P. Müller
▪ Publications
List of publications
⇲ A. Contributions to Mathematics ⇲ B. Contributions to Theoretical Physics
A. Contributions to Mathematics
As editor
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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
- Return probability on Bienaymé-Galton-Watson trees and spectral asymptotics of sparse Erdős-Rényi random graphs
co-authors: Markus Heydenreich, Sara Terveer
Abstract / full text from arXiv - Enhanced area law in the Widom–Sobolev formula for the free Dirac operator in arbitrary dimension
Pure Appl. Anal. 7, 595 – 613 (2025)
co-author: Leon Bollmann
Abstract / full text from arXiv Abstract / full text from journal - On the return probability of the simple random walk on Galton-Watson trees
Electron. J. Probab. 30, 10 - 1 – 23 (2025)
co-author: Jakob Stern
Abstract / full text from arXiv Abstract / full text from journal - 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 Rd
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 Zd
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