Related papers: Convergence Analysis of the Wolf Method for Coulom…
Scalar electrodynamics can be used to investigate the formation of cosmic strings in the early universe. We present the results of lattice Monte Carlo simulations of an effective three-dimensional U(1)+Higgs theory that describes the…
We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
We study the heavy charge potential in the Coulomb phase of pure gauge compact U(1) theory on the lattice. We calculate the static potential $V_W(T,{\vec R})$ from Wilson loops on a $16^3 \times 32$ lattice and compare with the predictions…
We study ionic liquids interacting with electrified interfaces. The ionic fluid is modeled as a Coulomb lattice gas. We compare the ionic density profiles calculated using a popular modified Poisson-Boltzmann equation with the explicit…
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
We present the efficient and universal numerical method for simulation of interacting quantum gas kinetics on a finite momentum lattice, based on the Boltzmann equation for occupation numbers. Usually, the study of models with two-particle…
We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between…
The Weizsacker-Williams method is a semiclassical approximation scheme used to analyze a wide variety of electromagnetic interactions. It can greatly simplify calculations that would otherwise be impractical or impossible to carry out using…
Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…
We derive the exact longitudinal plasmon dispersion relations, $\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb…
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the…
An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher…
For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice can be used to compute the ground state wave function and the dynamical…
We consider energies on a periodic set ${\mathcal L}$ of ${\mathbb R}^d$ of the form $\sum_{i,j\in{\mathcal L}} a^\varepsilon_{ij}|u_i-u_j|$, defined on spin functions $u_i\in\{0,1\}$, and we suppose that the typical range of the…
Nonlinear light-matter interaction, as the core of ultrafast optics, bulk photovoltaics, nonlinear optical sensing and imaging, and efficient generation of entangled photons, has been traditionally studied by first-principles theoretical…
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Comp. 89 (2020), Calcolo 57 (2020)] satisfies an energy…
A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order…
We show that a cooperative atom response in an optical lattice to resonant incident light can be employed for precise control and manipulation of light on a subwavelength scale. Specific collective excitation modes of the system that result…