Publications

  • M. Aizenman, H. Duminil-Copin, V. Tassion, S. Warzel
    Emergent Planarity in two-dimensional Ising Models with finite-range Interactions, Preprint arXive:1801.04960.

  • P. von Soosten, S. Warzel
    Non-Ergodic Delocalization in the Rosenzweig-Porter Model, arXiv:1709.10313.

  • P. von Soosten, S. Warzel
    Singular Spectrum and Recent Results on Hierarchical Operators, arXive:1705.04884.

  • P. Soosten, S. Warzel
    The Phase Transition in the Ultrametric Ensemble and Local Stability of Dyson Brownian Motion, arXive:1705.00923.

  • M. Aizenman, S. Warzel
    Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function, Preprint arXive:1709.06052.

  • 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)

Book

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