Related papers: Further generalization and numerical implementatio…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
We obtain almost-sure scattering for the cubic defocusing Schr{\"o}dinger equation in the Euclidean space {$\mathbb{R}^3$}, with randomized radially-symmetric initial data at some supercritical regularity scales. Since we make no smallness…
We present a time-dependent quantum algorithm for nuclear inelastic scattering in the time-dependent basis function on qubits approach. This algorithm aims to quantum simulate a subset of the nuclear inelastic scattering problems that are…
This work considers numerical methods for the time-dependent Schr\"{o}dinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that…
Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Algorithm, based on explicit representations for analytic continuation of the T-matrix Faddeev components on unphysical sheets, is worked out for calculations of resonances in the three-body quantum problem. According to the…
A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…
The time-dependent Schr\"odinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
Landauer-B\"uttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations.…
The projection formalism for calculating effective Hamiltonians and resonances is generalized to the nonlocal and/or nonhermitian case, so that it is applicable to the reduction of relativistic systems (Bethe-Salpeter equations), and to…
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
The cluster reduction method for the Yakubovsky equations in configuration space is used for calculations of zero-energy scattering in four-nucleon system. The main idea of the method consists in making use of expansions for the Yakubovsky…
We investigate the large time behavior of the solutions to the nonlinear focusing Schr\"odinger equation with a time-dependent damping in the energy sub-critical regime. Under non classical assumptions on the unsteady damping term, we prove…