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A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to…
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…
Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structure of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with…
This paper introduces Bohmian mechanics (BM) into the intense laser-atom physics to study high-order harmonic generation. In BM, the trajectories of atomic electrons in intense laser field can be obtained with the Bohm-Newton equation. The…
High harmonic generation (HHG) is a manifestation of the strongly nonlinear response of matter to intense laser fields and has, as the basis for coherent XUV sources a variety of applications. Recently, HHG from atoms in a phase and…
We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on…
High-harmonic generation (HHG) normally requires a careful adjustment of the driving laser intensity (typically $10^{14} - 10^{15}$ W/cm$^2$) and gas medium parameters to enable good phase matching conditions. In contrast with conventional…
We experimentally study the field-intensity dependence of high-harmonic generation in bulk gallium arsenide in reflection geometry. We find the oscillatory behavior at high fields where a perturbative scaling law no longer holds. By…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to…
Using Time-Dependent Density Functional Theory (TDDFT) nonlinear nonperturbative response of the molecular system is studied for photoisomerization reaction. The 1,3-cyclohexadiene photoisomerization is probed by the high-harmonic…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
One key parameter in the high-order harmonic generation (HHG) phenomenon is the exact frequency of the generated harmonic field. Its deviation from perfect harmonics of the laser frequency can be explained considering (i) the single-atom…
Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well-known…
The high-order harmonic spectrum generated in two-color intense laser field under certain conditions has a pronounced maximum caused by the so called spectral caustic. Using a numerical solution of the 3D time-dependent Schr\"odinger…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In…
A theory for laser-driven electron dynamics and high-harmonic generation in bulk solids with two lattice sites per unit cell of arbitrary dimension is formulated. In tight-binding approximation, such solids can be described by $2\times 2$…
The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate…