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An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
Quantum hydrodynamic theory (QHT) can describe some of the characteristic features of quantum electron dynamics that appear in metallic nanostructures, such as spatial nonlocality, electron spill-out, and quantum tunneling. Furthermore,…
The oscillator representation is used for the non-perturbative description of vacuum particle creation in a strong time-dependent electric field in the framework of scalar QED. It is shown that the method can be more effective for the…
We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree-Fock approximation. The present…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Nonlinear optical effects in vacuum have been investigated as a means to verify quantum electrodynamics in a region of low photon energy. By considering nonlinear electromagnetic waves in a three-dimensional cylindrical cavity, we report…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well-separated from relativistic-quantum scales. As a toy model, we study…
The stated overarching goal of the highly active field of quantum simulation of high-energy physics (HEP) is to achieve the capability to study \textit{ab-initio} real-time microscopic dynamics of $3+1$D quantum chromodynamics (QCD).…
We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on "diagonal"…
All-optical experiments at the high-intensity frontier offer a promising route to unprecedented precision tests of quantum electrodynamics in strong macroscopic electromagnetic fields. So far, most theoretical studies of all-optical…
The identification of prospective scenarios for observing quantum vacuum signals in high-intensity laser experiments requires both accurate theoretical predictions and the exploration of high-dimensional parameter spaces. Numerical…
We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…