@article{HaackRoeblitzScharkoietal.2010, author = {Haack, Fiete and R{\"o}blitz, Susanna and Scharkoi, Olga and Schmidt, Burkhard and Weber, Marcus}, title = {Adaptive Spectral Clustering for Conformation Analysis}, volume = {1281}, journal = {AIP Conference Proceedings}, number = {1}, publisher = {AIP}, doi = {10.1063/1.3498116}, pages = {1585 -- 1588}, year = {2010}, language = {en} } @article{SchaeferBungHartmannSchmidtetal.2011, author = {Sch{\"a}fer-Bung, B. and Hartmann, Carsten and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Dimension reduction by balanced truncation}, volume = {135}, journal = {J. Chem. Phys.}, number = {1}, pages = {014112}, year = {2011}, language = {en} } @article{MarsalekFrigatoVandeVondeleetal.2010, author = {Marsalek, Ondrej and Frigato, Tomaso and VandeVondele, Joost and Bradforth, Stephen E. and Schmidt, Burkhard and Sch{\"u}tte, Christof and Jungwirth, Pavel}, title = {Hydrogen Forms in Water by Proton Transfer to a Distorted Electron}, volume = {114}, journal = {J. Phys. Chem. B}, number = {2}, doi = {10.1021/jp908986z}, pages = {915 -- 920}, year = {2010}, language = {en} } @article{FrigatoVandeVondeleSchmidtetal.2008, author = {Frigato, Tomaso and VandeVondele, Joost and Schmidt, Burkhard and Sch{\"u}tte, Christof and Jungwirth, Pavel}, title = {Ab Initio Molecular Dynamics Simulation of a Medium-Sized Water Cluster Anion}, volume = {112}, journal = {J. Phys. Chem. A}, number = {27}, doi = {10.1021/jp711545s}, pages = {6125 -- 6133}, year = {2008}, language = {en} } @article{AntonySchmidtSchuette2005, author = {Antony, Jens and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Nonadiabatic Effects on Peptide Vibrational Dynamics Induced by Conformational Changes}, volume = {122}, journal = {J. Chem. Phys.}, number = {1}, doi = {10.1063/1.1829057}, pages = {014309}, year = {2005}, language = {en} } @article{HorenkoWeiserSchmidtetal.2004, author = {Horenko, Illia and Weiser, Martin and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Fully Adaptive Propagation of the Quantum-Classical Liouville Equation}, volume = {120}, journal = {J. Chem. Phys.}, number = {19}, doi = {10.1063/1.1691015}, pages = {8913 -- 8923}, year = {2004}, language = {en} } @incollection{MeerbachSchuetteHorenkoetal.2007, author = {Meerbach, E. and Sch{\"u}tte, Christof and Horenko, Illia and Schmidt, Burkhard}, title = {Metastable Conformational Structure and Dynamics}, volume = {87}, booktitle = {Analysis and Control of Ultrafast Photoinduced Reactions}, editor = {K{\"u}hn, O. and W{\"o}ste, L.}, publisher = {Springer}, address = {Berlin}, doi = {10.1007/978-3-540-68038-3_9}, pages = {796 -- 806}, year = {2007}, language = {en} } @article{NettesheimBornemannSchmidtetal.1996, author = {Nettesheim, Peter and Bornemann, Folkmar A. and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {An Explicit and Symplectic Integrator for Quantum-Classical Molecular Dynamics}, volume = {256}, journal = {Chem. Phys. Lett.}, number = {6}, doi = {10.1016/0009-2614(96)00471-X}, pages = {581 -- 588}, year = {1996}, language = {en} } @article{HorenkoSchmidtSchuette2002, author = {Horenko, Illia and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Multidimensional Classical Liouville Dynamics with Quantum Initial Conditions}, volume = {117}, journal = {J. Chem. Phys.}, number = {10}, doi = {10.1063/1.1498467}, pages = {4643 -- 4650}, year = {2002}, language = {en} } @article{HorenkoSalzmannSchmidtetal.2002, author = {Horenko, Illia and Salzmann, Ch. and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Quantum-Classical Liouville Approach to Molecular Dynamics}, volume = {117}, journal = {J. Chem. Phys.}, number = {24}, doi = {10.1063/1.1522712}, pages = {11075 -- 11088}, year = {2002}, language = {en} } @article{HorenkoSchmidtSchuette2001, author = {Horenko, Illia and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {A Theoretical Model for Molecules Interacting with Intense Laser Pulses}, volume = {115}, journal = {J. Chem. Phys.}, number = {13}, doi = {10.1063/1.1398577}, pages = {5733 -- 5743}, year = {2001}, language = {en} } @article{HaackFackeldeyRoeblitzetal.2013, author = {Haack, Fiete and Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, Olga and Weber, Marcus and Schmidt, Burkhard}, title = {Adaptive spectral clustering with application to tripeptide conformation analysis}, volume = {139}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.4830409}, pages = {110 -- 194}, year = {2013}, language = {en} } @misc{SchmidtZdanska1999, author = {Schmidt, Burkhard and Zdanska, Petra}, title = {Solution of the Time-Dependent Schroedinger Equation for Highly Symmetric Potentials}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3996}, number = {SC-99-11}, year = {1999}, abstract = {The method of symmetry adapted wavepackets (SAWP) to solve the time-dependent Schr{\"o}dinger equation for a highly symmetric potential energy surface is introduced. The angular dependence of a quantum-mechanical wavepackets is expanded in spherical harmonics where the number of close-coupled equations for the corresponding radial functions can be efficiently reduced by symmetry adaption of the rotational basis using the SWAP approach. Various techniques to generate symmetry adapted spherical harmonics (SASHs) for the point groups of highest symmetry (octahedral, icosahedral) are discussed. The standard projection operator technique involves the use of Wigner rotation matrices. Two methods to circumvent numerical instabilities occuring for large azimuthal quantum numbers are suggested. The first is based on a numerical scheme which employs Gaussian integrations yielding exact and stable results. The second is a recursive algorithm to generate higher order SASHs accurately and efficiently from lower order ones. The paper gives a complete set of ``seed functions'' generated by projection techniques which can be used obtain SASHs for all irreducible representations of the octahedral and icosahedral point groups recursively.}, language = {en} } @misc{BackhausSchmidtDantus1999, author = {Backhaus, Peter and Schmidt, Burkhard and Dantus, Marcos}, title = {Control of photoassociation yield: A quantum-dynamical study of the mercury system to explore the role of pulse duration from nanoseconds to femtoseconds}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4001}, number = {SC-99-12}, year = {1999}, abstract = {The photoassociation process shows strong dependence on the temporal duration of the electromagnetic field pulses and their frequencies. This dependence is investigated using quantum mechanical simulations that include all ranges of impact parameters and contributions from bound-to-bound transitions. The photoassociation yield of mercury atoms to produce excimer dimers is enhanced for short (ps) and for ultrashort (fs) pulse durations. Ultrashort laser pulses effectively overlap the entire range of free-to-bound transition, therefore achieving a maximum probability. Short pulses show a maximum in the photoassociation yield when their carrier frequency overlaps a particular free-to-bound spectroscopic resonance. Implications of these calculations on efforts to control bimolecular reactions are discussed.}, language = {en} } @inproceedings{SchemberaWuebbelingKleikampetal.2025, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Kleikamp, Hendrik and Schmidt, Burkhard and Shehu, Aurela and Reidelbach, Marco and Biedinger, Christine and Fiedler, Jochen and Koprucki, Thomas and Iglezakis, Dorothea and G{\"o}ddeke, Dominik}, title = {Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics}, volume = {2331}, booktitle = {Metadata and Semantic Research. MTSR 2024}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {9783031819735}, issn = {1865-0929}, doi = {10.1007/978-3-031-81974-2_8}, pages = {95 -- 109}, year = {2025}, abstract = {Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. To make this research data FAIR, we present how two previously distinct ontologies, MathAlgoDB for algorithms and MathModDB for models, were merged and extended into a living knowledge graph as the key outcome. This was achieved by connecting the ontologies through computational tasks that correspond to algorithmic tasks. Moreover, we show how models and algorithms can be enriched with subject-specific metadata, such as matrix symmetry or model linearity, essential for defining workflows and determining suitable algorithms. Additionally, we propose controlled vocabularies to be added, along with a new class that differentiates base quantities from specific use case quantities. We illustrate the capabilities of the developed knowledge graph using two detailed examples from different application areas of applied mathematics, having already integrated over 250 research assets into the knowledge graph.}, language = {en} } @article{GelssKleinMateraetal.2025, author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard}, title = {Quantum dynamics of coupled excitons and phonons in chain-like systems: tensor train approaches and higher-order propagators}, volume = {162}, journal = {The Journal of Chemical Physics}, doi = {10.1063/5.0258904}, year = {2025}, language = {en} } @inproceedings{SchemberaWuebbelingKleikampetal.2023, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Kleikamp, Hendrik and Biedinger, Christine and Fiedler, Jochen and Reidelbach, Marco and Shehu, Aurela and Schmidt, Burkhard and Koprucki, Thomas and Iglezakis, Dotothea and G{\"o}ddeke, Dominik}, title = {Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines}, booktitle = {Metadata and Semantic Research - MTSR 2023}, edition = {Communications in Computer and Information Science}, publisher = {Springer Nature Switzerland}, address = {Cham}, arxiv = {http://arxiv.org/abs/2310.20443}, doi = {10.1007/978-3-031-65990-4_14}, pages = {161 -- 168}, year = {2023}, abstract = {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.}, language = {en} } @article{SchemberaWuebbelingKopruckietal.2023, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Koprucki, Thomas and Biedinger, Christine and Reidelbach, Marco and Schmidt, Burkhard and G{\"o}ddeke, Dominik and Fiedler, Jochen}, title = {Building Ontologies and Knowledge Graphs for Mathematics and its Applications}, volume = {1}, journal = {Proceedings of the Conference on Research Data Infrastructure}, publisher = {TIB Open Publishing}, issn = {2941-296X}, doi = {10.52825/cordi.v1i.255}, year = {2023}, abstract = {Ontologies and knowledge graphs for mathematical algorithms and models are presented, that have been developed by the Mathematical Research Data Initiative. This enables FAIR data handling in mathematics and the applied disciplines. Moreover, challenges of harmonization during the ontology development are discussed.}, language = {en} } @article{RiedelGelssKleinetal.2023, author = {Riedel, Jerome and Gelß, Patrick and Klein, Rupert and Schmidt, Burkhard}, title = {WaveTrain: a Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains}, volume = {158}, journal = {The Journal of Chemical Physics}, number = {16}, doi = {10.1063/5.0147314}, pages = {164801}, year = {2023}, abstract = {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 Schr{\"o}dinger 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. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.}, language = {en} } @article{GelssKleinMateraetal.2022, author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard}, title = {Solving the time-independent Schr{\"o}dinger equation for chains of coupled excitons and phonons using tensor trains}, volume = {156}, journal = {The Journal of Chemical Physics}, number = {2}, arxiv = {http://arxiv.org/abs/2109.15104}, doi = {10.1063/5.0074948}, pages = {024109}, year = {2022}, abstract = {We demonstrate how to apply the tensor-train format to solve the time-independent Schr{\"o}dinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fr{\"o}hlich-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 that 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 the 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 central processing unit 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 wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fr{\"o}hlich-Holstein type Hamiltonians.}, language = {en} } @article{SchemberaWuebbelingShehuetal.2025, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Shehu, Aurela and Biedinger, Christine and Fiedler, Jochen and Reidelbach, Marco and Schmidt, Burkhard and Ferrer, Eloi and Koprucki, Thomas}, title = {FAIR Representation of Mathematical Research Data: MathModDB and MathAlgoDB as Knowledge Graphs for Mathematical Models and Numerical Algorithms}, journal = {2nd Conference on Research Data Infrastructure (CoRDI)}, doi = {10.5281/zenodo.16735911}, year = {2025}, language = {en} }