arXiv subjects

Burkhard Schmidt

Publications and source records attributed to Burkhard Schmidt.

At least 19 recordsLinked to original sources

arXiv2026

MathModDB: A Database for Mathematical Models

When researchers need a mathematical model for a research problem, they face a fragmented landscape: relevant formulas, quantities, assumptions, and model variants are scattered across publications and domain-specific conventions. The Mathematical Models Database (MathModDB) addresses this challenge by providing a curated knowledge graph for mathematical models, deployed on the MaRDI Portal as part of the German National Research Data Infrastructure (NFDI). Building on ontology designs presented in earlier work, this paper focuses on MathModDB as a publicly available service. It addresses researchers who use mathematical models in their work -- whether in applied mathematics, engineering, or the natural sciences. We describe its deployment on the Wikibase-powered MaRDI Portal, report on its current scale, and demonstrate its practical use through a walkthrough of an electric discharge modeling use case from plasma physics. We further discuss the ecosystem around MathModDB, including its connection to the MathAlgoDB knowledge graph for numerical algorithms and the MaRDMO documentation tool.

cs.DL↗

arXiv2026

Basal-plane anisotropy of field-induced multipolar order in tetragonal CeRh$_2$As$_2$

Unconventional superconductivity in Ce-based Kondo-lattice materials emerges almost exclusively in the vicinity of weak dipolar magnetic orders, while higher multipolar orders are only known to occur in a few Pr-based unconventional superconductors and possibly URu$_2$Si$_2$. The multiphase superconductor CeRh$_2$As$_2$ appears to be a notable exception from this trend. Showing clear signatures of magnetism, this tetragonal system is suspected to host a concomitant quadrupolar order, which could be causing the strong enhancement of the ordering temperature when a magnetic field is applied perpendicular to the fourfold ($c$) axis of the lattice. In this work, we show that the field-temperature phase diagram of CeRh$_2$As$_2$ has a remarkable basal-plane anisotropy. This finding supports the scenario of coupled magnetic and multipolar ordering, which may have implications for the pairing mechanism of the superconductivity, and guides the development of the next iteration of theoretical models.

cond-mat.str-el↗

arXiv2024

Thermodynamics, elastic anomalies and excitations in the field induced phases of CeRh2As2

The tetragonal heavy fermion compound CeRh2As2 exhibits unconventional superconductivity accompanied by other broken symmetry phases that have been identified as presumably small moment intrinsic antiferromagnetism at low magnetic fields and induced quadrupolar order at higher in-plane fields. The latter may extend to very large pulsed-field range. The phase boundaries can be investigated by following thermodynamic anomalies like specific heat, magnetocaloric coefficient, thermal expansion and magnetostriction. We calculate their discontinuities and identify the influence of the field induced quadrupole on them. Furthermore we investigate the elastic constant anomalies which are determined by the static homogeneous quadrupolar RPA response functions. We present a calculation of these anomalies for the appropriate symmetry mode both in the disordered and ordered regime and investigate their change with applied field. In addition we consider the dynamical momentum dependent magnetic susceptibility and the associated dispersion of low energy magnetic modes and how their characteristics change across the phase boundary.

cond-mat.str-el↗

arXiv2024

Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this research data FAIR, two previously distinct ontologies were merged and extended, becoming a living knowledge graph. The link between the two ontologies is established by introducing computational tasks, as they occur in modeling, corresponding to algorithmic tasks. Moreover, controlled vocabularies are incorporated and a new class, distinguishing base quantities from specific use case quantities, was introduced. Also, both models and algorithms can now be enriched with metadata. Subject-specific metadata is particularly relevant here, such as the symmetry of a matrix or the linearity of a mathematical model. This is the only way to express specific workflows with concrete models and algorithms, as the feasible solution algorithm can only be determined if the mathematical properties of a model are known. We demonstrate this using two examples from different application areas of applied mathematics. In addition, we have already integrated over 250 research assets from applied mathematics into our knowledge graph.

cs.AI↗

arXiv2024

Anisotropic magnetic and quadrupolar H-T phase diagram of CeRh2As2

The tetragonal heavy fermion compound CeRh2As2 has intriguing low temperature symmetry breaking phases whose nature is unclear. The unconventional superconducting phase is complemented by other normal state phases which presumably involve ordering of 4f electron multipoles supported by the Kramers doublets split by the tetragonal crystal electric field (CEF). The most striking aspect is the pronounced anisotropic H-T phase boundary for in-plane and out-of plane field direction. Using a localized 4f CEF model we demonstrate that its essential features can be understood as the result of competing low field easy-plane magnetic order and field-induced quadrupolar order of XY type. We present calculations based on a coupled multipole random-phase approximation (RPA) response function approach as well as a molecular field treatment in the ordered regime. We use an analytical approach for a reduced quasi-quartet model and numerical calculations for the complete CEF level scheme. We discuss the quantum critical properties as function of multipolar control parameters and explain the origin of a pronounced a-c anisotropy of the H-T phase diagram. Finally the field and temperature evolution of multipolar order parameters is derived and the high field phase diagram is predicted.

cond-mat.str-el↗

arXiv2024

Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies.

cs.AI↗

arXiv2024

Concurrence of directional Kondo transport and incommensurate magnetic order in the layered material AgCrSe$_2$

In this work, we report on the concurrent emergence of the directional Kondo behavior and incommensurate magnetic ordering in a layered material. We employ temperature- and magnetic field-dependent resistivity measurements, susceptibility measurements, and high resolution wavelength X-ray diffraction spectroscopy to study the electronic properties of AgCrSe$_2$. Impurity Kondo behavior with a characteristic temperature of $T_\text K$ = 32 K is identified through quantitative analysis of the in-plane resistivity, substantiated by magneto-transport measurements. The agreement between our experimental data and the Schlottmann's scaling theory allows us to determine the impurity spin as $S$ = 3/2. Furthermore, we discuss the origin of the Kondo behavior and its relation to the material's antiferromagnetic transition. Our study uncovers an unusual phenomenon -- the equivalence of the Néel temperature and the Kondo temperature -- paving the way for further investigations into the intricate interplay between impurity physics and magnetic phenomena in quantum materials, with potential applications in advanced electronic and magnetic devices.

cond-mat.str-el↗

arXiv2024

FSSH-2: Fewest Switches Surface Hopping with robust switching probability

This study introduces the FSSH-2 scheme, a redefined and numerically stable adiabatic Fewest Switches Surface Hopping (FSSH) method for mixed quantum-classical dynamics. It reformulates the standard FSSH hopping probability without non-adiabatic coupling vectors and allows for numerical time integration with larger step sizes. The advantages of FSSH-2 are demonstrated by numerical experiments for five different model systems in one and two spatial dimensions with up to three electronic states.

physics.comp-ph↗

arXiv2023

Topological paramagnetic excitons of localized f electrons on the honeycomb lattice

We investigate the dispersive paramagnetic excitons on the honeycomb lattice that originate from the crystalline-electric field (CEF) split localized f-electron states in the paramagnetic state due to intersite exchange. We start with a symmetry analysis of possible Ising-type singlet-singlet and xy-type singlet-doublet models. The former supports only symmetric intersite-exchange while the latter additionally allows for antisymmetric Dzyaloshinski-Moriya (DM) exchange interactions. We calculate the closed expressions for magnetic exciton dispersion using both response function formalism and the bosonic Bogoliubov approach. We do this for the most general model that shows inversion symmetry breaking on the honeycomb lattice but also discuss interesting special cases. By calculating Berry curvatures and Chern numbers of paramagnetic excitons we show that the xy model supports nontrivial topological states in a wide range of parameters. This leads to the existence of excitonic topological edge states with Dirac dispersion lying in the zone boundary gap without the presence of magnetic order.

cond-mat.str-el↗

arXiv2023

Elastocaloric effect of the heavy-fermion system YbPtBi

YbPtBi is one of the heavy-fermion systems with largest Sommerfeld coefficient $γ$ and is thus classified as a `super'-heavy fermion material. In this work, we resolve the long-debated question about the hierarchy of relevant energy scales, such as crystal-electric field (CEF) levels, Kondo and magnetic ordering temperature, in YbPtBi. Through measurements of the a.c. elastocaloric effect and generic symmetry arguments, we identify an \textit{elastic level splitting} that is uniquely associated with the symmetry-allowed splitting of a quartet CEF level. This quartet, which we identify to be the first excited state at $Δ/k_\text B\approx1.6\,\rm K$ above the doublet ground state at ambient pressure, is well below the Kondo temperature $T_\text K\approx10\,\rm K$. Thus, our analysis provides strong support for models that predict that the heavy electron mass is a result of an enhanced degeneracy of the CEF ground state, i.e., a quasi-sextet in YbPtBi. At the same time, our study shows the potential of the a.c. elastocaloric effect to control and quantify strain-induced changes of the CEF schemes, opening a different route to disentangle the CEF energy scales from other relevant energy scales in correlated quantum materials.

cond-mat.str-el↗

arXiv2023

WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit-tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schroedinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics on the fly, with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions, and with NN interactions only.

quant-ph↗

arXiv2023

Quantum dynamics of coupled excitons and phonons in chain-like systems: tensor train approaches and higher-order propagators

We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations, we aim at reducing memory consumption and computational costs. As an example, coupled excitons and phonons modeled in terms of Fr\"{o}hlich-Holstein type Hamiltonians are studied here. By comparing our tensor-train based results with semi-analytical results, we demonstrate the key role of the ranks of the quantum state vectors. Typically, an excellent quality of the solutions is found only when the maximum number of ranks exceeds a certain value. One class of propagation schemes builds on splitting the Hamiltonian into two groups of interleaved nearest-neighbor interactions commutating within each of the groups. In particular, the 4-th order Yoshida-Neri and the 8-th order Kahan-Li symplectic composition yield results close to machine precision. Similar results are found for 4-th and 8-th order global Krylov scheme. However, the computational effort currently restricts the use of these four propagators to rather short chains which also applies to propagators based on the time-dependent variational principle, typically used for matrix product states. Yet another class of propagators involves explicit, time-symmetrized Euler integrators. Especially the 4-th order variant is recommended for quantum simulations of longer chains, even though the high precision of the splitting schemes cannot be reached. Moreover, the scaling of the computational effort with the dimensions of the local Hilbert spaces is much more favorable for the differencing than for splitting or variational schemes.

quant-ph↗

arXiv2022

Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields

We show that two seemingly unrelated problems - the trapping of an atom in an optical superlattice (OSL) and the libration of a planar rigid rotor in combined electric and optical fields - have isomorphic Hamiltonians. Formed by the interference of optical lattices whose spatial periods differ by a factor of two, OSL gives rise to a periodic potential that acts on atomic translation via the AC Stark effect. The latter system, also known as the generalized planar pendulum (GPP), is realized by subjecting a planar rigid rotor to combined orienting and aligning interactions due to the coupling of the rotor's permanent and induced electric dipole moments with the combined fields. The mapping makes it possible to establish correspondence between concepts developed for the two eigenproblems individually, such as localization on the one hand and orientation/alignment on the other. Moreover, since the GPP problem is conditionally quasi-exactly solvable (C-QES), so is atomic trapping in an OSL. We make use of both the correspondence and the quasi-exact solvability to treat ultracold atoms in an optical superlattice as a semifinite-gap system. The band structure of this system follows from the eigenenergies and their genuine and avoided crossings obtained previously for the GPP as analytic solutions of the Whittaker-Hill equation. These solutions characterize both the squeezing and the tunneling of atoms trapped in an optical superlattice and pave the way to unraveling their dynamics in analytic form.

cond-mat.quant-gas↗

arXiv2022

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Frenkel-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach which directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in case of homogeneous systems the tensor-train ranks of state vectors only marginally depend on the chain length which results in a linear growth of the storage consumption. However, the CPU time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wavepacket width and the corresponding stabilization energy on the exciton-phonon coupling strength, though only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the restrictions of the Frenkel-Holstein type Hamiltonians.

physics.comp-ph↗

arXiv2021

Microchannel cooling for the LHCb VELO Upgrade I

The LHCb VELO Upgrade I, currently being installed for the 2022 start of LHC Run 3, uses silicon microchannel coolers with internally circulating bi-phase \cotwo for thermal control of hybrid pixel modules operating in vacuum. This is the largest scale application of this technology to date. Production of the microchannel coolers was completed in July 2019 and the assembly into cooling structures was completed in September 2021. This paper describes the R\&D path supporting the microchannel production and assembly and the motivation for the design choices. The microchannel coolers have excellent thermal peformance, low and uniform mass, no thermal expansion mismatch with the ASICs and are radiation hard. The fluidic and thermal performance is presented.

physics.ins-det↗

arXiv2021

Quantum dynamics of a polar rotor acted upon by an electric rectangular pulse of variable duration

As demonstrated in our previous work [J. Chem. Phys. 149, 174109 (2018)], the kinetic energy imparted to a quantum rotor by a non-resonant electromagnetic pulse with a Gaussian temporal profile exhibits quasi-periodic drops as a function of the pulse duration. Herein, we show that this behaviour can be reproduced with a simple waveform, namely a rectangular electric pulse of variable duration, and examine, both numerically and analytically, its causes. Our analysis reveals that the drops result from the oscillating populations that make up the wavepacket created by the pulse and that they are necessarily accompanied by drops in the orientation and by a restoration of the pre-pulse alignment of the rotor. Handy analytic formulae are derived that allow to predict the pulse durations leading to diminished kinetic energy transfer and orientation. Experimental scenarios are discussed where the phenomenon could be utilized or be detrimental.

quant-ph↗

arXiv2021

Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions

We investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work [Frontiers in Physics 2, 37 (2014); Eur. Phys. J. D 71, 149 (2017)]. This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory.

quant-ph↗

arXiv2019

Effective Spin-1/2 Moments on a Yb$^{3+}$ Triangular Lattice: an ESR Study

We investigated the spin dynamics by electron spin resonance (ESR) of the Yb-based, effective spin-1/2 delafossites NaYbO$_{2}$, AgYbO$_{2}$, LiYbS$_{2}$, NaYbS$_{2}$, and NaYbSe$_{2}$ which all show an absence of magnetic order down to lowest reachable temperatures and thus are prime candidates to host a quantum spin-liquid ground state in the vicinity of long range magnetic order. Clearly resolved ESR spectra allow to obtain well-defined $g$ values which are determined by the crystal field of the distorted octahedral surrounding of the Yb-ions in trigonal symmetry. This local crystal field information provides important input to characterize the effective $S = 1/2$ Kramers doublet as well as the anisotropic exchange coupling between the Yb ions which is crucial for the nature of the groundstate. The ESR linewidth $ΔB$ is characterised by the spin dynamics and is mainly determined by the anisotropic exchange coupling. We discuss and compare $ΔB$ of the above mentioned delafossites focussing on the low temperature behaviour which is dominated by the growing influence of spin correlations.

cond-mat.str-el↗