Prof. Dr. 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
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.
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 many-body systems (spectral gaps, Lieb-Robinson bounds)
- Matrix analysis (multivariate trace inequalities, quantum entropy)
- Random matrices (universal eigenvalue statistics for dynamically defined ensembles)
- Quantitative homogenization theory (Green's function estimates and the Bourgain-Spencer conjecture)
- Spectral theory of ergodic Schrödinger operators
My research is sponsored by the DFG (German Science Foundation) through the Collaborative Research Center (SFB TRR 352) with the name Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
International M.Sc. Program in Mathematical Physics
I serve as program coordinator of the interdisciplinary two-year M.Sc. program in mathematical physics that is offered jointly by the departments of mathematics and physics in Tübingen.
More info about the M.Sc. in Mathematical Physics (including how to apply)
Current Courses
Publications
- (with S. Rademacher) Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory arXiv
- (with B. Hinrichs and O. Siebert) On Lieb-Robinson bounds for a class of continuum fermions arXiv
- (with C. Rubiliani and J. Zhang) On the microscopic propagation speed of long-range quantum many-body systems arXiv
- (with J. González-Carbajal and J. Garcia-Suarez) On the lowest-frequency bandgap of 1D phononic crystals arXiv
- (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
- (with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang) Light cones for open quantum systems, to appear in Rev. Math. Phys. arXiv
- (with P. Hayden and J. Sorce) Reflected entropy: Not a correlation measure, Phys. Rev. A 107 (2023), L050401 arXiv Article
- (with O. Siebert) Thermal Area Law for Lattice Bosons, Quantum 7 (2023), 1083 arXiv Article
- (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
- (with R. Andrei and R. Movassagh) The spin-one Motzkin chain is gapped for any area weight t<1 arXiv
- (with O. Siebert) Bose-Einstein condensation on hyperbolic spaces, J. Math. Phys. 63 (2022), 081903 arXiv Article
- (with A. Adhikari) Universal Eigenvalue Statistics for Dynamically Defined Matrices, to appear in J. d'Analyse Math. arXiv Article
- (with D. Xiang) Quantitatively improved finite-size criteria for spectral gaps, J. Phys. A 55 (2022), 295203 arXiv Article
- (with I. Jauslin) Random translation-invariant Hamiltonians and their spectral gaps, Quantum 6, 790 (2022) arXiv Article
- (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
- (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
- (with M. Keller) Asymptotic expansion of the annealed Green's function and its derivatives, to appear in Math. Res. Lett. arXiv
- (with M. Keller) Optimal Hardy weights for the Euclidean lattice, Trans. Amer. Math. Soc. 376 (2023), 6033-6062 arXiv Article
- (with A. Adhikari) Local Law for Singular Values of Oscillatory Matrices, Int. Math. Res. Not. 2023 (2023), no. 5, 3907-3947 arXiv Article
- (with D. Sutter) Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities, Anal. Math. Phys. 12 (2022), 5 arXiv Article
- (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
- (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
- (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
- (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
- (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
- Gaplessness is not generic for translation-invariant spin chains, Phys. Rev. B 100 (2019) 035113 arXiv Article
- (with B. Nachtergaele) Gapped PVBS models for all species numbers and dimensions, Rev. Math. Phys. 31 (2019), no. 9, 1950028 arXiv Article
- (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
- 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
- (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
- (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
- (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
- (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
- (with E. Mozgunov) Spectral gaps of frustration-free spin systems with boundary, J. Math. Phys. 60 (2019) 051901 arXiv Article
- On multivariate trace inequalities of Sutter, Berta and Tomamichel, J. Math. Phys. 59 (2018) 012204 arXiv Article
- On the entropy of fermionic reduced density matrices, to appear in J. Stat. Mech. arXiv
- (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
- (with M.M. Wilde) Information-theoretic limitations on approximate quantum cloning and broadcasting, Phys. Rev. A 96 (2017) 012304 arXiv Article
- (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
- (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
- 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
- (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
- (with V. Markovic) Heat flows on hyperbolic spaces, J. Diff. Geom. 108 (2018), no. 3, 495 - 529 arXiv Article
- (with R.L. Frank) Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples, Ann. Henri Poincaré 17 (2016), no. 9, 2285-2340 arXiv Article
- (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
- (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
- (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
- 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)
Last update: February 9, 2024