arXiv subjects

Andreas Brunner

Publications and source records attributed to Andreas Brunner.

8 recordsLinked to original sources

arXiv2026

Some contributions to presheaf model theory, II -- back and forth

We discuss the back and forth technique in the context of presheaf model theory. The essence of the back and forth technique lies in showing the relationship between various hierarchies which calibrate similarity between two models and, more generally, between two pairs consisting of a model and a tuple from it. In this paper we define several such hierarchies for presheaf models (and tuples of sections from them): those based on the degree of extendibility of partial isomorphisms through literal back and forth conditions, on sharing specific, abstract invariants which we define (the $F^\alpha_{M,\bar{a}}$ of \S{}\ref{function_analysis} for example), on agreeing on the (truth) values of instantiations of formulae up to a given amount of quantifier completity, on the existence of winning strategies for player II in certain Ehrenfeucht-Fra\"iss\'e-type games and, finally, on satisfying certain infinitary sentences that arise in the construction of Scott sentences. We ultimately show that all of these hierarchies align.

math.LO↗

arXiv2026

Scott-Karp analysis without sentences

Scott and Karp gave an analysis which provides a level-by-level equivalence between global similarity between two structures and local commonality in terms of sharing particular invariants. Scott and Karp's local invariants were certain infinitary formulae. We give a more abstract version of the local side of Scott-Karp analysis which avoids the use of infinitary languages. We show the resulting hierarchies are still provide desired equivalences in the classical setting. Moreover, the abstract nature of our analysis, as we show, makes it suitable to provide local level-by-level equivalents to Hjorth's much more general version of global similarity in the context of topological group actions on topological groups. We, furthermore, provide, analogously to the classical work of Ehrenfeucht and Fra\"iss\'e, novel game theoretic equivalents for Hjorth's global similarity relations and some natural variants.

math.LO↗

arXiv2024

Some contributions to presheaf model theory

This paper makes contributions to ``pure'' sheaf model theory, the part of model theory in which the models are sheaves over a complete Heyting algebra. We start by outlining the theory in a way we hope is readable for the non-specialist. We then give a careful treatment of the interpretation of terms and formulae. This allows us to prove various preservation results, including strengthenings of the results of \cite{BM14}. We give refinements of Miraglia's work on directed colimits, \cite{M88}, and an analogue of Tarski's theorem on the preservation of $\forall_2$-sentences under unions of chains. We next show various categories whose objects are (pairs of) presheaves and sheaves with various notions of morphism are accessible in the category theoretic sense. Together these ingredients allow us ultimately to prove that these categories are encompassed in the AECats framework for independence relations developed by Kamsma in \cite{K22}.

math.LO↗

arXiv2020

Magnetic domains and domain wall pinning in two-dimensional ferromagnets revealed by nanoscale imaging

Magnetic-domain structure and dynamics play an important role in understanding and controlling the magnetic properties of two-dimensional magnets, which are of interest to both fundamental studies and applications[1-5]. However, the probe methods based on the spin-dependent optical permeability[1,2,6] and electrical conductivity[7-10] can neither provide quantitative information of the magnetization nor achieve nanoscale spatial resolution. These capabilities are essential to image and understand the rich properties of magnetic domains. Here, we employ cryogenic scanning magnetometry using a single-electron spin of a nitrogen-vacancy center in a diamond probe to unambiguously prove the existence of magnetic domains and study their dynamics in atomically thin CrBr$_3$. The high spatial resolution of this technique enables imaging of magnetic domains and allows to resolve domain walls pinned by defects. By controlling the magnetic domain evolution as a function of magnetic field, we find that the pinning effect is a dominant coercivity mechanism with a saturation magnetization of about 26~$\mu_B$/nm$^2$ for bilayer CrBr$_3$. The magnetic-domain structure and pinning-effect dominated domain reversal process are verified by micromagnetic simulation. Our work highlights scanning nitrogen-vacancy center magnetometry as a quantitative probe to explore two-dimensional magnetism at the nanoscale.

cond-mat.mtrl-sci↗

arXiv2014

Nano-engineered Diamond Waveguide as a Robust Bright Platform for Nanomagnetometry Using Shallow Nitrogen Vacancy Centers

Photonic structures in diamond are key to most of its application in quantum technology. Here, we demonstrate tapered nano-waveguides structured directly onto the diamond substrate hosting shallow-implanted nitrogen vacancy (NV) centers. By optimization based on simulations and precise experimental control of the geometry of these pillar-shaped nano-waveguides, we achieve a net photon flux up to ~ $1.7 \cdot 10^6 /s$. This presents the brightest monolithic bulk diamond structure based on single NV centers so far. We observe no impact on excited state lifetime and electronic spin dephasing time ($T_2$) due to the nanofabrication process. Possessing such high brightness with low background in addition to preserved spin quality, this geometry can improve the current nanomagnetometry sensitivity ~ 5 times. In addition, it facilitates a wide range of diamond defects-based magnetometry applications. As a demonstration, we measure the temperature dependency of $T_1$ relaxation time of a single shallow NV center electronic spin. We observe the two-phonon Raman process to be negligible in comparison to the dominant two-phonon Orbach process.

cond-mat.mes-hall↗

arXiv2013

Long-term drifts of stray electric fields in a Paul trap

We investigate the evolution of quasi-static stray electric fields in a linear Paul trap over a period of several months. Depending on how these electric fields are initially induced we observe very different time scales for the field drifts. Photo-induced electric fields decay on time scales of days. We interpret this as photo-electrically generated charges on insulating materials which decay via discharge currents. In contrast, stray fields due to the exposure of the ion trap to a beam of Ba atoms mainly exhibit slow dynamics on the order of months. We explain this observation as a consequence of a coating of the trap electrodes by the atomic beam. This may lead to contact potentials which can slowly drift over time due to atomic diffusion and chemical processes on the surface. In order not to perturb the field evolutions, we suppress the generation of additional charges and atomic coatings in the Paul trap during the measurements. For this, we shield the ion trap from ambient light and only allow the use of near-infrared lasers. Furthermore, we minimize the flux of atoms into the ion trap chamber. Long-term operation of our shielded trap led us to a regime of very low residual electric field drifts of less than 0.03 V/m per day.

quant-ph↗

arXiv2013

High precision nano scale temperature sensing using single defects in diamond

Measuring local temperature with a spatial resolution on the order of a few nanometers has a wide range of applications from semiconductor industry over material to life sciences. When combined with precision temperature measurement it promises to give excess to small temperature changes caused e.g. by chemical reactions or biochemical processes. However, nanoscale temperature measurements and precision have excluded each other so far owing to the physical processes used for temperature measurement of limited stability of nanoscale probes. Here we experimentally demonstrate a novel nanoscale temperature sensing technique based on single atomic defects in diamonds. Sensor sizes range from millimeter down to a few tens of nanometers. Utilizing the sensitivity of the optically accessible electron spin level structure to temperature changes we achieve a temperature noise floor of 5 mK Hz$^{-1/2}$ for single defects in bulk sensors. Using doped nanodiamonds as sensors yields temperature measurement with 130 mK Hz$^{-1/2}$ noise floor and accuracies down to 1 mK at length scales of a few ten nanometers. The high sensitivity to temperature changes together with excellent spatial resolution combined with outstanding sensor stability allows for nanoscale precision temperature determination enough to measure chemical processes of few or single molecules by their reaction heat even in heterogeneous environments like cells.

quant-ph↗

arXiv2012

A single ion as a three-body reaction center in an ultracold atomic gas

We report on three-body recombination of a single trapped Rb^+ ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K_3 depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is again an atomic Rb^+ ion suggesting that the ion merely acts as a catalyzer, possibly in the formation of deeply bound Rb_2 molecules.

physics.atom-ph↗