Publications
Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – TRR 352 – Project-ID 470903074
2025
Á. Capel, M. Moscolari, S. Teufel and T. Wessel. From Decay of Correlations to Locality and Stability of the Gibbs State. Commun. Math. Phys. 406, 43 (2025). https://doi.org/10.1007/s00220-024-05198-x
R. Frank, H. Kovařík. Lieb–Thirring Inequality for the 2D Pauli Operator. Commun. Math. Phys. 406, 23 (2025). https://doi.org/10.1007/s00220-024-05177-2
D. V. Hoang, P. Pickl. Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas. Ann. Henri Poincaré (2025). https://doi.org/10.1007/s00023-024-01532-0
M. Lemm, S. Rademacher. Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory. Quantum 9, 1587 (2025). https://doi.org/10.22331/q-2025-01-13-1587
L. Read. Negative Spectrum of Schrödinger Operators with Rapidly Oscillating Potentials. Ann. Henri Poincaré 26, 81–97 (2025). https://doi.org/10.1007/s00023-024-01457-8
P. Müller, J. Stern. On the return probability of the simple random walk on Galton–Watson trees, Electron. J. Probab. 30, 10, 23 pp. (2025). https://doi.org/10.1214/25-EJP1266
B. Roos, R. Seiringer. BCS Critical Temperature on Half-Spaces. Arch Rational Mech Anal 249, 20 (2025). https://doi.org/10.1007/s00205-025-02088-x
B. Roos, R. Seiringer. Enhanced Superconductivity at a Corner for the Linear BCS Equation. Forum of Mathematics, Sigma 13 (2025): e71. https://doi.org/10.1017/fms.2024.145
B. Roos. Linear criterion for an upper bound on the Bardeen-Cooper-Schrieffer critical temperature. J. Math. Phys. 66, 011901 (2025). https://doi.org/10.1063/5.0230179
O. Siebert. On the thermodynamic limit of interacting fermions in the continuum. Lett Math Phys 115, 33 (2025). https://doi.org/10.1007/s11005-025-01919-y
S. Teufel, R. Tumulka, C. Vogel. Canonical Typicality for Other Ensembles than Micro-canonical. Ann. Henri Poincaré 26, 1477–1518 (2025). https://doi.org/10.1007/s00023-024-01466-7
Preprints
R. Benguria, H. Siedentop. Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals. arXiv:2502.15444
A. Bluhm, Á. Capel, P. Costa Rico, A. Jenčová. Belavkin-Staszewski Quantum Markov Chains. arXiv:2501.09708
L. Bollmann. An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator. arXiv:2503.18622
A. Brollo, A. del Campo, A. Bastianello. Universal efficiency boost in prethermal quantum heat engines. arXiv:2504.02044
M. Brooks, J. Oldenburg, D. Saint Aubin, B. Schlein. Third Order Upper Bound for the Ground State Energy of the Dilute Bose Gas. arXiv:2506.04153
Á. Capel, A. Chowdhury, S. Scalet et al. Classical Estimation of the Free Energy and Quantum Gibbs Sampling from the Markov Entropy Decomposition. arXiv:2504.17405
E. Carlen, R. Frank, S. Larson. A Jensen inequality for partial traces and applications to partially semiclassical limits. arXiv:2502.09160
B. Chen, Y. Guo, P. T. Nam, D. H. Ou Yang. Mass-Critical Neutron Stars in the Hartree-Fock and Hartree-Fock-Bogoliubov Theories. arXiv:2504.16462
L. Chen, J. Jung, P. Pickl, Z. Wang. On the mean-field limit of Vlasov-Poisson-Fokker-Planck equations. arXiv:2505.13038
M. R. Christiansen. A Correlational Bound for Eigenvalues of Fermionic 2-Body Operators. arXiv:2505.21167
D. Denisov, A. Sakhanenko, S. Terveer, V. Wachtel. Random walks with square-root boundaries: the case of exact boundaries g(t) = c√t+b − a. arXiv:2501.04554
A. Deuchert, J. Lampart, M. Lemm. Dynamics and equilibrium states of infinite systems of lattice bosons. arXiv:2505.13170
J. Dolbeault, M. Esteban, R. Frank, M. Loss. The CKN inequality for spinors: symmetry and symmetry breaking. arXiv:2504.16909
G. Duong, P. T. Nam. Lieb–Thirring inequalities for large quantum systems with inverse nearest-neighbor interactions. arXiv:2501.00866
J. Faupin, M. Lemm, I. M. Sigal, J. Zhang. Macroscopic suppression of supersonic quantum transport. arXiv:2503.19788
R. Frank, S. Larson, P. Pfeiffer. Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian. arXiv:2502.02388
R. Frank, J. Mateu, M. Mora, L. Rondi, L. Scardia, J. Verdera. Explicit minimisers for anisotropic Riesz energies. arXiv:2504.11644
E. Giacomelli, Ch. Hainzl, P. T. Nam, R. Seiringer. The Huang-Yang conjecture for the low-density Fermi gas. arXiv:2505.22340
L. Junge, F. Visconti. Derivation of Hartree theory for two-dimensional attractive Bose gases in very dilute regime. arXiv:2410.23150v2
A. Kouraich, Ch. Manai, S. Warzel. The Quantum Random Energy Model is the Limit of Quantum p-Spin Glasses. arXiv:2505.02458
M. Lemm, C. Rubiliani, J. Zhang. On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians. arXiv:2505.01786
Ch. Lubich, J. Nick. Regularized dynamical parametric approximation of stiff evolution problems. arXiv:2501.12118
T. Möbus, A. Bluhm, T. Gefen, Y. Tong, A. Werner, C. Rouzé. Heisenberg-limited Hamiltonian learning continuous variable systems via engineered dissipation. arXiv:2506.00606
H. Rall, M. Wolf. Quantum tomography from the evolution of a single expectation. arXiv:2501.10118
M. Scheifinger, K. Busch, M. Hochbruck, C. Lasser. Time-integration of Gaussian variational approximation for the magnetic Schrödinger equation. arXiv:2504.03407
J. Ph. Solovej. Mathematical physics of dilute Bose gases. arXiv:2504.03314
F. Visconti. Hilbert-Schmidt norm estimates for fermionic reduced density matrices. arXiv:2504.03488
2024
L. Araujo, C. Lasser, B. Schmidt. FSSH-2: Fewest Switches Surface Hopping with robust switching probability, J. Chem. Theory Comput 20, 3413, 7 pages (2024), DOI 10.1021/acs.jctc.4c00089
P. Bergold, C. Lasser. The Gaussian wave packet transform via quadrature rules, IMA J. Numer. Anal., 44(3):1785–1820 (2024), https://doi.org/10.1093/imanum/drad049
A. Brollo, H. Spohn, Particle scattering and fusion for the Ablowitz-Ladik chain, J. Phys. A: Math. Theor. 57 325202 (2024), DOI 10.1088/1751-8121/ad6411
S. Burkhard, B. Dörich, M. Hochbruck, C. Lasser. Variational Gaussian approximation for the magnetic Schrödinger equation, J. Phys. A 57, 295202, 36 pages (2024), DOI 10.1088/1751-8121/ad591e
Á. Capel, Y. Jia. A generic quantum Wielandt's inequality. Quantum 8, 1331 (2024), https://doi.org/10.22331/q-2024-05-02-1331
V. Blakaj, M. Wolf. On the set of reduced states of translation invariant, infinite quantum systems. Lett Math Phys 114, 28 (2024), https://doi.org/10.1007/s11005-024-01776-1
C. Brennecke, M. Brooks, C. Caraci, J. Oldenburg. A Short Proof of Bose–Einstein Condensation in the Gross–Pitaevskii Regime and Beyond. Ann. Henri Poincaré (2024). https://doi.org/10.1007/s00023-024-01465-8
C. Caraci, J. Oldenburg, B. Schlein. Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024). DOI 10.4171/AIHPC/132
M. Christiansen. Hilbert–Schmidt Estimates for Fermionic 2-Body Operators. Communications in Mathematical Physics, 405:18 (2024). https://doi.org/10.1007/s00220-023-04914-3
G. K. Duong, R. Frank, T. M. T. Le, P. T. Nam, P. Nguyen. Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator. J. Math. Pures Appl. 190 (2024). https://doi.org/10.1016/j.matpur.2024.103598
R. Frank. A div-curl inequality for orthonormal functions. Pure and Applied Functional Analysis 9 (2024), no. 4, 1081–1091. http://yokohamapublishers.jp/online2/oppafa/vol9/p1083.html
R. Frank, A. Laptev and L. Read. Weighted CLR type bounds in two dimensions. Transactions of the American Mathematical Society, 377 (2024), https://doi.org/10.1090/tran/9124
R. Frank, Th. Hoffmann-Ostenhof, A. Laptev, J. Ph. Solovej. Hardy inequalities for large fermionic systems. J. Spectr. Theory 14 (2024), no. 2, pp. 805–835, DOI 10.4171/JST/511
T. Gonda, T. Reinhart, S. Stengele, G. De les Coves. A Framework for Universality in Physics, Computer Science, and Beyond. Compositionality, Volume 6 (2024). https://doi.org/10.46298/compositionality-6-3
J. Henheik, A. B. Lauritsen and B. Roos. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics (2024), doi: 10.1142/S0129055X2360005X
J. Lampart, M. Moscolari, S. Teufel, T. Wessel. Equality of magnetization and edge current for interacting lattice fermions at positive temperature. Mathematical Physics, Analysis and Geometry, 27 (2024), p. 24., https://doi.org/10.1007/s11040-024-09495-8
A. Lauritsen, R. Seiringer. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 2024;12. doi:10.1017/fms.2024.56
D. Sulz, Ch. Lubich, G. Ceruti, I. Lesanovsky, F. Carollo. Numerical simulation of long-range open quantum many-body dynamics with tree tensor networks. Phys. Rev. A, 109(2):022420, 9, (2024), DOI: https://doi.org/10.1103/PhysRevA.109.022420
S. Teufel, R. Tumulka, C. Vogel. Typical Macroscopic Long-Time Behavior for Random Hamiltonians. Ann. Henri Poincaré (2024), https://doi.org/10.1007/s00023-024-01521-3
Preprints
M. Aizenman, S. Warzel. Entanglement entropy bounds for pure states of rapid decorrelation. arXiv:2406.10194
K. Audenaert, B. Bergh, N. Datta, M. Jabbour, Á. Capel, P. Gondolf. Continuity bounds for quantum entropies arising from a fundamental entropic inequality. arXiv:2408.15306
A. Bluhm, Á. Capel and A. Pérez-Hernández. Strong decay of correlations for Gibbs states in any dimension. arXiv: 2401.10147
L. Bollmann, P. Müller. Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension. arXiv:2405.14356
L. Brenner, L. Caha, X. Coiteux-Roy, R. Koenig. Factoring an integer with three oscillators and a qubit. arXiv:2412.13164
L. Brenner, L. Caha, X. Coiteux-Roy, R. Koenig. The complexity of Gottesman-Kitaev-Preskill states. arXiv:2410.19610
A. Brollo, H. Spohn. Scattering theory and fusion for the Ablowitz-Ladik chain. arXiv:2404.07095
Á. Capel, P. Gondolf, J. Kochanowski, C. Rouzé. Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics. arXiv:2412.01732
Á. Capel, Á. Alhambra, P. Gondolf, A. Ruiz-de-Alarcón, S. Scalet. Conditional Independence of 1D Gibbs States with Applications to Efficient Learning. arXiv:2402.18500
G. Ceruti, L. Einkemmer, J. Kusch, Ch. Lubich. A robust second-order low-rank BUG integrator based on the midpoint rule. arXiv:2402.08607
G. Ceruti, D. Kressner and D. Sulz. Low-rank Tree Tensor Network Operators for Long-Range Pairwise Interactions. arXiv:2405.09952
G. Ceruti, J. Kusch, Ch. Lubich, D. Sulz. A parallel Basis Update and Galerkin Integrator for Tree Tensor Networks. arXiv:2412.00858
M. Christiansen, Ch. Hainzl and P. T. Nam. The Correlation Energy of the Electron Gas in the Mean-Field Regime. arXiv:2405.01386
T. Cubitt, M. Gu, Á. Perales-Eceiza, D. Pérez-García, M. Wolf. Undecidability in Physics: a Review. arXiv:2410.16532
J. Cuenin, R. Frank. Open problem: Violation of locality for Schrödinger operators with complex potentials. arXiv:2409.11285
Ch. Dietze, L. Read. Concentration of eigenfunctions on singular Riemannian manifolds. arXiv:2410.20563
Ch. Dietze, P. T. Nam. Minimizing sequences of Sobolev inequalities revisited. arXiv:2412.08616
M. Duerinckx, M. Lemm, F. Pagano. On Bourgain's approach to stochastic homogenization. arXiv:2406.09909
M. Feischl, C. Lasser, Ch. Lubich, J. Nick. Regularized dynamical parametric approximation. arXiv:2403.19234
M. Ferrero, D. Monaco. Effective quantum dynamics for magnetic fermions. arXiv:2406.15041
L. Fresta, M. Porta, B. Schlein. Effective Dynamics of Local Observables for Extended Fermi Gases in the High-Density Regime. arXiv:2409.14841
S. Fournais, L. Junge, T. Girardot, L. Morin, M. Olivieri, A. Triay. The free energy of dilute Bose gases at low temperatures interacting via strong potentials. arXiv:2408.14222
R. Frank. Minimizing Schrödinger eigenvalues for confining potentials. arXiv:2407.15103
R. Frank, B. Helffer. On Courant and Pleijel theorems for sub-Riemannian Laplacians. arXiv:2402.13953
R. Frank, J. Peteranderl. The sharp σ2-curvature inequality on the sphere in quantitative form. arXiv:2412.12819
R. Frank, B. Helffer, A. Laptev. Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups. arXiv:2411.11168
R. Frank, S. Larson. Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains. arXiv:2407.11808
R. Frank, S. Larson. Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains. arXiv:2410.04769
E. Giacomelli. An optimal lower bound for the low density Fermi gas in three dimensions. arXiv:2410.08904
E. Giacomelli, Ch. Hainzl, P. T. Nam, R. Seiringer. The Huang-Yang formula for the low-density Fermi gas: upper bound. arXiv:2409.17914
P. Gondolf, S. Scalet, A. Ruiz-de-Alarcon, A. Alhambra, Á. Capel. Conditional Independence of 1D Gibbs States with Applications to Efficient Learning. arXiv:2402.18500
F. Haberberger, Ch. Hainzl, B. Schlein, A. Triay. Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature. arXiv:2405.03378
P. Hege, M. Moscolari, S. Teufel. Computing the spectrum and pseudospectrum of infinite-volume operators from local patches. arXiv:2403.19055
J. Henheik, E. Langmann, A. Lauritsen. Multi-band superconductors have enhanced critical temperatures. arXiv:2409.17297
J. Henheik and A. Lauritsen. Multi-band superconductors have enhanced critical temperatures. arXiv:2409.17297
J. Henheik, T. Wessel. Response theory for locally gapped systems. arXiv:2410.10809
L. Junge, F. Visconti. Derivation of Hartree theory for two-dimensional attractive Bose gases in very dilute regime. arXiv:2410.23150
L. Junge, F. Visconti. Ground state energy of a dilute Bose gas with three-body hard-core interactions. arXiv:2406.09019
J. Kochanowski, A. Alhambra, Á. Capel, C. Rouzé. Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians. arXiv:2404.16780
F. Kröninger, C. Lasser, J. Vanicek. Sampling strategies for expectation values within the Herman–Kluk approximation. arXiv:2408.00130
T. Kuwahara, M. Lemm. Enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians. arXiv:2405.04672
J. Lampart, A. Triay. The excitation spectrum of a dilute Bose gas with an impurity in the Gross-Pitaevskii regime. arXiv:2401.14911
J. Lampart, A. Triay. Validity of the Fröhlich model for a mobile impurity in a Bose-Einstein condensate. arXiv:2411.11655
A. Lauritsen, R. Seiringer. Ground state energy of the dilute spin-polarized Fermi gas: Lower bound. arXiv:2402.17558
A. Lauritsen, R. Seiringer. Pressure of a dilute spin-polarized Fermi gas: Upper bound. arXiv:2407.05990
M. Lemm, A. Lucia. On the critical finite-size gap scaling for frustration-free Hamiltonians. arXiv:2409.09685
M. Lemm, B. Nachtergaele, S. Warzel, Amanda Young. The charge gap is greater than the neutral gap in fractional quantum Hall systems. arXiv:2410.11645
M. Lemm, S. Rademacher, J. Zhang. Local enhancement of the mean-field approximation for bosons. arXiv:2412.13868
M. Lemm, T. Wessel. Enhanced Lieb-Robinson bounds for commuting long-range interactions. arXiv:2411.19241
C. Manai, S. Warzel. A Parisi Formula for Quantum Spin Glasses. arXiv:2403.06155
G. Marcelli, T. Miyao, D. Monaco, S. Teufel, M. Wesle. Near linearity of the macroscopic Hall current response in infinitely extended gapped fermion systems. arXiv:2411.06967
L. Meng, H. Siedentop. The Ground State Energy of Heavy Atoms: Leading and Subleading Asymptotics. arXiv:2411.07046
L. Meng, H. Siedentop, M. Tiefenbeck. Relativistic Exchange Bounds. arXiv:2408.17158
T. Möbus. Multi-product Zeno effect with higher order convergence rates. arXiv:2410.16260
T. Möbus. On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications. arXiv:2404.01422
Á. Perales-Eceiza, T. Cubitt, M. Gu, D. Pérez-García, M. Wolf. Undecidability in Physics: a Review. arXiv:2410.16532
L. Read. On the asymptotic number of low-lying states in the two-dimensional confined Stark effect. arXiv:2404.14363
B. Roos, S. Teufel, R. Tumulka, C. Vogel. Macroscopic Thermalization for Highly Degenerate Hamiltonians. arXiv:2408.15832
B. Roos, S. Teufel, R. Tumulka, C. Vogel. Macroscopic Thermalization for Highly Degenerate Hamiltonians After Slight Perturbation. arXiv:2408.15832
F. Visconti. Ground state energy of the low density Bose gas with two-body and three-body interactions. arXiv:2402.05646
2023
A. Bluhm, Á. Capel, P. Gondolf and A. Pérez-Hernández. Continuity of Quantum Entropic Quantities via Almost Convexity, IEEE Transactions on Information Theory (2023), doi: 10.1109/TIT.2023.3277892
A. Bluhm, Á. Capel, P. Gondolf and A. Pérez-Hernández. General continuity bounds for quantum relative entropies, IEEE Transactions on Information Theory (2023), 162-167, doi: 10.1109/ISIT54713.2023.10206734
G. Ceruti, C. Lubich, D. Sulz, Rank-Adaptive Time Integration of Tree Tensor Networks, SIAM J. Numer. Anal. 61 (2023), 194-222, https://doi.org/10.1137/22M1473790
M. Christiansen, Ch. Hainzl, P. T. Nam. The Gell-Mann–Brueckner formula for the correlation energy of the electron gas: a rigorous upper bound in the mean-field regime, Comm. Math. Phys., 401 (2023), pp. 1469–1529. https://doi.org/10.1007/s00220-023-04672-2
E. L. Giacomelli. An optimal upper bound for the dilute Fermi gas in three dimensions, Journal of Functional Analysis, 285, 110073 (2023), https://doi.org/10.1016/j.jfa.2023.110073
Y. Jia, M. Wolf. Hay from the Haystack: Explicit Examples of Exponential Quantum Circuit Complexity. Commun. Math. Phys. 402, 141–156 (2023), https://doi.org/10.1007/s00220-023-04720-x
M. Lemm, C. Rubiliani, I. M. Sigal, and J. Zhang, Information propagation in long-range quantum many-body systems, Physical Review A, 108, L060401 (2023), doi:10.1103/PhysRevA.108.L060401
C. Manai, S. Warzel, The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems. Forum of Mathematics, Sigma, 11, E112. doi: https://doi.org/10.1017/fms.2023.111
Preprints
A. Bluhm, A. Capel, P. Gondolf and T. Möbus. Unified framework for continuity of sandwiched Rényi divergences. arXiv:2308.12425
L. Bollmann, P. Müller. The Widom-Sobolev formula for discontinuous matrix-valued symbols. arXiv:2311.06036
S. Breteaux, J. Faupin, M. Lemm, D. H. O. Yang, I. Sigal, J. Zhang. Light cones for open quantum systems. arXiv:2303.08921
Á. Capel, Y. Jia. A generic quantum Wielandt's inequality. arXiv: 2301.08241
C. Caraci, A. Olgiati, D. Saint Aubin, B. Schlein. Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime. arXiv:2311.07433
G. Ceruti, J. Kusch, Ch. Lubich. A parallel rank-adaptive integrator for dynamical low-rank approximation. arXiv:2304.05660
M. Christiansen. Hilbert-Schmidt Estimates for Fermionic 2-Body Operators. arXiv:2305.00834
C. Fermanian Kammerer, C. Lasser, D. Robert. Asymptotic initial value representation of the solutions of semi-classical systems presenting smooth codimension one crossings. arXiv:2305.17053
R. Frank, R. Matzke. Minimizers for an aggregation model with attractive-repulsive interaction. arXiv:2307.13769
R. Frank, J. Peteranderl. Degenerate Stability of the Caffarelli-Kohn-Nirenberg Inequality along the Felli-Schneider Curve. arXiv:2308.07917
P. Gondolf, T. Möbus, C. Rouzé. Energy preserving evolutions over Bosonic systems. arXiv:2307.13801
F. Haberberger, Ch. Hainzl, Phan Thành N., R. Seiringer, A. Triay. The free energy of dilute Bose gases at low temperatures. arXiv:2304.02405
J. Henheik, A. Lauritsen. Universal behavior of the BCS energy gap. arXiv:2312.11310
B. Hinrichs, M. Lemm, O. Siebert. On Lieb-Robinson bounds for a class of continuum fermions. arXiv:2310.17736
F. R. Klausen, S. Warzel. Exponential decay of coherences in single-particle open quantum systems. arXiv:2310.09880
A. Lauritsen. Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion. arXiv:2301.08005
A. Lauritsen, R. Seiringer. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. arXiv:2301.04894
M. Lemm, C. Rubiliani, J. Zhang. On the microscopic propagation speed of long-range quantum many-body systems. arXiv:2310.14896
D. Mitrouskas, P. Pickl. Exponential decay of the number of excitations in the weakly interacting Bose gas. arXiv:2307.11062
E. Onorati, C. Rouzé, D. Stilck França, J. Watson. Provably Efficient Learning of Phases of Matter via Dissipative Evolutions. arXiv:2311.07506
A. Young. Quantum Spin Systems. arXiv:2308.07848
A. Young. On a bulk gap strategy for quantum lattice models. arXiv:2308.01405