Related papers: On the Numerical Solution of the Exact Factorizati…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
The dynamics of highly magnetized plasmas in extreme astrophysical environments are effectively modeled by Force-Free Electrodynamics (FFE), a framework essential for studying objects like neutron stars and accreting black holes. The…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
In parallel with the evolution of femtosecond and attosecond laser as well as free-electron laser technology, a variety of theoretical methods have been developed to describe the behavior of atoms, molecules, clusters, and solids under the…
A one-electron Schroedinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single-…
We introduce a simple and stable computational method for ill-posed partial differential equation (PDE) problems. The method is based on Schr\"odingerization, introduced in [S. Jin, N. Liu and Y. Yu, arXiv:2212.13969][S. Jin, N. Liu and Y.…
We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$. The…
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…
The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data. Accurate solutions can be systematically derived by decomposing the exponential in a product form. For…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…
An approach to non-adiabatic dynamics of atoms in molecular and condensed matter systems under general non-equilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second…
An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely-spaced electronic states. We propose a mixed quantum-classical scheme…
A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order…
The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wavepackets that generally will have…
Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and…
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A…