Related papers: Explicitly correlated Gaussians with tensor pre-fa…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
We evaluate the squeezing of a probe beam with a transverse Gaussian profile interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor {\mu} \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients…
In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer, Berlin, 1998)] present the stochastic variational method in a very exhaustive way. In this…
Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic,…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
An overview of quantum-mechanical methods to generate cross-section data for electron collisions with atoms and molecules is presented. Particular emphasis is placed on the time-independent close-coupling approach, since it is particularly…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
The Feynman--Hellmann approach to computing matrix elements in lattice QCD by first adding a perturbing operator to the action is described using the transition matrix and the Dyson expansion formalism. This perturbs the energies in the…
Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary…
Using multiple scattering theory, we derived for the first time analytical formulas for electrostrictive tensors for two dimensional metamaterial systems. The electrostrictive tensor terms are found to depend explicitly on the symmetry of…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
We present an efficient algorithm for constructing all the matrix elements of covariant tensor currents of massless particles of arbitrary spins in the covariant formulation. The construction of matrix elements can be taken simply by…
Approximating significance scans of searches for new particles in high-energy physics experiments as Gaussian fields is a well-established way to estimate the trials factors required to quantify global significances. We propose a novel,…