Parallel numerical method for nonlocal-in-time Schr\"odinger equation

TL;DR

This paper introduces a parallel numerical method for solving the non-stationary Schrödinger equation with nonlocal conditions and time-dependent potentials, enhancing computational efficiency and accuracy.

Contribution

The paper develops a novel parallel algorithm for nonlocal-in-time Schrödinger equations using polynomial collocation, with theoretical analysis and practical implementation details.

Findings

Method achieves efficient parallel computation

Provides error estimates and solution existence conditions

Applicable to complex quantum systems with nonlocal interactions

Abstract

We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given problem is discretized in-time using a polynomial-based collocation scheme. We establish the conditions on the existence of solution to the discretized problem, estimate the accuracy of the discretized solution and propose the method how this solution can be approximately found in an efficient parallel manner.