相关论文: The WKB Approximation without Divergences
In this paper, two high order complex contour discretization methods are proposed to simulate wave propagation in locally perturbed periodic closed waveguides. As is well known the problem is not always uniquely solvable due to the…
The classical field approximation is widely used to better understand the predictions of ultra-light dark matter. Here, we use the truncated Wigner approximation method to test the classical field approximation of ultra-light dark matter.…
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the…
Minkowski spacetime can be mapped by a series of projections in a higher-dimensional spacetime to a Euclidean space, constituting a process of Euclideanization shown here in detail for two dimensions. The result allows regularizations and…
We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…
In this paper we are interested in constructing WKB approximations for the non linear cubic Schr\"odinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of…
The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed matter physics to high-energy physics because of its non-perturbative…
Imaging with optical resolution through highly scattering media is a long sought-after goal with important applications in deep tissue imaging. Although being the focus of numerous works, this goal was considered impractical until recently.…
We revisit the fundamentals of two different methods for calculating classical observables: the eikonal method, which is a scattering amplitude-based method, and the worldline quantum field theory (WQFT) method. The latter has been…
This work is concerned with optical imaging in strongly diffusive environments. We consider a typical setting in optical coherence tomography where a sample is probed by a collection of wavefields produced by a laser and propagating through…
A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets…
The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-zero asymptotic behavior at large internuclear separations. The asymptotic solutions at…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
We consider the EBT algorithm (a particle method) for the non-local equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel which is not Lipschitz continuous, thus preventing the…
A scheme for approximating the kernel $w$ of the fractional $\alpha$-integral by a linear combination of exponentials is proposed and studied. The scheme is based on the application of a composite Gauss-Jacobi quadrature rule to an integral…
Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier…
The J-matrix method of scattering was developed to handle regular short-range potentials with applications in atomic, nuclear and molecular physics. Its accuracy, stability, and convergence properties compare favorably with other successful…
A deep learning-assisted inversion method is proposed to solve the inhomogeneous background imaging problem. Three non-iterative methods, namely the distorted-Born (DB) major current coefficients method, the DB modified Born approximation…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…