An open scattering model in polymerized quantum mechanics

TL;DR

This paper develops a quantum master equation for a polymerized open quantum system inspired by loop quantum gravity, exploring how such a model affects scattering and decoherence in a Brownian particle within an ideal gas.

Contribution

It introduces a novel polymerized quantum scattering model using a non-standard representation of canonical commutation relations, extending previous collisional decoherence models.

Findings

Derived a master equation for polymerized quantum systems.

Compared properties of the new model with existing collisional decoherence models.

Discussed implications of polymerization on physical properties and assumptions.

Abstract

We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle in an ideal gas environment. The model is formulated in a top-down approach by choosing a Hamiltonian with a coupling between the system and environment that is generally associated with spatial decoherence. We extend the existing work on such models by using a non-standard representation of the canonical commutation relations, inspired by the quantization procedure applied in loop quantum gravity, which yields a model in which position operators are replaced by holonomies. The derivation of the master equation in a top-down approach opens up the possibility to investigate in detail whether the assumptions, usually used in such models in order to obtain a tractable form of the dissipator, hold also in the polymerized case or whether they need to be dropped or modified. Furthermore, we discuss some physical properties of the master equation associated to effective equations for the expectation values of the fundamental operators and compare our results to the already existing models of collisional decoherence.