On Matrix Schr\"odinger Unitary Groups in Particular Representations of Finite Dimensional Quantum Dynamical Systems

TL;DR

This paper investigates specific matrix Schr"odinger unitary groups in finite-dimensional quantum systems, focusing on their properties, approximation methods, and numerical implementation for solving the Schr"odinger equation.

Contribution

It introduces particular types of matrix Schr"odinger unitary groups and provides estimates for their approximation and numerical implementation.

Findings

Derived estimates for matrix Schr"odinger semigroup approximations

Analyzed the numerical implementation of these groups in quantum evolution

Enhanced methods for finite-dimensional quantum system simulations

Abstract

In this paper we study some particular types of matrix Schr\"odinger semigroups of the form $\exp(-it\mathbb{H})$ where $\mathbb{H}\in M_N(\mathbf{C})$ is the Hamiltonian of a given quantum dynamical system modeled in the finite dimensional Hilbert space $\mathcal{H}$. Once we have defined a particular matrix Schr\"odinger unitary group we perform some estimates for its approximation and its corresponding implementation in the numerical solution of the finite dimensional Schr\"odinger evolution equation to that it is related.