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An Open Scattering Model in Polymerized Quantum Mechanics

Author

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  • Kristina Giesel

    (Institute for Quantum Gravity, Theoretical Physics III, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
    These authors contributed equally to this work.)

  • Michael Kobler

    (Institute for Quantum Gravity, Theoretical Physics III, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Kristina Giesel & Michael Kobler, 2022. "An Open Scattering Model in Polymerized Quantum Mechanics," Mathematics, MDPI, vol. 10(22), pages 1-32, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4248-:d:971389
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    References listed on IDEAS

    as
    1. Neill Lambert & Shahnawaz Ahmed & Mauro Cirio & Franco Nori, 2019. "Modelling the ultra-strongly coupled spin-boson model with unphysical modes," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    2. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
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