Fachbereich Mathematik

Prof. Dr. Marius Lemm

Area: Mathematical Physics
Marius Lemm


Contact Information

Universität Tübingen
Fachbereich Mathematik
AB Mathematische Physik
Auf der Morgenstelle 10
72076 Tübingen

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

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)

Current Courses

Summer Term 2022

Winter Term 2021/22

Archiv


Publications

      1. (with O. Siebert) Thermal Area Law for the Bose-Hubbard Model   arXiv
      2. (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
      3. (with R. Andrei and R. Movassagh) The spin-one Motzkin chain is gapped for any area weight t<1   arXiv
      4. (with O. Siebert) Bose-Einstein condensation on hyperbolic spaces, to appear in J. Math. Phys.,   arXiv
      5. (with A. Adhikari) Universal Eigenvalue Statistics for Dynamically Defined Matrices   arXiv
      6. (with D. Xiang) Quantitatively improved finite-size criteria for spectral gaps, J. Phys. A 55 (2022), 295203  arXiv   Article
      7. (with I. Jauslin) Random translation-invariant Hamiltonians and their spectral gaps, to appear in Quantum  arXiv
      8. (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
      9. (with J. Faupin and I.M. Sigal) On Lieb-Robinson bounds for the Bose-Hubbard model, to appear in Commun. Math. Phys.   arXiv   Article
      10. (with M. Keller) Asymptotic expansion of the annealed Green's function and its derivatives   arXiv
      11. (with M. Keller) Optimal Hardy weights for the Euclidean lattice   arXiv
      12. (with A. Adhikari) A Local Law for Singular Values from Diophantine Equations, to appear in Int. Math. Res. Not.   arXiv   Article
      13. (with D. Sutter) Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities, Anal. Math. Phys. 12 (2022), 5   arXiv   Article
      14. (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
      15. (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
      16. (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
      17. (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
      18. (with M. de Courcy-Ireland) A central limit theorem for integrals of random waves, to appear in J. Reine Angew. Math. (Crelle) arXiv   Article
      19. Gaplessness is not generic for translation-invariant spin chains, Phys. Rev. B 100 (2019) 035113   arXiv   Article
      20. (with B. Nachtergaele) Gapped PVBS models for all species numbers and dimensions, Rev. Math. Phys. 31 (2019), no. 9, 1950028   arXiv   Article
      21. (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
      22. 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
      23. (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
      24. (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  
      25. (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
      26. (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
      27. (with E. Mozgunov) Spectral gaps of frustration-free spin systems with boundary, J. Math. Phys. 60 (2019) 051901   arXiv   Article
      28. On multivariate trace inequalities of Sutter, Berta and Tomamichel, J. Math. Phys. 59 (2018) 012204   arXiv Article
      29. On the entropy of fermionic reduced density matrices   arXiv
      30. (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
      31. (with M.M. Wilde) Information-theoretic limitations on approximate quantum cloning and broadcasting, Phys. Rev. A 96 (2017) 012304   arXiv   Article
      32. (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
      33. (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
      34. On the Hölder regularity for the fractional Schr&oumldinger equation and its improvement for radial data, Comm. Part. Diff. Eq. 41 (2016), no. 11, 1761-1792   arXiv   Article
      35. (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
      36. (with V. Markovic) Heat flows on hyperbolic spaces, J. Diff. Geom. 108 (2018), no. 3, 495 - 529   arXiv   Article
      37. (with R.L. Frank) Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples, Ann. Henri Poincaré 17 (2016), no. 9, 2285-2340   arXiv   Article
      38. (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
      39. (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
      40. (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
      41. New counterexamples for sums-differences, Proc. Amer. Math. Soc. 143 (2015), no. 9, 3863-3868   arXiv   Article

Last update: August 17, 2022