Related papers: Time-frequency analysis and Harmonic Gaussian Func…
We show that, by using the quantum orthogonal functions invariant, we are able to solve a coupled of time dependent harmonic oscillators where all the time dependent frequencies are arbitrary. We do so, by transforming the time dependent…
We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST) to model and analyze oscillatory physiological signals. To…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
Any pure quantum state can be equivalently represented by means of its wave function psi(q) or of the Fermi function g_F(q,p), with q and p coordinates and conjugate momenta of the system under investigation.We show that a Gaussian wave…
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions.…
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for…
In this article we wish to present a new method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group (FRG). The FRG offers a powerful non-perturbative tool to deal with phase transitions…
We evaluate an adaptive gaussian quadrature integration scheme that will be suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for "full non-LTE" radiation…
We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point…
An efficient algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for…
Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
Objective: We present a technique for identification and statistical analysis of quasiperiodic spatiotemporal pressure signals recorded from multiple closely spaced sensors in the human colon. Methods: Identification is achieved by…
We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the…
Time-frequency analysis has been applied successfully in many fields. However, the traditional methods, like short time Fourier transform and Cohen distribution, suffer from the low resolution or the interference of the cross terms. To…
The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…
Time-frequency transforms represent a signal as a mixture of its time domain representation and its frequency domain representation. We present efficient algorithms for the quantum Zak transform and quantum Weyl-Heisenberg transform.
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…