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@article{faucris.298194725,
abstract = {We consider the coupling of a scalar field to linearised gravity and derive a relativistic gravitationally induced decoherence model using Ashtekar variables. The model is formulated at the gauge invariant level using suitable geometrical clocks in the relational formalism, broadening existing gauge invariant formulations of decoherence models. For the construction of the Dirac observables we extend the known observable map by a kind of dual map where the role of clocks and constraints is interchanged. We also discuss a second choice of geometrical clocks existing in the ADM literature. Then we apply a reduced phase space quantisation on Fock space and derive the final master equation choosing a Gibbs state for the gravitational environment and using the projection operator technique. The resulting master equation is not automatically of Lindblad type, a starting point sometimes assumed for phenomenological models, but still involves a residual time dependence at the level of the effective operators in the master equation due to the form of the correlation functions that we express in terms of thermal Wightman functions. Furthermore, we discuss why in the model analysed here the application of a second Markov approximation in order to obtain a set of time independent effective system operators is less straightforward than in some of the quantum mechanical models.},
author = {Fahn, Max Joseph and Giesel, Kristina and Kobler, Michael},
doi = {10.1088/1361-6382/acc5d5},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {decoherence; Dirac observables; geometrical clocks; linearised gravity; master equation},
note = {CRIS-Team Scopus Importer:2023-04-28},
peerreviewed = {Yes},
title = {{A} gravitationally induced decoherence model using {Ashtekar} variables},
volume = {40},
year = {2023}
}
@article{faucris.224623141,
abstract = {We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context of inflation considering a quasi-de Sitter spacetime. Our main interest lies in the question of to which extent these already well-established methods at the classical and quantum level for finitely many degrees of freedom can be generalized to field theory. As our results show, a straightforward generalization does in general not lead to a unitary operator on Fock space that implements the corresponding time-dependent canonical transformation associated with the Lewis-Riesenfeld invariant. The action of this operator can be rewritten as a time-dependent Bogoliubov transformation, where we also compare our results to already existing ones in the literature. We show that its generalization to Fock space has to be chosen appropriately in order to not violate the Shale-Stinespring condition. Furthermore, our analysis relates the Ermakov differential equation that plays the role of an auxiliary equation, whose solution is necessary to construct the Lewis-Riesenfeld invariant, as well as the corresponding time-dependent canonical transformation, to the defining differential equation for adiabatic vacua. Therefore, a given solution of the Ermakov equation directly yields a full solution of the differential equation for adiabatic vacua involving no truncation at some adiabatic order. As a consequence, we can interpret our result obtained here as a kind of non-squeezed Bunch-Davies mode, where the term non-squeezed refers to a possible residual squeezing that can be involved in the unitary operator for certain choices of the Bogoliubov map.},
author = {Fahn, Max Joseph and Giesel, Kristina and Kobler, Michael},
doi = {10.3390/universe5070170},
faupublication = {yes},
journal = {Universe},
keywords = {Adiabatic vacua; Bogoliubov transformation; Cosmological perturbation theory; Lewis-Riesenfeld invariant; Quantum cosmology},
note = {CRIS-Team Scopus Importer:2019-08-16},
peerreviewed = {Yes},
title = {{Dynamical} properties of the {Mukhanov}-{Sasaki} hamiltonian in the context of adiabatic vacua and the {Lewis}-{Riesenfeld} invariant},
volume = {5},
year = {2019}
}
@masterthesis{faucris.247208528,
author = {Fahn, Max Joseph},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Gravitationally} induced decoherence in open quantum systems using linearised gravity formulated in {Ashtekar} variables.},
year = {2020}
}
@masterthesis{faucris.320671726,
abstract = {In this thesis we consider the coupling of Maxwell theory to linearised gravity and derive a master
equation which suggests gravitationally induced decoherence on vector fields. The model is based
on the linear Hamiltonian formulation of general relativity with the use of Ashtekar variables.
The matter is coupled to linearised gravity, consistently using the framework of post-Minkowski
formalism. In order to formulate the model at the gauge invariant level, the relational formalism
is used. Therefore, we will consistently connect linearised gravity to the constrained system of
Maxwell’s theory by constructing suitable geometrical and electromagnetic reference fields. This
will be used to construct Dirac observables for the coupled system. Then we will use a reduced
phase space quantisation on the Fock space. To construct a TCL master equation we apply
the projecting operator technique with the time-convolutionless approach to the model, using a
Gibbs state as the initial state for linearised gravity. All assumptions and approximations in the
intermediate steps will be carefully analysed. In addition, the final TCL master equation is formulated in terms of thermal Wightmann functions and is not automatically of the Lindblad type,
which is often the starting point for phenomenological models, and in contrast to the existing
literature. For the derived master equation, we will also discuss why the Markov approximation
is not easily applicable. Furthermore, we will motivate that the formalism used in this thesis to
couple a constrained system to linearised gravity could be generalised to all Yang-Mills theories.