arXiv subjects

Mario Pitschmann

Publications and source records attributed to Mario Pitschmann.

At least 19 recordsLinked to original sources

arXiv2025

Directly computing Wigner functions for open quantum systems

The Wigner function is a well-known phase space distribution function with many applications in quantum mechanics. In this article, we consider an open quantum system consisting of a non-relativistic single particle interacting with a general, possibly relativistic environment. For this system, we derive an expression for directly computing the time-dependent Wigner function from its initial values. This result renders time-dependent Wigner functions more applicable without having to make additional approximations that would otherwise be required in order to solve the corresponding equation of motion. As an illustration of our findings, we discuss the example of a non-relativistic single scalar particle interacting via a Yukawa interaction with an environment comprising another type of scalar field that is treated relativistically.

quant-ph↗

arXiv2025

Equivalence of scalar-tensor theories and scale-dependent gravity

We present a novel equivalence between scale-dependent gravity and scalar-tensor theories that have only a single scalar field with a canonical kinetic term in the Einstein frame and a conformal coupling to the metric tensor. In particular, we show that the set of well-behaved scale-dependent gravity theories can be fully embedded into scalar-tensor theories in a unique way. Conversely, there are multiple ways to write a scalar-tensor theory as a scale-dependent theory. This equivalence is established both on the level of the actions and on the level of field equations. We find that, in the context of this equivalence, the scale-setting relation $k(x)$ is naturally promoted to a dynamical field, which is made manifest by including a corresponding kinetic term in the scale-dependent action. In addition, we demonstrate that the new equivalence fits well into the framework of existing equivalences involving the aforementioned theories and $f(R)$-gravity. Finally, we apply the equivalence relations to explicit examples from both scale-dependent gravity and scalar-tensor theories.

gr-qc↗

arXiv2025

Density matrices in quantum field theory: Non-Markovianity, path integrals and master equations

Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo field dynamics (TFD) and the Schwinger-Keldysh formalism. In this article, we provide a more detailed discussion of these methods and derive expressions for density matrix elements of closed and open systems. At first, we look at closed systems by discussing general solutions to the Schr\"odinger-like form of the quantum Liouville equations in TFD, showing that the dynamical map is indeed divisible, deriving a path integral-based expression for the density matrix elements in Fock space, and explaining why perturbation theory enables us to use the last even in situations where all initial states in Fock space are occupied. Subsequently, we discuss open systems in the same manner after tracing out environmental degrees of freedom from the solutions for closed systems. We find that, even in a general basis, the dynamical map is not divisible, which renders the dynamics of open systems non-Markovian. Finally, we show how the resulting expressions for open systems can be used to obtain quantum master equations, and comment on the artificiality of time integrals over density matrices that usually appear in many other master equations in the literature but are absent in ours.

hep-th↗

arXiv2024

Quantum and thermal pressures from light scalar fields

Light scalar fields play a variety of roles in modern physics, especially in cosmology and modified theories of gravity. For this reason, there is a zoo of experiments actively trying to find evidence for many scalar field models that have been proposed in theoretical considerations. Among those are setups in which the pressures expected to be induced by light scalar fields between two parallel plates are studied, for example, Casimir force experiments. While it is known that classical and quantum pressures caused by light scalar fields could have significant impacts on such experiments, in this article, we show that this can also be the case for thermal pressure. More specifically, we derive expressions for the quantum and thermal pressures induced by exchanges of light scalar field fluctuations between two thin parallel plates. As particular examples, we then look at screened scalar fields. For chameleon, symmetron and environment-dependent dilaton models, we find large regions in their parameter spaces that allow for thermal pressures to equal or exceed the quantum pressures. By comparing with earlier constraints from quantum pressure calculations, we conclude that thermal pressures induced by chameleons are actually of experimental significance.

hep-ph↗

arXiv2024

Screened Scalar Fields in the Laboratory and the Solar System

The last few decades have provided abundant evidence for physics beyond the two standard models of particle physics and cosmology. As is now known, the by far largest part of our universe's matter/energy content lies in the `dark' and consists of dark energy and dark matter. Despite intensive efforts on the experimental as well as the theoretical side, the origins of both are still completely unknown. Screened scalar fields have been hypothesized as potential candidates for dark energy or dark matter. Among these, some of the most prominent models are the chameleon, symmetron, and environment-dependent dilaton. In this article, we present a summary containing the most recent experimental constraints on the parameters of these three models. For this, experimental results have been employed from the qBOUNCE collaboration, neutron interferometry, and Lunar Laser Ranging (LLR), among others. In addition, constraints are forecast for the Casimir And Non Newtonian force EXperiment (CANNEX). Combining these results with previous ones, this article collects the most up-to-date constraints on the three considered screened scalar field models.

gr-qc↗

arXiv2024

Force metrology with plane parallel plates: Final design review and outlook

During the past few decades, abundant evidence for physics beyond the two standard models of particle physics and cosmology was found. Yet, we are tapping into the dark regarding our understanding of the dark sector. For more than a century, open problems related to the nature of the vacuum remain unresolved. Besides the traditional high-energy frontier and cosmology, technological advancement provides complementary access to new physics via high-precision experiments. Among the latter, the Casimir And Non-Newtonian force EXperiment (\cannex{}) has successfully completed its proof-of-principle phase and will soon commence operation. Benefiting from its plane parallel plate geometry, both interfacial and gravity-like forces are maximized, leading to increased sensitivity. A wide range of dark sector forces, Casimir forces in and out of thermal equilibrium, and gravity will be tested. This article describes the final experimental design, its sensitivity, and expected results.

hep-ex↗

arXiv2023

Search for dark energy with neutron interferometry

We use previously obtained experimental results by neutron interferometry to effectively constrain the parameter space of several prominent dark energy models. This investigation encompasses the environment-dependent dilaton field, a compelling contender for dark energy that emerges naturally within the strong coupling limit of string theory, alongside symmetron and chameleon fields. Our study presents substantial improvements over previous constraints of the dilaton and symmetron fields, improving parameter constraints by several orders of magnitude. However, the analysis does not yield any new constraints on the chameleon field. Furthermore, we establish constraints for the projected neutron split interferometer, which has recently concluded a decisive proof-of-principle demonstration. Our symmetron simulations reveal that depending on the parameter values there are multiple static solutions with increasing number of nodes and increasing energy inside a cylindrical vacuum chamber. This agrees with results obtained earlier in the literature for infinitely parallel plates. Interestingly, while these multiple solutions can correspond to domain walls forming inside the vacuum chamber, we also find solutions that do not reach their vacuum expectation value inside the vacuum chamber, but display multiple nodes nonetheless.

hep-ph↗

arXiv2023

Search for environment-dependent dilatons

The environment-dependent dilaton field is a well-motivated candidate for dark energy and naturally arises in the strong coupling limit of string theory. In this article, we present the very first experimental constraints on the parameters of this model. For this, we employ data obtained from the qBounce collaboration and the Lunar Laser Ranging (LLR) experiment. Furthermore, we forecast expected exclusion plots for the Casimir And Non Newtonian force EXperiment (Cannex) soon to be realised in an improved setup. Finally, we provide a detailed analysis of the screening mechanism and additional symmetries of the dilaton field theory.

gr-qc↗

arXiv2023

Dilaton-induced open quantum dynamics

In modern cosmology, scalar fields with screening mechanisms are often used as explanations for phenomena like dark energy or dark matter. Amongst a zoo of models, the environment dependent dilaton, screened by the Polyakov-Damour mechanism, is one of the least constrained ones. Using recently developed path integral tools for directly computing reduced density matrices, we study the open quantum dynamics of a probe, modelled by another real scalar field, induced by interactions with an environment comprising fluctuations of a dilaton. As the leading effect, we extract a correction to the probe's unitary evolution, which can be observed as a frequency shift. Assuming the scalar probe to roughly approximate a cold atom in matter wave interferometry, we show that comparing the predicted frequency shifts in two experimentally distinct setups has the potential to exclude large parts of the dilaton parameter space.

hep-ph↗

arXiv2023

Green's function analysis of the Neutron Lloyd interferometer

The neutron optical Lloyd interferometer can serve as a potent experiment for probing fundamental physics beyond the standard models of particles and cosmology. In this article, we provide a full Green's function analysis of a Lloyd interferometer in the limit that the reflecting mirror extends to the screen. We consider two distinct situations: first, we will review the theoretical case of no external fields being present. Subsequently, we will analyze the case in which a gravitational field is acting on the neutrons. The latter case provides the theory necessary for using a Lloyd interferometer as a probe of gravitational fields.

quant-ph↗

arXiv2023

qBounce: First Measurement of the Neutron Electric Charge with a Ramsey-type GRS Experiment

The qBounce collaboration built over the last years a new Ramsey-type Gravitational Resonance Spectroscopy (GRS) experiment. After commissioning between 2016 and 2018, the setup was able to measure the Ramsey transitions with GRS for the first time. Here we present a search of the hypothetical charge of the neutron as an application of GRS to study nonstandard model interactions. This article will describe the measuring principle and the setup in detail.

hep-ex↗

arXiv2022

Vacuum energy, the Casimir effect, and Newton's non-constant

We explore two hypotheses. First, the possibility that the quantum vacuum energy density of the Casimir effect contributes to a (local) gravitational vacuum energy density. Second, the possibility that a change in the gravitational coupling implies a change in the cosmological constant. We parametrize these two possibilities in a covariant framework and show that the next generation of Casimir experiments does have a surprisingly good chance of exploring this parameter space.

hep-th↗

arXiv2022

Density matrix formalism for interacting quantum fields

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar-scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo field dynamics and the Schwinger-Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at finite times and other non-equilibrium processes including those found in the theory of open quantum systems.

hep-th↗

arXiv2022

A new method for directly computing reduced density matrices

We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is based on techniques from non-equilibrium quantum field theory like thermo field dynamics, the Schwinger-Keldsyh formalism, and the Feynman-Vernon influence functional. It does not require the Markov approximation and is essentially a Lehmann-Szymanzik-Zimmermann-like reduction. In order to illustrate this method, we consider a real scalar field as an open quantum system interacting with an environment comprising another real scalar field. We give a general formula that allows for the perturbative computation of density matrix elements for any number of particles in a momentum basis. Finally, we consider a simple toy model and use this formula to obtain expressions for some of the system's reduced density matrix elements.

hep-th↗

arXiv2022

Dilaton Solutions for Laboratory Constraints and Lunar Laser Ranging

We derive approximate analytical solutions to the environment-dependent dilaton field theory equations in the presence of a one or two mirror system or a sphere. The one-dimensional equations of motion are integrated for each system. The solutions obtained herein can be applied to \textit{q}BOUNCE experiments, neutron interferometry and for the calculation of the dilaton field induced "Casimir force" in the \textsc{Cannex} experiment as well as for Lunar Laser Ranging. They are typical of the Damour-Polyakov screening mechanism whereby deviations from General Relativity are suppressed by a vanishingly small direct coupling of the dilaton to matter in dense environments.

gr-qc↗

arXiv2021

Spectra of Neutron Wave Functions in Earth's Gravitational Field

The time evolution of a quantum wave packet in the linear gravity potential is known as Quantum Bouncing Ball. The qBounce collaboration recently observed such a system by dropping wave packets of ultracold neutrons by a height of roughly 30 microns. In this article, space and momentum spectra as well as Wigner functions of the neutron wave functions in the gravitational field of the Earth are analyzed. We investigate the quantum states in the "preparation region", into which they transition after exiting a narrow double-mirror system and where we would expect to observe free fall and bounces in classical physics. For this, we start from the stationary solutions and eigenvalues of the Schr\"odinger equation in terms of Airy functions and their zeros. Subsequently, we examine space and momentum distributions as well as Wigner functions in phase space for pure and mixed quantum states. The eventual influence of Yukawa-like forces for small distances of several micrometers from the mirror is included through first order perturbation calculations. Those allow us to study the resulting modifications of space and momentum distributions, and phase space functions.

quant-ph↗

arXiv2021

Next generation design and prospects for CANNEX

The Casimir And Non-Newtonian force EXperiment (CANNEX) implements the unique geometry of macroscopic plane parallel plates that guarantees an optimum sensitivity with respect to interfacial forces and their gradients. Based on experience from the recently completed proof-of-principle phase, we have started a re-design of the setup aiming to reduce systematic effects and maximize the achievable sensitivity. Several propositions have been made to measure Casimir forces in and out of thermal equilibrium, hypothetical axion and axion-like dark matter interactions, and forces originating from chameleon or symmetron dark energy interactions. In the present article, we give details on the design for the next implementation stage of CANNEX and discuss the experimental opportunities as well as limitations expected for this new setup.

physics.ins-det↗

arXiv2020

Exact Solutions to Non-Linear Symmetron Theory II: One and Two Mirror Systems

We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one or two mirror system in the case of a spontaneously broken phase in vacuum as well as in matter. This complements a similar analysis performed in a previous article [1], in which the symmetron is in the spontaneously broken phase in vacuum but in the symmetric phase in matter. Here again, the one dimensional equations of motion are integrated exactly for both systems and their solutions are expressed in terms of Jacobi elliptic functions. In the case of two parallel mirrors the equations of motion provide also in this case a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and to the calculation of the symmetron field induced "Casimir force" in the Cannex experiment and allow to extend the investigation to hitherto unavailable regions in symmetron parameter space.

gr-qc↗