SFB TRR 352 Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
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Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – TRR 352 – Project-ID 470903074


2025

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

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

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. 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

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

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

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

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, M. Moscolari, S. Teufel, T. Wessel. Equality of magnetization and edge current for interacting lattice fermions at positive temperature. arXiv:2403.17566

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

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

P. Müller, J. Stern. On the return probability of the simple random walk on Galton-Watson trees. arXiv:2402.01600

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

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

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

Á. Capel, M. Moscolari, S. Teufel and T. Wessel. From decay of correlations to locality and stability of the Gibbs state. arXiv: 2310.09182

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

R. Frank. A div-curl inequality for orthonormal functions. arXiv:2309.08014

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, I. Sigal, J. Zhang. Information propagation in long-range quantum many-body systems. arXiv:2303.06506

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

L. Read. Negative spectrum of Schrödinger operators with rapidly oscillating potentials. arXiv:2309.06434 

A. Young. Quantum Spin Systems. arXiv:2308.07848

A. Young. On a bulk gap strategy for quantum lattice models. arXiv:2308.01405