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Previous studies of the response of the Moon to gravitational waves have been carried out using analytical or semi-analytical models assuming ideal lunar structures. Such models are advantageous for their high-speed calculation but fail to…
We present an off-resonant excitation scheme that realizes pronounced stationary inversion in a two level system. The created inversion exploits a cavity-assisted two photon resonance to enhance the multi-photon regime of nonlinear cavity…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…
We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…
Electromagnetic transient (EMT) simulation is a crucial tool for power system dynamic analysis because of its detailed component modeling and high simulation accuracy. However, it suffers from computational burdens for large power grids…
Problems in the field of open quantum systems often involve an environment that strongly influences the dynamics of excited states. Here we present a numerical method to model optical spectra of non-Markovian open quantum systems. The…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
Many quantum algorithms can be seen as a transition from a well-defined initial quantum state of a complex quantum system, to an unknown target quantum state, corresponding to a certain eigenvalue either of the Hamiltonian or of a…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
The explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a…
We present a novel three-dimensional (3D) imaging approach that combines two-dimensional spatial Fourier-domain imaging techniques with traditional radar pulse compression to recover both cross-range and down-range scene information. The…
Molecular absorption and photo-electron spectra can be efficiently predicted with real-time time-dependent density-functional theory (TDDFT). We show here how these techniques can be easily extended to study time-resolved pump-probe…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
Noise and decoherence are ubiquitous in the dynamics of quantum systems coupled to an external environment. In the regime where environmental correlations decay rapidly, the evolution of a subsytem is well described by a Lindblad quantum…
We introduce a computational framework for simulating non-adiabatic vibronic dynamics on circuit quantum electrodynamics (cQED) platforms. Our approach leverages hybrid oscillator-qubit quantum hardware with mid-circuit measurements and…
We propose and discuss a numerical method to model electromagnetic emission from the oscillating relativistic charged particles and its coherent amplification. The developed technique is well suited for free electron laser simulations, but…