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The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
We consider a nonlinear autonomous random dynamical system of $N$ degrees of freedom coupled by Gaussian random interactions and characterized by a continuous spectrum $n_{\mu}(\lambda)$ of real positive relaxation rates. Using Kac-Rice…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
In our recent publication, we have proposed an analytical method for solving the problem of electronic relaxation in solution, modeled by a particle undergoing diffusive motion under the influence of two arbitrary potentials and the…
Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…
We consider a one dimensional mesoscopic capacitor in the presence of strong electron interactions and compute its admittance in order to probe the universal nature of the relaxation resistance. We use a combination of perturbation theory,…
The accurate modeling of mode hybridization and calculation of radiative relaxation rates have been crucial to the design and optimization of superconducting quantum devices. In this work, we introduce a spectral theory for the…
In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe inhomogeneous accelerating sections. It was shown that the single mode…
A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the…
Quantum sensing encompasses highly promising techniques with diverse applications including noise-reduced imaging, super-resolution microscopy as well as imaging and spectroscopy in challenging spectral ranges. These detection schemes use…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of…
Demonstrating and exploiting the quantum nature of larger, more macroscopic mechanical objects would help us to directly investigate the limitations of quantum-based measurements and quantum information protocols, as well as test long…
In a recent class of phase field crystal (PFC) models, the density order parameter is coupled to powers of its mean field. This effectively introduces a phenomenology of higher-order direct correlation functions acting on long wavelengths,…
The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into…
The Coupled-Cluster theory is one of the most successful high precision methods used to solve the stationary Schr\"odinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in…
The paper proposes a novel general definition of coherency among power system devices of any type. The proposed approach is thus not limited to synchronous machines. With this aim, the paper shows that coherency can be formally based on the…
We study a network of finitely many interacting clusters where each cluster is a collection of globally coupled circle maps in the thermodynamic (or mean field) limit. The state of each cluster is described by a probability measure, and its…