A gravitationally induced decoherence model using Ashtekar variables - Fahn, Max Joseph; Giesel, Kristina; Kobler, Michael (Classical and Quantum Gravity, 2023)
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.
CRIS-Team Scopus Importer:2023-04-28
Keywords: decoherence; Dirac observables; geometrical clocks; linearised gravity; master equation

An Open Scattering Model in Polymerized Quantum Mechanics - Giesel, Kristina; Kobler, Michael (Mathematics, 2022)
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.
CRIS-Team Scopus Importer:2022-12-02
Keywords: decoherence models; open quantum systems; polymer quantum mechanics

Dynamical Properties of the Mukhanov-Sasaki Hamiltonian - Kobler, Michael; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2018)
The inflationary epoch at the beginning of the universe is commonly described within the frame- work of (linear) cosmological perturbation theory. The corresponding equation of motion for the gauge-invariant perturbations is the Mukhanov-Sasaki equation, which resembles a time-dependent harmonic oscillator. At first we will consider a mechanical analogue of the Mukhanov-Sasaki equa- tion and use the known Lewis-Riesenfeld invariant and the extended phase space formalism in- troduced in previous works in order to analyse the system. These techniques allow to construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one. The generators of this symplectic map can in turn be canonically quan- tised on the original part of the phase space, which is the constraint hypersurface of the extended theory, connecting to recent publications. Our further analysis leads us to a closed form of the time-evolution operator for the single-mode Mukhanov-Sasaki Hamiltonian, that is to the associ- ated Dyson series. We will analyse the characteristic properties of this time-evolution operator and discuss whether it can be extended to the full Fock space. Finally we give an outlook towards possible applications of these techniques to inflationary quantum cosmology.

Dynamical properties of the Mukhanov-Sasaki hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant - Fahn, Max Joseph; Giesel, Kristina; Kobler, Michael (Universe, 2019)
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.
CRIS-Team Scopus Importer:2019-08-16
Keywords: Adiabatic vacua; Bogoliubov transformation; Cosmological perturbation theory; Lewis-Riesenfeld invariant; Quantum cosmology

Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method - Gartner, Mathias; Miesbauer, David; Kobler, Michael; Freund, Julia; Carleo, Giuseppe; Zillich, Robert E. (SciPost Physics, 2025)
We present a new variational method to study the dynamics of a closed bosonic many-body system, the time-dependent hypernetted-chain Euler-Lagrange method, tHNC. Based on the Jastrow ansatz, it accounts for quantum fluctuations in a non-perturbative way. The tHNC method scales well with the number of dimensions, as demonstrated by our results on one-, two-, and three-dimensional systems. We apply the tHNC method to interaction quenches, i.e. sudden changes of the interaction strength, in homogeneous Bose gases. When the quench is strong enough that the final state has roton excitations (as found and predicted for dipolar and Rydberg-dressed Bose-Einstein condensates, respectively), the pair distribution function exhibits stable oscillations. For validation, we compare tHNC results with time-dependent variational Monte Carlo results in one and two dimensions.
CRIS-Team Scopus Importer:2025-04-25

The Lewis-Riesenfeld Invariant in the context of a Loop Quantum Cosmology quantisation - Matas, Bystrik; Giesel, Kristina; Kobler, Michael (2018)

The Spin-Boson Model with a time-dependent Oscillator Environment - Banarescu, Marvin; Kobler, Michael; Giesel, Kristina (2021)

Understanding gravitationally induced decoherence parameters in neutrino oscillations using a microscopic quantum mechanical model - Domi, Alba; Eberl, Thomas; Fahn, Max Joseph; Giesel, Kristina; Hennig, Lukas; Katz, Uli; Kemper, Roman; Kobler, Michael (Journal of Cosmology and Astroparticle Physics, 2024)
In this work, a microscopic quantum mechanical model for gravitationally induced decoherence introduced by Blencowe and Xu is investigated in the context of neutrino oscillations. The focus is on the comparison with existing phenomenological models and the physical interpretation of the decoherence parameters in such models. The results show that for neutrino oscillations in vacuum gravitationally induced decoherence can be matched with phenomenological models with decoherence parameters of the form Γij ∼ Δ m 4ij E -2. When matter effects are included, the decoherence parameters exhibit a dependence on the varying matter density across the Earth layers. This behavior can be explained by the nature of the coupling between neutrinos and the gravitational wave environment, as suggested by linearised gravity. On a theoretical level, these different models can be characterised by a different choice of Lindblad operators, with the model with decoherence parameters that do not include matter effects being less suitable from the point of view of linearised gravity. Consequently, in the case of neutrino oscillations in matter, the microscopic model does not agree with many existing phenomenological models that assume constant decoherence parameters in matter. Nonetheless, we identify the KamLAND experimental setup as particularly well-suited to establish the first experimental constraints on the model parameters, namely the neutrino coupling to the gravitational wave environment and its temperature, based on a prior analysis using the phenomenological model.
CRIS-Team Scopus Importer:2024-11-22
Keywords: gravity; neutrino experiments; neutrino theory; solar and atmospheric neutrinos