An open scattering model in polymerized quantum mechanics
- URL: http://arxiv.org/abs/2207.08749v1
- Date: Mon, 18 Jul 2022 16:52:18 GMT
- Title: An open scattering model in polymerized quantum mechanics
- Authors: Kristina Giesel and Michael Kobler
- Abstract summary: We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle.
We discuss some physical properties of the master equation associated to effective equations for the expectation values of the fundamental operators.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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