operator has higher forecasting accuracy
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