Related papers: Time-parallel simulation of the Schr\"odinger Equa…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
Simulating large scale lattice dynamics directly is computationally demanding due to the high complexity involved, yet such simulations are crucial for understanding the mechanical and thermal properties of many physical systems. In this…
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a…
Time dependent Schr\"odinger equations with conservative force field U commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the semiclassical regime. Extremely high oscillations…
The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrodinger equation in an explicitly iterative process. However, the method requires the spatial grid…
In this paper, we studied the space-time estimates for the solution to the Schr\"odinger equation. By polynomial partitioning, induction arguments, bilinear to linear arguments and broad norm estimates, we set up several maximal estimates…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
The purpose of the present paper is to discuss the time dependent Schr\"odinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show…
With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits…
A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to…
This paper is about the fractional Schr\"odinger equation expressed in terms of the Caputo time-fractional and quantum Riesz-Feller space fractional derivatives for particle moving in a potential field. The cases of free particle (zero…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
Many search-based quantum algorithms that achieve a theoretical speedup are not practically relevant since they require extraordinarily long coherence times, or lack the parallelizability of their classical counterparts.This raises the…
In the present work we consider a time-dependent Schr\"odinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not…
Linear combinations of complex gaussian functions, where the linear and nonlinear parameters are allowed to vary, are shown to provide an extremely flexible and effective approach for solving the time-dependent Schr\"odinger equation in one…
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
We prove optimal convergence rates for certain low-regularity integrators applied to the one-dimensional periodic nonlinear Schr\"odinger and wave equations under the assumption of $H^1$ solutions. For the Schr\"odinger equation we analyze…
We present an ab initio approach to solve the time-dependent Schr\"odinger equation to treat electron and photon impact multiple ionization of atoms or molecules. It combines the already known time scaled coordinate method with a new high…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…