arXiv subjects

Eric Petermann

Publications and source records attributed to Eric Petermann.

4 recordsLinked to original sources

arXiv2026

Inherent Altermagnetism on regular hyperbolic lattices

Altermagnets are a novel class of magnetic systems characterized by their momentum-dependent spin splitting without net magnetization. In this work, we extend established Euclidean tight-binding models of altermagnets to regular hyperbolic lattices in two spatial dimensions defined on a discretized Poincar\'e disk. Using hyperbolic crystallography and hyperbolic band theory, we show that the inclusion of next-nearest neighbor hopping is sufficient to induce spin splitting in bipartite hyperbolic lattices. While certain families and special cases of hyperbolic lattices remain antiferromagnetic, we identify an entire family and a special case that show spin splitting in this framework. Hence, altermagnetism is inherent to certain hyperbolic lattices. Since hyperbolic band theory yields a momentum space that is at least four-dimensional, we classify the leading spin-splitting harmonics using four-dimensional atomic orbitals.

cond-mat.mes-hall↗

arXiv2025

Spin-resolved quasiparticle interference patterns on altermagnets via non-spin-resolved scanning tunneling microscopy

We investigate quasiparticle interference on an altermagnetic Lieb-like lattice and show how a non-spin-polarized scanning tunneling microscopy measurement can yield effectively spin-resolved information. Within a four-site tight-binding model, which can be tuned between an antiferromagnetic and a Lieb-type altermagnetic state, we introduce on-site impurities at distinct sublattice sites and compute the real space local density of states (LDOS) via a Green's function approach. A Fourier transformation of the impurity-induced LDOS yields the characteristic $d$-wave spin-split Fermi surface contours of the altermagnetic phase. Notably, by choosing which sublattice the impurity is placed upon, we show that the scattering amplitudes effectively encode spin-dependent contrasts: Impurities on one of the magnetic sublattices highlights predominantly spin-up contributions along one crystallographic direction, while impurities on the other one favor the complementary spin-down channel and orientation.

cond-mat.str-el↗

arXiv2023

Development of a high-resolution indoor radon map using a new machine learning-based probabilistic model and German radon survey data

Accurate knowledge of indoor radon concentration is crucial for assessing radon-related health effects or identifying radon-prone areas. Indoor radon concentration at the national scale is usually estimated on the basis of extensive measurement campaigns. However, characteristics of the sampled households often differ from the characteristics of the target population owing to the large number of relevant factors that control the indoor radon concentration, such as the availability of geogenic radon or floor level. We propose a model-based approach that allows a more realistic estimation of indoor radon distribution with a higher spatial resolution than a purely data-based approach. A modeling approach was used by applying a quantile regression forest to estimate the probability distribution function of indoor radon for each floor level of each residential building in Germany. Based on the estimated probability distribution function,a probabilistic Monte Carlo sampling technique was applied, enabling the combination and population weighting of floor-level predictions. In this way,the uncertainty of the individual predictions is effectively propagated into the estimate of variability at the aggregated level. The results show an approximate lognormal distribution of indoor radon in dwellings in Germany with an arithmetic mean of 63 Bq/m3, a geometric mean of 41 Bq/m3, and a 95th percentile of 180 Bq/m3. The exceedance probabilities for 100 and 300 Bq/m3 are 12.5% (10.5 million people affected) and 2.2 % (1.9 million people affected), respectively. The advantages of our approach are that it yields a) an accurate estimation of indoor radon concentration even if the survey is not fully representative with respect to floor level and radon concentration in soil, and b) an estimate of the indoor radon distribution with a much higher spatial resolution than basic descriptive statistics.

stat.ML↗

arXiv2023

Eigenmodes of the Laplacian on Hyperbolic Lattices

We examine a specific category of eigenfunctions of the lattice Laplacian on $\{p,q\}$-tessellations of the Poincar\'e disk that bear resemblance to plane waves in the continuum case. Our investigation reveals that the lattice eigenmodes deviate from the continuum solutions by a factor that depends solely on the local inclination of the vertex in relation to the wave's propagation direction. This allows us to compute certain eigenfunctions by numerical and analytical methods. For various special cases we find explicit exact eigenfunctions and their eigenvalues on the infinite lattice.

cond-mat.other↗