List of Publications

A.  Contributions to Mathematics

B.  Contributions to Theoretical Physics

A.  Contributions to Mathematics

As editor

• Rev. Math. Phys. 33, issue 1 (2021)
  special issue with papers from QMath14 in Aarhus, August 2019
  co-editors: Matthias Christandl, Horia Cornean, Søren Fournais, Jacob Schach Møller

• Markov Processes Relat. Fields 21, issue 3 (2015)
  special issue dedicated to Leonid Andreyevich Pastur
  co-editors: Boris Khoruzhenko, Werner Kirsch

As author

• Enhanced area law in the Widom–Sobolev formula for the free Dirac operator in arbitrary dimension
  co-author: Leon Bollmann
  Abstract / full text from arXiv

• On the return probability of the simple random walk on Galton-Watson trees
  co-author: Jakob Stern
  Abstract / full text from arXiv

• The Widom–Sobolev formula for discontinuous matrix-valued symbols
  J. Funct. Anal. 287, 110651 - 1 – 54 (2024)
  co-author: Leon Bollmann
  Abstract / full text from arXiv     Abstract / full text from journal

• Stability of a Szegő-type asymptotics
  J. Math. Phys. 64, 022101 - 1 – 11 (2023)
  co-author: Ruth Schulte
  Abstract / full text from arXiv     Abstract / full text from journal

• Localisation for Delone operators via Bernoulli randomisation
  J. Anal. Math. 147, 297 – 331 (2022)
  co-author: Constanza Rojas-Molina
  Abstract / full text from arXiv     Abstract / full text from journal

• Stability of the enhanced area law of the entanglement entropy
  Ann. Henri Poincaré 21, 3639 – 3658 (2020)
  co-author: Ruth Schulte
  Abstract / full text from arXiv     Abstract / full text from journal

• How much delocalisation is needed for an enhanced area law of the entanglement entropy?
  Commun. Math. Phys. 376, 649 – 679 (2020);    Erratum: Commun. Math. Phys. 382, 655 – 656 (2021)
  co-authors: Leonid Pastur, Ruth Schulte
  Abstract / full text from arXiv (corrected)     Abstract / full text from journal     Erratum from journal

• Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function
  J. Spectr. Theory 9, 921 – 965 (2019)
  co-authors: Adrian Dietlein, Martin Gebert
  Abstract / full text from arXiv     Abstract / full text from journal

• A bound on the averaged spectral shift function and a lower bound on the density of states for random Schrödinger operators on R^d
  Intern. Math. Research Not. (IMRN) 2018, 6673 – 6697 (2018)
  co-authors: Adrian Dietlein, Martin Gebert, Peter Hislop, Abel Klein
  Abstract / full text from arXiv     Abstract / full text from journal

• The exponent in the orthogonality catastrophe for Fermi gases
  J. Spectr. Theory 6, 643 – 683 (2016)
  co-authors: Martin Gebert, Heinrich Küttler, Peter Otte
  Abstract / full text from arXiv     Abstract / full text from journal

• Ergodicity and dynamical localization for Delone-Anderson operators
  Rev. Math. Phys. 27, 1550020 - 1 – 36 (2015)
  co-authors: François Germinet, Constanza Rojas-Molina
  Abstract / full text from arXiv     Abstract / full text from journal

• Ac-conductivity and electromagnetic energy absorption for the Anderson model in linear response theory
  Markov Processes Relat. Fields 21, 575 – 590 (2015)
  co-author: Abel Klein
  Abstract / full text from arXiv    

• Random colourings of aperiodic graphs: Ergodic and spectral properties
  (26 pages)
  co-author: Christoph Richard
  Abstract / full text from arXiv    

• Anderson's orthogonality catastrophe
  Commun. Math. Phys. 329, 979 – 998 (2014)
  co-authors: Martin Gebert, Heinrich Küttler
  Abstract / full text from arXiv     Abstract / full text from journal

• Localization for random block operators
  Oper. Theory Adv. Appl. 232, 229 – 246 (2013)
  co-author: Martin Gebert
  Abstract / full text from arXiv     Abstract / full text from journal

• Ergodic properties of randomly coloured point sets
  Canad. J. Math. 65, 349 – 402 (2013)
  co-author: Christoph Richard
  Abstract / full text from arXiv     Abstract / full text from journal

• Lifshits tails in the hierarchical Anderson model
  Ann. Henri Poincaré 13, 525 – 541 (2012)
  co-author: Simon Kuttruf
  Abstract / full text from arXiv     Abstract / full text from journal

• Uniform convergence of spectral shift functions
  RIMS Kôkyûroku Bessatsu B27, 35 – 43 (2011)
  co-author: Peter D. Hislop
  Abstract / full text from arXiv     Abstract / full text from journal

• Random Block Operators
  J. Stat. Phys. 143, 1035 – 1054 (2011)
  co-authors: Werner Kirsch, Bernd Metzger
  Abstract / full text from arXiv     Abstract / full text from journal

• Percolation Hamiltonians
  in Random Walks, Boundaries and Spectra, edited by D. Lenz, F. Sobieczky and W. Woess
  Progress in Probability, vol. 64, 235 – 258
  (Springer, Basel, 2011)
  co-author: Peter Stollmann
  Abstract / full text from arXiv     Abstract / full text from book

• The spectral shift function for compactly supported perturbations of Schrödinger operators on large bounded domains
  Proc. Amer. Math. Soc. 138, 2141 – 2150 (2010)
  co-author: Peter D. Hislop
  Abstract / full text from arXiv     Abstract / full text from journal

• Uniform existence of the integrated density of states for models on Z^d
  Positivity 12, 571 – 589 (2008)
  co-authors: Daniel Lenz, Ivan Veselić
  Abstract / full text from arXiv     Abstract / full text from journal

• A lower bound for the density of states of the lattice Anderson model
  Proc. Amer. Math. Soc. 136, 2887 – 2893 (2008)
  co-author: Peter D. Hislop
  Abstract / full text from arXiv     Abstract / full text from journal

• The conductivity measure for the Anderson model
  Zh. Mat. Fiz. Anal. Geom. 4, 128 – 150 (2008)
  co-author: Abel Klein
  Abstract / full text from arXiv     Abstract / full text from journal

• On Mott's formula for the ac-conductivity in the Anderson model
  Ann. of Math. (2) 166, 551 – 579 (2007)
  co-authors: Abel Klein, Olivier Lenoble
  Abstract / full text from arXiv     Abstract / full text from journal

• Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs
  J. Funct. Anal. 252, 233 – 246 (2007)
  co-author: Peter Stollmann
  Abstract / full text from arXiv     Abstract / full text from journal

• Persistence of Anderson localization in Schrödinger operators with decaying random potentials
  Ark. Mat. 45, 15 – 30 (2007)
  co-authors: Alex Figotin, François Germinet, Abel Klein
  Abstract / full text from arXiv     Abstract / full text from journal

• Lifshits tails for spectra of Erdös-Rényi random graphs
  Ann. Appl. Probab. 16, 295 – 309 (2006)
  co-authors: Oleksiy Khorunzhiy, Werner Kirsch
  Abstract / full text from arXiv     Abstract / full text from journal

• Spectral properties of the Laplacian on bond-percolation graphs
  Math. Z. 252, 899 – 916 (2006)
  co-author: Werner Kirsch
  Abstract / full text from arXiv     Abstract / full text from journal

• Unordnung ist das halbe Leben
  DMV-Mitteilungen 13, 192 – 196 (2005)
                                                  Abstract / full text from journal

• Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections
  J. Funct. Anal. 212, 287 – 323 (2004)
  co-authors: Kurt Broderix, Hajo Leschke
  Abstract / full text from arXiv    Abstract / full text from journal

• A survey of rigorous results on random Schrödinger operators for amorphous solids
  Markov Processes Relat. Fields 9, 729 – 760 (2003)
  co-authors: Hajo Leschke, Simone Warzel

  A slightly longer and updated version appeared in
  Interacting Stochastic Systems, edited by J.-D. Deuschel and A. Greven
  (Springer, Berlin, 2005) pp. 119 – 151
  Abstract / full text from arXiv    Abstract / full text from book

• 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)
  co-authors: Thomas Hupfer, Hajo Leschke, Simone Warzel
  Abstract / full text from arXiv     Abstract / full text from journal

• The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials
  Commun. Math. Phys. 221, 229 – 254 (2001)
  co-authors: Thomas Hupfer, Hajo Leschke, Simone Warzel
  Abstract / full text from arXiv    Abstract / full text from journal

• Spectral localization by Gaussian random potentials in multi-dimensional continuous space
  J. Stat. Phys. 101, 935 – 985 (2000)
  co-authors: Werner Fischer, Hajo Leschke
  Abstract / full text from arXiv    Abstract / full text from journal

• Dynamical properties of random Schrödinger operators
  e-print math-ph/9907002, 1999
  co-authors: Jean-Marie Barbaroux, Werner Fischer
  Abstract / full text from arXiv

• Comment on ‘On the Coulomb potential in one dimension’ by P Kurasov
  J. Phys. A 30, 5579 – 5581 (1997)
  co-authors: Werner Fischer, Hajo Leschke
                                                      Abstract / full text from journal

• Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
  Commun. Math. Phys. 190, 133 – 141 (1997)
  co-authors: Werner Fischer, Thomas Hupfer, Hajo Leschke
  Abstract / full text from arXiv     Abstract / full text from journal

• Rigorous results on Schrödinger operators with certain Gaussian random potentials in multi-dimensional continuous space
  in Differential equations, asymptotic analysis, and mathematical physics, edited by M. Demuth, B.-W. Schulze
  (Akademie Verlag, Berlin, 1997), pp. 105 – 112
  co-authors: Werner Fischer, Thomas Hupfer, Hajo Leschke
  Abstract / full text from arXiv

• Towards localisation by Gaussian random potentials in multi-dimensional continuous space
  Lett. Math. Phys. 38, 343 – 348 (1996)
  co-authors: Werner Fischer, Hajo Leschke
  Abstract / full text from arXiv     Abstract / full text from journal

• The functional-analytic versus the functional-integral approach to quantum Hamiltonians: The one-dimensional hydrogen atom
  J. Math. Phys. 36, 2313 – 2323 (1995)
  co-authors: Werner Fischer, Hajo Leschke
  Abstract / full text from arXiv     Abstract / full text from journal

B.  Contributions to Theoretical Physics

• Variational bounds for the shear viscosity of gelling melts
  Europhys. Lett. 78, 46002 -1 – 5 (2007)
  co-authors: Claas H. Köhler, Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv     Abstract / full text from journal

• Local heat flux and energy loss in a 2D vibrated granular gas
  Phys. Rev. E 72, 041303 -1 – 6 (2005)
  co-authors: Olaf Herbst, Annette Zippelius
  Abstract / full text from arXiv     Abstract / full text from journal

• Dynamics of gelling liquids: a short survey
  J. Phys.: Condens. Matter 17, S1659 – S1680 (2005)
  co-authors: Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv     Abstract / full text from journal

• Rheology of gelling polymers in the Zimm model
  J. Chem. Phys. 122, 014905 -1 – 8 (2005)
  co-authors: Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv     Abstract / full text from journal

• Local equation of state and velocity distributions of a driven granular gas
  Phys. Rev. E 70, 051313 -1 – 14 (2004)
  co-authors: Olaf Herbst, Matthias Otto, Annette Zippelius
  Abstract / full text from arXiv     Abstract / full text from journal

• Diffusion of gelation clusters in the Zimm model
  Eur. Phys. J. E 12, 325 – 331 (2003)
  co-authors: Matthias Küntzel, Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv     Abstract / full text from journal

• Critical behaviour of the Rouse model for gelling polymers
  J. Phys. A 36, 10443 – 10450 (2003)
  Abstract / full text from arXiv     Abstract / full text from journal

• Normal stresses at the gelation transition
  Phys. Rev. E 65, 041505 -1 – 6 (2002)
  co-authors: Kurt Broderix, Annette Zippelius
  Abstract / full text from arXiv    Abstract / full text from journal

• Anomalous stress relaxation in random macromolecular networks
  Physica A 302, 279 – 289 (2001)
  co-authors: Kurt Broderix, Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv    Abstract / full text from journal

• Critical dynamics of gelation
  Phys. Rev. E 63, 011510 -1 – 17 (2001)
  co-authors: Kurt Broderix, Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv    Abstract / full text from journal

• Shear viscosity of a crosslinked polymer melt
  Europhys. Lett. 48, 421 – 427 (1999)
  co-authors: Kurt Broderix, Henning Löwe, Annette Zippelius
  Abstract / full text from arXiv    Abstract / full text from journal

• On the averaged quantum dynamics by white-noise Hamiltonians with and without dissipation
  Ann. Physik (Leipzig) 7, 59 – 100 (1998)
  co-authors: Werner Fischer, Hajo Leschke
  Abstract / full text from arXiv     Abstract / full text from journal

  Appeared also in
  Understanding physics, edited by A. K. Richter
  (Copernicus Gesellschaft e.V., Katlenburg-Lindau, 1998) pp. 79 – 121

• Dynamics by white-noise Hamiltonians
  Phys. Rev. Lett. 73, 1578 – 1581 (1994)
  co-authors: Werner Fischer, Hajo Leschke
  Abstract / full text from arXiv     Abstract / full text from journal

• How to get a lower bound on the polaron ground-state energy from the path-integral representation?
  in Path Integrals in Physics, edited by V. Sa-yakanit, J.-O. Berananda, W. Sritrakool
  (World Scientific, Singapore, 1994), pp. 347 – 354
  co-authors: Werner Fischer, Hajo Leschke
  Abstract

• Path integration in quantum mechanics by changing drift and time of the underlying diffusion process
  in Path Integrals from meV to MeV: Tutzing '92, edited by H. Grabert, A. Inomata, L. Schulman, U. Weiss
  (World Scientific, Singapore, 1993), pp. 259 – 267
  co-authors: Werner Fischer, Hajo Leschke
  Abstract

• Path integration in quantum physics by changing the drift of the underlying diffusion process: applications of Legendre processes
  Ann. Phys. (N.Y.) 227, 206 – 221 (1993)
  co-authors: Werner Fischer, Hajo Leschke
                                                      Abstract / full text from journal

• Changing dimension and time: two well-founded and practical techniques for path integration in quantum physics
  J. Phys. A 25, 3835 – 3853 (1992)
  co-authors: Werner Fischer, Hajo Leschke
                                                      Abstract / full text from journal