Related papers: Fractional Bi-Spectrum
A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is…
If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often…
Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample…
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We obtain analytical approximations for the expectation and variance of the Spectral Kurtosis estimator in the case of Gaussian and coherent transient time domain signals mixed with a quasi-stationary Gaussian background, which are suitable…
It is shown, that the requirement of invariance under spatial rotations reveales an intrinsic fractional extended translation-rotation-like property for particles described with the fractional Schroedinger equation, which we call fractional…
We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario…
We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…
We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine…
Based on the Caputo definition of the fractional derivative the ground state spectra of mesons are classified as multiplets of the fractional rotation group. The comparison with the experimental values leads to the conclusion, that quarks…
The known solutions to the zero-sound dispersion equation are considered as placed on the physical and unphysical sheets in the complex plane of frequency.
For several types of correlations: mixed-state entanglement in systems of distinguishable particles, particle entanglement in systems of indistinguishable bosons and fermions and non-Gaussian correlations in fermionic systems we estimate…
The spectrum of the fermion zero modes in the vicinity of the vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev. Lett. 76…
High-quality quantum oscillators are preferred for precision sensing of external physical parameter because if the noise level due to interactions with the environment is too high, metrological information can be lost due to quantum…
If two signals are phase synchronous then the respective Fourier component at each spectral band should exhibit certain properties. In a pair of artificially generated phase synchronous signals the phase difference at each frequency band…
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the…
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
The gravitational frequency shift of light signals from the center of a spherically symmetric non-static matter distribution is considered. Explicit formulas for the ratio of the emitted and received frequencies are obtained in the case of…
Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the…