Fachbereich Mathematik

Prof. Dr. Marius Lemm

Area: Mathematical Physics
Marius Lemm

Contact Information

University of Tübingen
Department of Mathematics
Auf der Morgenstelle 10
72076 Tübingen

Room: C4 P39
Tel: +49 (0)7071 29 78563
E-Mail: marius.lemm[at]uni-tuebingen.de

If you're a young researcher interested in working with me as a Ph.D. student or Postdoc, please feel invited to message me. Ideally, you can include a CV and a transcript or research statement. Please note that during certain busy periods, I may not be able to respond to all messages of this kind.

Scientific background

I moved to the University of Tübingen in 2021 from EPFL where I was Assistant Professor of Mathematics. Before that, I held a Benjamin Peirce fellowship at Harvard University and I was a postdoctoral member at the Institute for Advanced Study in Princeton. My postdoc mentors were Horng-Tzer Yau, Wilhelm Schlag, and Tom Spencer. I obtained my Ph.D. in mathematics in 2017 at Caltech under the supervision of Rupert L. Frank.

Detailed CV

Research Interests 

I am mainly interested in developing tools in mathematical analysis for problems originating in quantum physics. The methods I use come from the calculus of variations, ergodic theory, harmonic analysis, and spectral theory. Topics that I have worked on recently include:

  • Quantum many-body systems (spectral gaps, Lieb-Robinson bounds)
  • Random elliptic PDE (homogenization theory and the Bourgain-Spencer conjecture)
  • Random matrices (universal spectral statistics for dynamically defined matrices)

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From January 2025, my research is supported by an ERC Starting Grant in mathematics MathQuantProp: The Mathematics of Quantum Propagation. 

My research is also supported by the DFG (German Science Foundation) through the Collaborative Research Center Mathematics of Many-Body Quantum Systems and Their Collective Phenomena (SFB TRR 352), a joint initiative between Tübingen, TU Munich, and LMU Munich

International M.Sc. Program in Mathematical Physics

I serve as program coordinator of the interdisciplinary two-year M.Sc. program in mathematical physics offered jointly by the math and physics departments in Tübingen.

More info about Tübingen M.Sc. Mathematical Physics (including how to apply)

 

Current Courses

Summer Term 2026

Winter Term 2025/26


Archive

Publications

    1. (with C. Rubiliani) Lieb-Robinson bounds for Bose-Hubbard Hamiltonians: A review with a simplified proof   arXiv
    2. (with I.M. Sigal and J. Zhang) Diffusion bounds for non-autonomous degenerate parabolic equations   arXiv
    3. (with S. Rademacher and J. Zhang) On Bose-Einstein condensates in disordered media  arXiv
    4. (with T. Kuwahara and C. Rubiliani) A ballistic upper bound on the accumulation of bosonic on-site energies, to appear in Pure and Applied Functional Analysis, In: PDE and Mathematical Physics, special issue dedicated to Israel Michael Sigal, Stephen Gustafson et al. (eds.)   arXiv
    5. (with B. McDonough and A. Lucas) Non-perturbatively slow spread of quantum correlations in non-resonant systems   arXiv
    6. (with A. Bluhm, T. Möbus, and O. Siebert) Learning Coulomb Potentials and Beyond with Free Fermions in Continuous Space   arXiv
    7. (with N. Hunter-Jones) Two classes of quantum spin systems that are gapped on any bounded-degree graph   arXiv
    8. (with A. Adhikari, J. Henheik, and T. Wessel) Uniform-in-temperature locality estimates for weakly interacting quantum systems   arXiv
    9. (with B. Nachtergaele, S. Warzel, and A. Young) Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems, J. Math. Phys. 67 (2026), 011901   arXiv   Article
    10. (with A. Deuchert and J. Lampart) Dynamics and equilibrium states of infinite systems of lattice bosons  arXiv
    11. (with C. Rubiliani and J. Zhang) On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians  arXiv
    12. (with J. Faupin, I.M. Sigal, and J. Zhang) Macroscopic suppression of supersonic quantum transport, Phys. Rev. Lett. 135 (2025), 160405   arXiv   Article
    13. (with S. Rademacher and J. Zhang) Local enhancement of the mean-field approximation for bosons  arXiv
    14. (with T. Wessel) Enhanced Lieb-Robinson bounds for commuting long-range interactions  J. Math. Phys. 66 (2025), 091901  arXiv   Article
    15. (with A. Lucia) On the critical finite-size gap scaling for frustration–free Hamiltonians, Rev. Math. Phys. 37 (2025), no. 7,  2550015  arXiv   Article
    16. (with M. Duerinckx and F. Pagano) On Bourgain's approach to stochastic homogenization, Arch. Ration. Mech. Anal. 249 (2025), 81  arXiv   Article
    17. (with T. Kuwahara) Symmetry-enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians   arXiv
    18. (with S. Rademacher) Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory, Quantum 9 (2025), 1587  arXiv  Article
    19. (with B. Hinrichs and O. Siebert) On Lieb-Robinson bounds for a class of continuum fermions, Ann. Henri Poincaré 26 (2025), 41-80  arXiv   Article
    20. (with C. Rubiliani and J. Zhang) On the microscopic propagation speed of long-range quantum many-body systems, to appear in J. Math. Pures Appl.  arXiv
    21. (with J. González-Carbajal and J. Garcia-Suarez) On the lowest-frequency bandgap of 1D phononic crystals, Eur. J. Mech. A-Solid. 109 (2025) 105466   arXiv   Article
    22. (with C. Rubiliani, I.M. Sigal, and J. Zhang) Information propagation in long-range quantum many-body systems, Phys. Rev. A 108 (2023), L060401  arXiv    Article
    23. (with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang) Light cones for open quantum systems, Rev. Math. Phys. 36 (2024), no. 09, 2460004  arXiv   Article
      1. (with P. Hayden and J. Sorce) Reflected entropy: Not a correlation measure, Phys. Rev. A  107 (2023), L050401   arXiv   Article
      2. (with O. Siebert) Thermal Area Law for Lattice Bosons, Quantum 7 (2023), 1083   arXiv  Article
      3. (with S. Breteaux, J. Faupin and I.M. Sigal) Maximal speed of propagation in open quantum systems, In: The Physics and Mathematics of Elliott Lieb, The 90th Anniversary Volume I, Rupert L. Frank et al. (eds.), 109–130, EMS Press, Berlin, 2022   arXiv   Article
      4. (with R. Andrei and R. Movassagh) The spin-one Motzkin chain is gapped for any area weight t<1   arXiv
      5. (with O. Siebert) Bose-Einstein condensation on hyperbolic spaces, J. Math. Phys. 63 (2022), 081903   arXiv   Article
      6. (with A. Adhikari) Universal Eigenvalue Statistics for Dynamically Defined Matrices, J. d'Analyse Math. 153 (2024), 169–218
        arXiv   Article
      7. (with D. Xiang) Quantitatively improved finite-size criteria for spectral gaps, J. Phys. A 55 (2022), 295203  arXiv   Article
      8. (with I. Jauslin) Random translation-invariant Hamiltonians and their spectral gaps, Quantum 6, 790 (2022)  arXiv   Article
      9. (with J. Faupin and I.M. Sigal) Maximal speed for macroscopic particle transport in the Bose-Hubbard model, Phys. Rev. Lett. 128 (2022), 150602   arXiv   Article
      10. (with J. Faupin and I.M. Sigal) On Lieb-Robinson bounds for the Bose-Hubbard model, Commun. Math. Phys. 394 (2022), 1011–1037  arXiv   Article
      11. (with M. Keller) Asymptotic expansion of the annealed Green's function and its derivatives, Math. Res. Lett. 32 (2025), no. 1, 269–291  arXiv  Article
      12. (with M. Keller) Optimal Hardy weights for the Euclidean lattice, Trans. Amer. Math. Soc. 376 (2023), 6033-6062   arXiv   Article
      13. (with A. Adhikari) Local Law for Singular Values of Oscillatory Matrices, Int. Math. Res. Not. 2023 (2023), no. 5, 3907-3947   arXiv   Article
      14. (with D. Sutter) Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities, Anal. Math. Phys. 12 (2022), 5   arXiv   Article
      15. (with A.W. Sandvik and L. Wang) Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice, Phys. Rev. Lett. 124 (2020), 177204   arXiv   Article
      16. (with P.M. Kielstra) On the finite-size Lyapunov exponent for the Schrödinger operator with skew-shift potential, Comm. Math. Sci.   18 (2020), no. 5, 1305-1314   arXiv   Article
      17. (with A.W. Sandvik and S. Yang) The AKLT model on a hexagonal chain is gapped, J. Stat. Phys. 177 (2019), no. 6, 1077-1088   arXiv   Article
      18. (with A. Adhikari and H.-T. Yau) Global eigenvalue distribution of matrices defined by the skew-shift, Anal. PDE 14 (2021), no. 4, 1153 - 1198   arXiv   Article
      19. (with M. de Courcy-Ireland) A central limit theorem for integrals of random waves, J. Reine Angew. Math. (Crelle), 785 (2022), 1–30   arXiv   Article
      20. Gaplessness is not generic for translation-invariant spin chains, Phys. Rev. B 100 (2019) 035113   arXiv   Article
      21. (with B. Nachtergaele) Gapped PVBS models for all species numbers and dimensions, Rev. Math. Phys. 31 (2019), no. 9, 1950028   arXiv   Article
      22. (with H. Abdul-Rahman, A. Lucia, B. Nachtergaele and A. Young) A class of two-dimensional AKLT models with a gap, Analytic trends in mathematical physics, Contemp. Math. 741, Amer. Math. Soc., Providence, RI 2020   arXiv   Article
      23. Finite-size criteria for spectral gaps in D-dimensional quantum spin systems, Analytic trends in mathematical physics, Contemp. Math. 741, Amer. Math. Soc., Providence, RI 2020   arXiv   Article
      24. (with M. Duerinckx and A. Gloria) A remark on a surprising result by Bourgain in homogenization, Comm. Part. Diff. Eq. 44 (2019), no. 12, 1345-1357   arXiv   Article
      25. (with R. Han and W. Schlag) Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle, J. Spectr. Theory 10 (2020), no. 4, 1139-1172.  arXiv   Article  
      26. (with J. Kim) On the averaged Green's function of an elliptic equation with random coefficients, Arch. Ration. Mech. Anal. 234 (2019), no. 3, 1121-1166   arXiv   Article
      27. (with R. Han and W. Schlag) Effective multi-scale approach to the Schrödinger cocycle over a skew shift base, Ergod. Theory Dyn. Syst. 40 (2020), no. 10, 2788-2853  arXiv   Article
      28. (with E. Mozgunov) Spectral gaps of frustration-free spin systems with boundary, J. Math. Phys. 60 (2019) 051901   arXiv   Article
      29. On multivariate trace inequalities of Sutter, Berta and Tomamichel, J. Math. Phys. 59 (2018) 012204   arXiv   Article
      30. Entropic relations for indistinguishable quantum particles J. Stat. Mech. (2024) 043101 arXiv   Article
      31. (with P. Plucinsky and K. Bhattacharya) Actuation of thin nematic elastomer sheets with controlled heterogeneity, Arch. Ration. Mech. Anal. 227 (2018), no. 1, 149-214   arXiv   Article
      32. (with M.M. Wilde) Information-theoretic limitations on approximate quantum cloning and broadcasting, Phys. Rev. A 96 (2017) 012304   arXiv   Article
      33. (with R.L. Frank and B. Simon) Condensation of fermion pairs in a domain, Calc. Var. Partial Differential Equations 56 (2017), no. 2, 54,   arXiv   Article
      34. (with P. Plucinsky and K. Bhattacharya) Programming complex shapes in thin nematic elastomer and glass sheets, Phys. Rev. E 94 (2016) 010701(R), rapid communication   arXiv   Article
      35. On the Hölder regularity for the fractional Schrödinger equation and its improvement for radial data, Comm. Part. Diff. Eq. 41 (2016), no. 11, 1761-1792   arXiv   Article
      36. (with M. Gebert) On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field, J. Stat. Phys. 164 (2016), no. 3, 667-679   arXiv   Article
      37. (with V. Markovic) Heat flows on hyperbolic spaces, J. Diff. Geom. 108 (2018), no. 3, 495 - 529   arXiv   Article
      38. (with R.L. Frank) Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples, Ann. Henri Poincaré 17 (2016), no. 9, 2285-2340   arXiv   Article
      39. (with M. Berta and M.M. Wilde) Monotonicity of quantum relative entropy and recoverability, Q. Inf. Comp. 15 (2015), no. 15 & 16, 1333-1354   arXiv   Article
      40. (with D. Damanik, M. Lukic and W. Yessen) New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains, Phys. Rev. Lett. 113 (2014), 127202   arXiv   Article
      41. (with D. Damanik, M. Lukic and W. Yessen) On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain, J. Spectr. Theory 6 (2016), no. 8, 601-628   arXiv   Article
      42. New counterexamples for sums-differences, Proc. Amer. Math. Soc. 143 (2015), no. 9, 3863-3868   arXiv   Article

      Links

      International Association of Mathematical Physics (IAMP)

      Association of Women in Mathematical Physics (AWMP)

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      Last update: December 10, 2025