Relations between the Hepp-Lieb and the Alli-Sewell laser models

TL;DR

This paper demonstrates how the Alli-Sewell laser model can be derived from the Hepp-Lieb Hamiltonian using the stochastic limit, establishing a theoretical connection between these models.

Contribution

It shows that the dissipative Alli-Sewell laser model emerges from the Hepp-Lieb Hamiltonian via the stochastic limit, linking two foundational laser models.

Findings

Dissipative Alli-Sewell model derived from Hepp-Lieb Hamiltonian.

Dicke-Haken-Lax Hamiltonian yields similar equations of motion after the stochastic limit.

Models are shown to be equivalent under certain conditions.

Abstract

In this paper we show that the dissipative version of the laser model proposed by Alli and Sewell can be obtained by considering the stochastic limit of the (open system) hamiltonian introduced by Hepp and Lieb in their seminal work. We also prove that the Dicke-Haken-Lax hamiltonian produces, after the stochastic limit is considered, the generator of a semigroup with equations of motion very similar to those of Alli-Sewell, and coinciding with these under suitable conditions.