Related papers: Exponential propagators for the Schr\"odinger equa…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
The eigenvalue-function pair of the 3D Schr\"odinger equation can be efficiently computed by use of high order, imaginary time propagators. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms…
We demonstrate how to apply the tensor-train format to solve the time-independent Schr\"{o}dinger equation for quasi one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are…
Strongly interacting electrons in solids are generically described by Hubbardtype models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
After introducing the formalism of the general space and time fractional Schr\"odinger equation, we concentrate on the time fractional Schr\"odinger equation and present new results via the elegant language of Fox's H-functions. We show…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free…
We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…
In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration…
The transfer matrix ${\mathbf{M}}$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system with a time-dependent non-Hermitian Hamiltonian. This leads to a dynamical…
An efficient algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for…
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional…
The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a…
In this paper we discuss the relation between non-homogeneous nonlinear fractional diffusive equations and the Schrodinger equation with time-dependent harmonic potential. It is well known that the Cole-Hopf transformation allows to…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The…
We consider the time-dependent Schr\"odinger equation on a Riemannian manifold $\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\mathcal{C}$. When we scale the potential in the directions…
We deal with fixed-time and Strichartz estimates for the Schr\"odinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical…
We present quantum algorithms for the loading of probability distributions using Hamiltonian simulation for one dimensional Hamiltonians of the form ${\hat H}= \Delta + V(x) \mathbb{I}$. We consider the potentials $V(x)$ for which the…