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Technische Universität München
Technische Universität München

Picture of Simone Warzel

Prof. Dr. Simone Warzel

Technical University of Munich

Associate Professorship of Analysis and its applications (Prof. Warzel)

Postal address

Postal:
Boltzmannstr. 3
85748 Garching b. München

About

I am a mathematical physicist with a background in condensed matter theory focusing on quantum systems. One set of research topics broadly concerns the interplay of randomness and quantum effects as e.g. in quantum glasses and other disordered quantum systems. Another research topic are correlated many-body quantum systems and their emergent (topological) properties such as fractional quantum Hall or quantum spin systems. Mathematically speaking, this involves combining and uncovering techniques from analysis to probability such as random matrix or operator theory as well as spectral theory and methods from statistical mechanics.

Editorial work and other services for the community
Letters in Mathematical Physics (Chief editor)
Journal of Mathematical Physics, Journal of Statistical Physics, Probability and Mathematical Physics

I am currently the German representative and vice-chair in Commission 18: Mathematical Physics at IUPAP, and a member of the EC of Munich Center for Quantum Science and Technology. From 2015-2020 I served as the treasurer of the International Association of Mathematical Physics.

Curriculum Vitae

  • Since 2008
    Professor, TU Munich
  • 2006-2008
    Assistant Professor, Princeton University
  • 2003-2006
    Postdoc and lecturer at Princeton University
  • 2002
    Postdoc at Friedrich-Alexander-University Erlangen & Universidad de Chile
  • 1997-2001
    PhD student at Friedrich-Alexander-University Erlangen

 

Grants, Fellowships and Awards

  • 2019-
    Collaborative DFG Grant
  • 2014-2018
    DFG Grant
  • 2014-2017
    International Scholar Princeton University
  • 2013
    von Neumann Fellowship Award IAS
  • 2009
    Young Scientist Award by IUPAP
  • 2007-2010
    Alfred P. Sloan Fellowship
  • 2007-2013
    NSF Grant
  • 2003-2005
    DFG Postdoctorial Fellowship

Publications

  • J. P. Garrahan, C. Manai, S. Warzel
    Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model. Preprint arXive:2205.07487.

     

  • C. Manai, S. Warzel
    Spectral analysis of the quantum random energy model. Preprint arXive:2202.00334.

     

  • S. Warzel, A. Young
    The spectral gap of a fractional quantum Hall system on a thin torus, J. Math. Phys. 63: 041901 (2022). https://doi.org/10.1063/5.0084677.

     

  • S. Warzel, A. Young
    A Bulk Spectral Gap in the Presence of Edge States for a Truncated Pseudopotential, Ann. Henri Poincare (2022). https://doi.org/10.1007/s00023-022-01210-z.

     

  • C. Manai, S. Warzel
    The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses, J. Stat. Phys. 186:14 (2022). https://doi.org/10.1007/s10955-021-02860-9

     

  • C. Manai, S. Warzel
    Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams, Probab. Math. Phys. 3: 215-245 (2022). https://doi.org/10.2140/pmp.2022.3.215.

     

  • H. Leschke, C. Manai, R. Ruder, S. Warzel
    Existence of replica-symmetry breaking in quantum glasses, Phys. Rev. Lett. 127: 207204 (2021). https://doi.org/10.1103/PhysRevLett.127.207204

     

  • G. De Tomasi, I. M. Khaymovich, F. Pollmann, S. Warzel
    Rare thermal bubbles at the many-body localization transition from the Fock space point of view, Phys. Rev. B 104: 024202 (2021). https://doi.org/10.1103/PhysRevB.104.024202

     

  • B. Nachtergaele, S. Warzel, A. Young
    Spectral gaps and incompressibility in a ν=1/3 fractional quantum Hall system, Commun. Math. Phys. 383: 1093--1149 (2021). https://doi.org/10.1007/s00220-021-03997-0

     

  • B. Nachtergaele, S. Warzel, A. Young
    Low-complexity eigenstates of a ν=1/3 fractional quantum Hall system, J. Phys. A: Math. Theor. 54: 01LT01 (2021). https://doi.org/10.1088/1751-8121/abca73

     

  • C. Manai, S. Warzel
    The Quantum Random Energy Model as a Limit of p-Spin Interactions, Rev. Math. Phys. 33: 2060013 (2020).

     

  • M. Aizenman, H. Duminil-Copin, S. Warzel
    Dimerization and Néel order in different quantum spin chains through a shared loop representation, Ann. Henri Poincare 21: 2737--2774 (2020).

     

  • C. Manai, S. Warzel
    Phase Diagram of the Quantum Random Energy Model, J. Stat. Phys. 180: 654--664 (2020).

     

  • P. von Soosten, S. Warzel
    Random characteristics for Wigner matrices, Electronic Communications in Probability 24, paper no. 75, 1-12 (2019).

     

  • M. Aizenman, H. Duminil-Copin, V. Tassion, S. Warzel
    Emergent Planarity in two-dimensional Ising Models with finite-range Interactions, Invent. Math. 216: 661–743 (2019).

     

  • P. von Soosten, S. Warzel
    Delocalization and continuous spectrum for ultrametric random operators, Ann. Henri Poincare 20: 2877–2898 (2019).

     

  • V. Beaud, J. Sieber, S. Warzel
    Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder, J. Phys. A 52: 235202 (2019).

     

  • P. von Soosten, S. Warzel
    Non-Ergodic Delocalization in the Rosenzweig-Porter Model, Lett. Math. Phys. 109: 905-922 (2019).

     

  • P. von Soosten, S. Warzel
    Singular spectrum and recent results on hierarchical operators In: Mathematical Problems in Quantum Physics, Eds.: F. Bonetto, D. Borthwick, E. Harrell, M. Loss Contemporary Math. Series 717: 215-226 (2018).

     

  • P. von Soosten, S. Warzel
    The phase transition in the ultrametric ensemble and local stability of Dyson Brownian motion, Electron J. Probab. 23, 24pp (2018).

     

  • M. Aizenman, S. Warzel
    Kac–Ward Formula and Its Extension to Order–Disorder Correlators Through a Graph Zeta Function, J. Stat. Phys. 173: 1755-1778 (2018).

     

  • V. Beaud, S. Warzel
    Bounds on the entanglement entropy of droplet states in the XXZ spin chain, J. Math. Phys. 59: 012109 (2018).

     

  • M. Aizenman, H. Schanz, U. Smilansky, S. Warzel
    Edge switching transformations of quantum graphs, Acta Physica Polonica A 132: 1699-1703 (2017).

     

  • V. Beaud, S. Warzel
    Low-energy Fock-space localization for attractive hard-core particles in disorder, Ann. Henri Poincare 18: 3143-3166 (2017).

     

  • M. Aizenman, M. Lainz Valcazar, S. Warzel
    Pfaffian Correlation Functions of Planar Dimer Covers, J. Stat. Phys. 166: 1078-1091 (2017).

     

  • P. von Soosten, S. Warzel
    Renormalization Group Analysis of the Hierarchical Anderson Model, Ann. Henri Poincare, 18: 1919-1947 (2017).

     

  • R. Sims, S. Warzel
    Decay of Determinantal and Pfaffian Correlation Functionals in One-dimensional Lattices. Comm. Math. Phys. 347: 903-931 (2016).

     

  • R. Seiringer, S. Warzel
    Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas, New J. Phys. 18: 035002 (2016).

     

  • W. Hochstättler, W. Kirsch, S. Warzel
    Semicircle law for a matrix ensemble with dependent entries, J. Theor. Probab. 29: 1047-1068 (2016).

     

  • M. Aizenman, S. Warzel
    A Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization, Commun. Pure Appl. Math. 69: 2195-2218 (2016).

     

  • J. Adame, S. Warzel
    Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing. J. Math. Phys. 56: 113301 (2015)

     

  • M. Aizenman, M. Shamis, S. Warzel
    Resonances and partial delocalization on the complete graph, Ann. Henri Poincare 16: 1969-2003 (2015).

     

  • M. Keller, D. Lenz, S. Warzel
    An invitation to trees of finite cone type: random and deterministic operators, Markov Processes Relat. Fields 21, 557-574 (2015).

     

  • M. Fauser, S. Warzel
    Multiparticle localization for disordered systems on continuous space via the fractional moment method, Rev. Math. Phys. 27, 1550010 (2015).

     

  • M. Aizenman, S. Warzel
    On the ubiquity of the Cauchy distribution in spectral problems, Probab. Theory Relat. Fields 163: 61-87 (2015).

     

  • S. Warzel
    Surprises in the phase diagram of the Anderson model on the Bethe lattice, pp. 239-253 in: XVIIth International Congress on Mathematical Physics Ed.: A. Jensen World Scientific 2013.

     

  • M. Aizenman, S. Warzel
    Resonant delocalization for random Schrödinger operators on tree graphs, J. Eur. Math. Soc. 15: 1167-1222 (2013)

     

  • M. Keller, D. Lenz, S. Warzel
    On the spectral theory of trees with finite cone type, Israel Journal of Mathematics 194: 1-29 (2013)

     

  • M. Keller, D. Lenz, S. Warzel
    Absolutely continuous spectrum for random operators on trees of finite cone type, Journal d'Analyse Mathematique 118: 363--396 (2012)

     

  • M. Aizenman, S. Warzel
    Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs, J. Math. Phys. 53, 095205 (2012)

     

  • M. Aizenman, S. Warzel
    Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder, EPL 96: 37004 (2011).

     

  • M. Aizenman, S. Warzel
    Extended states in a Lifshitz tail regime for random Schrödinger operators on trees, Phys. Rev. Lett. 106: 136804 (2011).

     

  • M. Aizenman, S. Warzel
    Disorder-induced delocalization on tree graphs. In: Mathematical Results in Quantum Mechanics , Ed. P. Exner, 107-109, World Scientific 2011.

     

  • M. Aizenman, S. Warzel
    Complete dynamical localization in disordered quantum multi-particle systems. XVIth International Congress on Mathematical Physics, 556–565, World Sci. 2010.

     

  • H. Siedentop, R. Frank, S. Warzel
    The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Doc. Math. 14: 463–516 (2009).

     

  • M. Aizenman, S. Warzel
    Localization Bounds for Multiparticle Systems, Comm. Math. Phys. 290: 903–934 (2009)

     

  • M. Aizenman, S. Warzel
    On the joint distribution of energy levels of random Schrödinger operators, J. Phys. A: Math. Theor. 42: 045201 (2009).

     

  • M. Aizenman, F. Germinet, A. Klein, S. Warzel
    On Bernoulli decompositions for random variables, concentration bounds, and spectral localization, Probab. Theory Relat. Fields 143: 219-238 (2009).

     

  • R. Frank, H. Siedentop, S. Warzel
    The ground state energy of heavy atoms: relativistic lowering of the leading energy correction, Commun. Math. Phys. 278 : 549-566 (2008)

     

  • M. Aizenman, S. Warzel
    The canopy graph and level statistics for random operators on trees, Math. Phys. Anal. Geom. 9: 291-333 (2007)

     

  • M. Aizenman, B. Sims, S. Warzel
    Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs, Probab. Theory Relat. Fields 136: 363-394 (2006)

     

  • M. Aizenman, B. Sims, S. Warzel
    Fluctuation based proof of the stability of ac spectra of random operators on tree graphs, In: Recent Advances in Differential Equations and Mathematical Physics , Eds.: N. Chernov, Y. Karpeshina, I.W. Knowles, R.T. Lewis, R. Weikard Contemporary Math. Series 412: 1-14 (2006)

     

  • M. Aizenman, B. Sims, S. Warzel
    Absolutely continuous spectra of quantum tree graphs with weak disorder, Commun. Math. Phys. 264: 371-389 (2006)

     

  • W. Kirsch, S. Warzel
    Anderson localization and Lifshits tails for random surface potentials, J. Funct. Anal. 230: 222-250 (2006)

     

  • H. Leschke, S. Warzel, A. Weichlein
    Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction, Ann. Henri Poincare 7: 335-363 (2006)

     

  • M. Aizenman, S. Warzel
    Persistence under weak disorder of ac spectra of quasi-periodic Schrödinger operators on trees graphs, Mosc. Math. J. 5: 499-506 (2005)

     

  • W. Kirsch, S. Warzel
    Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime, Math. Phys. Anal. Geom. 8: 257-285 (2005)

     

  • H. Leschke, S. Warzel, A. Weichlein
    Ballistic transport in random magnetic fields with anisotropic long-ranged correlations, J. Phys. A: Math. Gen. 38: L235-L240 (2005)

     

  • H. Leschke, S. Warzel
    Quantum-classical transitions in Lifshits tails with magnetic fields, Phys. Rev. Lett. 92: 086402:1-4 (2004)

     

  • H. Leschke, P. Müller, S. Warzel
    A survey of rigorous results on random Schrödinger operators for amorphous solids, Markov Proc. Relat. Fields 9: 729-760 (2003); Reprinted on p. 119-151 in: J.-D. Deuschel, A. Greven (eds.), Interacting Stochastic Systems, Springer, Berlin 2005.

     

  • D. Hundertmark, W. Kirsch, S. Warzel
    Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay, Markov Proc. Relat. Fields 9: 651-660 (2003)

     

  • G. Raikov, S.Warzel
    Quasi-classical versus non-classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials, Rev. Math. Phys. 14: 1051-1072 (2002)

     

  • G. Raikov, S.Warzel
    Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials, C. R. Acad. Sci. Paris Ser. I, 335: 683-688 (2002)

     

  • H. Leschke, R. Ruder, S. Warzel
    Simple diamagnetic monotonicities for Schrödinger operators with inhomogeneous magnetic fields of constant direction, J. Phys. A: Math. Gen. 35:5701-5709 (2002)

     

  • T. Hupfer, H. Leschke, S. Warzel
    Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials, J. Math. Phys. 42: 5626-5641 (2001)

     

  • T. Hupfer, H. Leschke, P. Müller, S. Warzel
    The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials, Comm. Math. Phys. 221: 229-254 (2001)

     

  • T. Hupfer, H. Leschke, P. Müller, S. Warzel
    Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials, Rev. Math. Phys. 13: 1547-1581 (2001)

     

  • T. Hupfer, H. Leschke, S. Warzel
    The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity, AMS/IP Studies in Adv. Math. 16: 233-247 (2000)

     

  • T. Hupfer, H. Leschke, S. Warzel
    Poissonian obstacles with Gaussian walls discriminate between classical and quantum Lifshits tailing in magnetic fields, J. Stat. Phys. 97: 725-750 (1999)

     

  • B. Bodmann, H. Leschke, S. Warzel
    A rigorous path-integral for quantum spin dynamics via planar Brownian motion, Pages 173-176 in: Path-integrals from peV to TeV - Firenze '98, eds. V. Tognetti, R. Vaia, R. Casalbuoni, R. Gachetti, P. Verrucchi, World Scientific 1999

     

  • B. Bodmann, H. Leschke, S. Warzel, A rigorous path-integral for quantum spin using flat-space Wiener regularization, J. Math. Phys. 40: 2549-2559 (1999)

 

Books

 

  • M. Aizenman, S. Warzel:
    Random Operators: Disorder Effects on Quantum Spectra and Dynamics AMS 2015.
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