Related papers: Anomaly-free singularities in the generalized Kohn…
The variational method employing the amplitude and width as collective coordinates of the Klein-Gordon oscillon leads to a dynamical system with unstable periodic orbits that blow up when perturbed. We propose a multiscale variational…
A method combining the Lagrange-mesh and the complex Kohn variational methods is developed for computing the $\mathcal{S}$ matrix of a 2$+$1 elastic scattering in the frame of three-body Coulomb systems. Resonance parameters can be obtained…
Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…
Two mechanisms of anomalous attenuation of probe waves in the experiments of ionosphere modification are discussed in the paper. The first mechanism is the well-known conversion of ordinary wave into plasma waves due to scattering from…
We present a simple method for obtaining elastic scattering phase shifts and cross sections from energies of atoms or ions in cavities. This method does not require calculations of wavefunctions of continuum states, is very general, and is…
In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…
Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is…
One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…
In this article we study a coupled system of differential equations with Allen-Cahn type non-linearity. Motivated by physical phenomena one of the unknowns in the system is accompanied by a singular perturbation parameter ${\epsilon}^2$ .…
In the era of noisy intermediate-scale quantum computers, variational quantum algorithms are promising approaches for solving optimization tasks by training parameterized quantum circuits with the aid of classical routines informed by…
Variational quantum metrology represents a powerful tool for optimizing generic estimation strategies, combining the principles of variational optimization with the techniques of quantum metrology. Such optimization procedures result…
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
Eigenvector continuation EC has been shown to accurately and efficiently reproduce ground states for targeted sets of Hamiltonian parameters. It uses as variational basis vectors the corresponding ground-state eigensolutions from selected…
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…
We consider the scattering of two-bosons with negative parity and spin 0 or 1. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to…
Distance-dependent phase shifts, amplitude functions, and radial wave functions for neutron-alpha elastic scattering are studied using the Variable Phase Approach. The microscopic KKNN potential is employed to calculate scattering…
In 2D acoustic and elastodynamic problems the spatial variability of a constitutive parameter such as the mass density makes it difficult to employ boundary integral and domain integral techniques to solve the forward and inverse wave…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…