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

Announcements

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 2017 at Caltech under the supervision of Rupert L. Frank.

Detailed CV

Research Interests 

I am mainly interested in applying tools from mathematical analysis to 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 lattice systems (spectral gaps, Lieb-Robinson bounds)
  • Matrix analysis (multivariate trace inequalities, quantum entropy)
  • Random matrices (universal eigenvalue statistics)
  • Quantitative homogenization theory (Green's function estimates)
  • Ergodic Schrödinger operators (Lyapunov exponents)

logo-dfg.jpeg

My research is sponsored by the DFG (German Science Foundation) through the Collaborative Research Center (SFB TRR 352) Mathematics of Many-Body Quantum Systems and Their Collective Phenomena  link to CRC website

Current Courses

Winter Term 2023/24

Summer Term 2023

      Archive

      Publications

          1. (with C. Rubiliani, I.M. Sigal, and J. Zhang) Information propagation in long-range quantum many-body systems  arXiv 
          2. (with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang) Light cones for open quantum systems   arXiv
          3. (with P. Hayden and J. Sorce) Reflected entropy: Not a correlation measure, Phys. Rev. A  107 (2023), L050401   arXiv   Article
          4. (with O. Siebert) Thermal Area Law for Lattice Bosons, Quantum 7 (2023), 1083   arXiv  Article
          5. (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
          6. (with R. Andrei and R. Movassagh) The spin-one Motzkin chain is gapped for any area weight t<1   arXiv
          7. (with O. Siebert) Bose-Einstein condensation on hyperbolic spaces, J. Math. Phys. 63 (2022), 081903   arXiv   Article
          8. (with A. Adhikari) Universal Eigenvalue Statistics for Dynamically Defined Matrices, to appear in J. d'Analyse Math.   arXiv
          9. (with D. Xiang) Quantitatively improved finite-size criteria for spectral gaps, J. Phys. A 55 (2022), 295203  arXiv   Article
          10. (with I. Jauslin) Random translation-invariant Hamiltonians and their spectral gaps, Quantum 6, 790 (2022)  arXiv   Article
          11. (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
          12. (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
          13. (with M. Keller) Asymptotic expansion of the annealed Green's function and its derivatives   arXiv
          14. (with M. Keller) Optimal Hardy weights for the Euclidean lattice, to appear in Trans. Amer. Math. Soc.   arXiv
          15. (with A. Adhikari) Local Law for Singular Values of Oscillatory Matrices, Int. Math. Res. Not. 2023 (2023), no. 5, 3907-3947   arXiv   Article
          16. (with D. Sutter) Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities, Anal. Math. Phys. 12 (2022), 5   arXiv   Article
          17. (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
          18. (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
          19. (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
          20. (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
          21. (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
          22. Gaplessness is not generic for translation-invariant spin chains, Phys. Rev. B 100 (2019) 035113   arXiv   Article
          23. (with B. Nachtergaele) Gapped PVBS models for all species numbers and dimensions, Rev. Math. Phys. 31 (2019), no. 9, 1950028   arXiv   Article
          24. (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
          25. 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
          26. (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
          27. (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  
          28. (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
          29. (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
          30. (with E. Mozgunov) Spectral gaps of frustration-free spin systems with boundary, J. Math. Phys. 60 (2019) 051901   arXiv   Article
          31. On multivariate trace inequalities of Sutter, Berta and Tomamichel, J. Math. Phys. 59 (2018) 012204   arXiv   Article
          32. On the entropy of fermionic reduced density matrices   arXiv
          33. (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
          34. (with M.M. Wilde) Information-theoretic limitations on approximate quantum cloning and broadcasting, Phys. Rev. A 96 (2017) 012304   arXiv   Article
          35. (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
          36. (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
          37. 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
          38. (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
          39. (with V. Markovic) Heat flows on hyperbolic spaces, J. Diff. Geom. 108 (2018), no. 3, 495 - 529   arXiv   Article
          40. (with R.L. Frank) Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples, Ann. Henri Poincaré 17 (2016), no. 9, 2285-2340   arXiv   Article
          41. (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
          42. (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
          43. (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
          44. New counterexamples for sums-differences, Proc. Amer. Math. Soc. 143 (2015), no. 9, 3863-3868   arXiv   Article

      Last update: September 1, 2023