Prof. Dr. Simone Warzel
Technical University of Munich
Chair of Mathematical Quantum Physics (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
- M. Aizenman, S. Warzel
Entanglement bounds for pure states of rapid decorrelations - C. Manai, S. Warzel
A Parisi Formula for Quantum Spin Glasses - F. R. Klausen, S. Warzel
Dehorence is an echo of Anderson localization in open quantum systems - C. Manai, S. Warzel
The spectral gap and low-energy spectrum in mean-field quantum spin systems, Forum of Mathematics, Sigma 11:e112 1–34 (2023). https://doi:10.1017/fms.2023.111. - J. P. Garrahan, C. Manai, S. Warzel
Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model. Phil. Trans. R. Soc. A.381: 20210415 (2023) https://doi.org/10.1098/rsta.2021.0415. - C. Manai, S. Warzel
Spectral analysis of the quantum random energy model. Commun. Math. Phys 402: 1259–1306 (2023). https://doi.org/10.1063/5.0084677. - 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.