Approximation and limit theorems for quantum stochastic models with unbounded coefficients

TL;DR

This paper establishes a limit theorem for quantum stochastic differential equations with unbounded coefficients, extending classical results and providing insights into approximation convergence in quantum models.

Contribution

It introduces a new limit theorem for quantum stochastic differential equations with unbounded coefficients, extending the Trotter-Kato theorem.

Findings

Extended Trotter-Kato theorem for quantum stochastic models

Provided convergence results for approximations and perturbations

Illustrated results with physically relevant examples

Abstract

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular perturbations are obtained. The results are illustrated in several examples of physical interest.