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
Open postdoc position
I currently have an open postdoc position in mathematical physics
- starting date: early-mid 2025 (flexible)
- duration: 2 years
- application deadline: January 15, 2025
More information here
Open Ph.D. position
I currently have an open Ph.D. position in mathematical physics
- starting date: early-mid 2025 (flexible)
- duration: 3 years
- application deadline: January 15, 2025
More information here
In general, if you're a young researcher interested in working with me, please feel invited to message me if you are interested in a Ph.D. or Postdoc position at any time. Be sure to 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.
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 supported by the DFG (German Science Foundation) through the Collaborative Research Center (SFB TRR 352) Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
From January 2025, my research is also supported by the ERC Starting Grant in mathematics MathQuantProp: The Mathematics of Quantum Propagation.
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
Publications
- (with T. Wessel) Enhanced Lieb-Robinson bounds for commuting long-range interactions arXiv
- (with B. Nachtergaele, S. Warzel, and A. Young) The charge gap is greater than the neutral gap in fractional quantum Hall systems arXiv
- (with A. Lucia) On the critical finite-size gap scaling for frustration–free Hamiltonians arXiv
- (with M. Duerinckx and F. Pagano) On Bourgain's approach to stochastic homogenization arXiv
- (with T. Kuwahara) Enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians arXiv
- (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, to appear in Ann. Henri Poincaré 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, to appear in Eur. J. Mech. A-Solid. arXiv Article
- (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, Rev. Math. Phys. 36 (2024), no. 09, 2460004 arXiv Article
- (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, J. d'Analyse Math. 153 (2024), 169–218
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
- Entropic relations for indistinguishable quantum particles J. Stat. Mech. (2024) 043101 arXiv Article
- (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: December 2, 2024