Prof. Dr. Simone Warzel

Technische Universität München
Zentrum Mathematik - M7
Boltzmannstraße 3
85747 Garching

Room: 03.08.040
Phone: +49-89-289-17911
eMail: warzelma.tum.de

Office hours: Thursday 10:30-12:00

Current events

• Vorlesung: Spectral theory of random Schrödinger operators
• Proseminar: Einführung in die Fourieranalysis
• Forschungsseminar: Analysis und Zufall (zusammen mit P. Müller (LMU)).

Research interests

My research interests are within mathematical physics, where I have mainly been concerned with the following topics:

• Quantum systems with disorder
• Schrödinger operators with magnetic fields
• Analysis of large atoms: relativistic many-particle operators

Short CV

• Since 2008: Professor, TU Munich and Visiting Research Collaborator, Princeton University
• 2006-2008: Assistant Professor, Princeton University
• 2003-2006: Postdoc and lecturer at Princeton University
• 2001-2002: Postdoc at Friedrich-Alexander-University Erlangen
• 1997-2001: PhD student at Friedrich-Alexander-University Erlangen

Grants, Fellowships and Awards

• 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

• M. Aizenman, M. Shamis, S. Warzel: Resonances and partial delocalization on the complete graph (http://lanl.arxiv.org/abs/1405.3951)
• M. Keller, D. Lenz, S. Warzel: An invitation to trees of finite cone type: random and deterministic operators, (http://xxx.lanl.gov/abs/1403.4426).
• M. Fauser, S. Warzel: Multiparticle localization for disordered systems on continuous space via the fractional moment method, (http://xxx.lanl.gov/abs/1402.5832).
• W. Hochstättler, W. Kirsch, S. Warzel: Semicircle law for a matrix ensemble with dependent entries, (http://http://xxx.lanl.gov/abs/1401.6636).
• M. Aizenman, S. Warzel: On the ubiquity of the Cauchy distribution in spectral problems, (http://http://xxx.lanl.gov/abs/1312.7769).
• S. Warzel: Surprises in the phase diagram of the Anderson model on the Bethe lattice, 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).
• H. Siedentop, R. Frank, S. Warzel: The energy of heavy atoms according to Brown and Ravenhall: the Scott correction, Comm. Math. Phys. 278: 549–566 (2008).
• 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 transport 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)