On the Approximation of Contractive Semigroups of Operators in Discretizable Hilbert Spaces

TL;DR

This paper investigates the properties and computational approximation of discrete contractive semigroups of operators in discretizable Hilbert spaces, with applications to quantum dynamical semigroups.

Contribution

It introduces new methods for approximating contractive semigroups in discretizable Hilbert spaces and applies these to quantum dynamical systems.

Findings

Properties of discrete contractive semigroups are characterized.

Implementation strategies for computational methods are developed.

Applications to the Heisenberg representation of quantum dynamical semigroups are demonstrated.

Abstract

The Computation of discrete Contractive semigroups becomes necessary when we deal with several types of evolution equations in Discretizable Hilbert spaces, in this work we study some properties of the discrete forms of the contractive semigroups induced by an approximation scheme in a prescribed Hilbert space, we also deal with the implementation of computational methods in this Hilbert Space and apply some of the results presented here in the Heisenberg representation of quantum dynamical semigroups.