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Stolz, Gunter
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E-mail
stolz@uab.edu
Office Address
UH 4028
UNIVERSITY HALL
Birmingham, AL 35294-1241
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Stolz, Gunter
Professor
Positions
Professor (P)
,
Mathematics
,
College of Arts and Sciences
2011 -
Publications
Research
Teaching
Background
Contact
Publications
Selected Publications
Academic Article
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Year
Title
Altmetric
2018
Many-body localization in the droplet spectrum of the random XXZ quantum spin chain
.
Journal of Functional Analysis
. 275:211-258.
2018
2018
Droplet states in quantum XXZ spin systems on general graphs
.
Journal of Mathematical Physics
. 59.
2018
2018
Droplet localization in the random XXZ model and its manifestations
.
Journal of Physics A: Mathematical and General
. 51.
2018
2018
Manifestations of dynamical localization in the disordered XXZ spin chain
.
Communications in Mathematical Physics
. 361:1083-1113.
2018
2017
Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-Periodic Potential in Dimension Two
.
Communications in Mathematical Physics
. 354:85-113.
2017
2017
Localization properties of the disordered XY spin chain: A review of mathematical results with an eye toward many-body localization
.
Annalen der Physik
. 529.
2017
2016
Entanglement Dynamics of Disordered Quantum XY Chains
.
Letters in Mathematical Physics
. 106:649-674.
2016
2016
Many-body localization for disordered Bosons
.
New Journal of Physics
. 18.
2016
2016
Localization for transversally periodic random potentials on binary trees
.
Journal of Spectral Theory
. 6:557-600.
2016
2015
A uniform area law for the entanglement of eigenstates in the disordered XY chain
.
Journal of Mathematical Physics
. 56.
2015
2015
Many-body localization: Concepts and simple models
.
Markov Processes and Related Fields
. 21:791-822.
2015
2014
Localization for Random Block Operators Related to the XY Spin Chain
.
Helvetica Physica Acta
. 16:405-435.
2014
2014
Localization for Random Block Operators Related to the XY Spin Chain
.
Helvetica Physica Acta
. 16:405-435.
2014
2014
The infinite XXZ quantum spin chain revisited: Structure of low lying spectral bands and gaps
.
Mathematical Modelling of Natural Phenomena
. 9:44-72.
2014
2013
An area law for the bipartite entanglement of disordered oscillator systems
.
Journal of Mathematical Physics
. 54.
2013
2013
Simplicity of eigenvalues in Anderson-type models
.
Arkiv för Matematik
. 51:157-183.
2013
2012
Quantum Harmonic Oscillator Systems with Disorder
.
Journal of Statistical Physics
. 149:969-1012.
2012
2012
Dynamical Localization in Disordered Quantum Spin Systems
.
Communications in Mathematical Physics
. 315:215-239.
2012
2012
Localization for the random displacement model
.
Duke Mathematical Journal
. 161:587-621.
2012
2011
A continuum version of the Kunz-Souillard approach to localization in one dimension
.
Journal für die reine und angewandte Mathematik
. 99-130.
2011
2011
Spectral properties of the discrete random displacement model
.
Journal of Spectral Theory
. 1:123-153.
2011
2010
A note on fractional moments for the one-dimensional continuum Anderson model
.
Journal of Mathematical Analysis and Applications
. 365:435-446.
2010
2009
Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices
.
International Mathematics Research Notices
. 2009:736-764.
2009
2009
Dynamical localization for unitary anderson models
.
Mathematical Physics, Analysis and Geometry
. 12:381-444.
2009
2009
Low energy properties of the random displacement model
.
Journal of Functional Analysis
. 256:2725-2740.
2009
2009
Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence
.
Oberwolfach Reports
. 2965-2992.
2009
2008
Minimizing the ground state energy of an electron in a randomly deformed lattice
.
Communications in Mathematical Physics
. 283:397-415.
2008
2007
Correlation estimates in the anderson model
.
Journal of Statistical Physics
. 129:649-662.
2007
2007
Lyapunov exponents for unitary Anderson models
.
Journal of Mathematical Physics
. 48.
2007
2007
Positivity of Lyapunov exponents for anderson-type models on two coupled strings
.
Electronic Journal of Differential Equations
. 2007:1-18.
2007
2007
Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a cone
.
Journal of Mathematical Analysis and Applications
. 326:192-208.
2007
2006
Localization near fluctuation boundaries via fractional moments and applications
.
Journal d'Analyse Mathématique
. 100:83-116.
2006
2006
Lower transport bounds for one-dimensional continuum Schrödinger operators
.
Mathematische Annalen
. 336:361-389.
2006
2006
Moment analysis for localization in random Schrödinger operators
.
Inventiones Mathematicae
. 163:343-413.
2006
2006
Localization for random unitary operators
.
Letters in Mathematical Physics
. 75:255-272.
2006
2005
Absence of continuous spectral types for certain non-stationary random schrödinger operators
.
Helvetica Physica Acta
. 6:309-326.
2005
2004
Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: Elementary methods
.
Journal of Computational and Applied Mathematics
. 171:265-276.
2004
2004
Localization for discrete one-dimensional random word models
.
Journal of Functional Analysis
. 208:423-445.
2004
2003
Delocalization in random polymer models
.
Communications in Mathematical Physics
. 233:27-48.
2003
2002
The spectral minimum for random displacement models
.
Journal of Computational and Applied Mathematics
. 148:133-146.
2002
2002
Localization for one-dimensional, continuum, Bernoulli-Anderson models
.
Duke Mathematical Journal
. 114:59-100.
2002
2002
Strategies in localization proofs for one-dimensional random Schrödinger operators
.
Proceedings of the Indian Academy of Sciences. Mathematical sciences
. 112:229-243.
2002
2001
Two-parameter spectral averaging and localization for non-monotonic random schrödinger operators
.
Transactions of the American Mathematical Society
. 353:635-653.
2001
2000
A generalization of gordon's theorem and applications to quasiperiodic schrödinger operators
.
Electronic Journal of Differential Equations
. 2000.
2000
2000
Non-monotonic random Schrödinger operators: The Anderson model
.
Journal of Mathematical Analysis and Applications
. 248:173-183.
2000
2000
Localization in one dimensional random media: A scattering theoretic approach
.
Communications in Mathematical Physics
. 213:575-597.
2000
1998
Anderson localization for random schrödinger operators with long range interactions
.
Communications in Mathematical Physics
. 195:495-507.
1998
1998
Localization for random perturbations of periodic Schrödinger operators
.
Random Operators and Stochastic Equations
. 6:241-268.
1998
1997
Localization for Schrödinger operators with effective barriers
.
Journal of Functional Analysis
. 146:416-429.
1997
1997
Errata in the paper: “Spectral theory for slowly oscillating potentials. II. Schrödinger operators”
.
Mathematical News / Mathematische Nachrichten
. 185:307-307.
1997
1997
Spectral theory for slowly oscillating potentials .2. Schrodinger operators (vol 183, pg 275, 1997)
.
Mathematical News / Mathematische Nachrichten
. 185:307-307.
1997
1997
Spectral theory for slowly oscillating potentials II. Schrödinger operators
.
Mathematical News / Mathematische Nachrichten
. 183:275-294.
1997
1996
Operators with singular continuous spectrum, V. Sparse potentials
.
Proceedings of the American Mathematical Society
. 124:2073-2080.
1996
1995
Trace norm estimates for products of integral operators and diffusion semigroups
.
Integral Equations and Operator Theory
. 23:145-153.
1995
1995
Absence of Absolutely Continuous Spectra for Multidimensional Schrödinger Operators with High Barriers
.
Bulletin of the London Mathematical Society
. 27:162-168.
1995
1995
Approximation of isolated eigenvalues of general singular ordinary differential operators
.
Results in Mathematics
. 28:345-358.
1995
1995
LOCALIZATION FOR RANDOM SCHRODINGER-OPERATORS WITH POISSON POTENTIAL
.
Helvetica Physica Acta
. 63:297-314.
1995
1995
One-dimensional Schrödinger operators with local point interactions
.
Journal für die reine und angewandte Mathematik
. 1995:169-186.
1995
1994
Spectral theory for slowly oscillating potentials I. Jacobi matrices
.
manuscripta mathematica
. 84:245-260.
1994
1994
Spectral Theory of One-Dimensional Schrödinger Operators with Point Interactions
.
Journal of Mathematical Analysis and Applications
. 184:491-516.
1994
1994
Singular spectrum for multidimensional Schrödinger operators with potential barriers
.
JOURNAL OF OPERATOR THEORY
. 32:91-109.
1994
1994
Stability of Spectral Types for Sturm-Liouville Operators
.
Mathematical Research Letters
. 1:437-450.
1994
1993
STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS
.
Reviews in Mathematical Physics
. 5:453-456.
1993
1993
APPROXIMATION OF ISOLATED EIGENVALUES OF ORDINARY DIFFERENTIAL-OPERATORS
.
Journal für die reine und angewandte Mathematik
. 445:31-44.
1993
1993
On eigenfunction expansions and scattering theory
.
Mathematische Zeitschrift
. 212:337-357.
1993
1992
Polynomial boundedness of eigensolutions and the spectrum of schrödinger operators
.
Mathematische Annalen
. 294:195-211.
1992
1992
Bounded solutions and absolute continuity of Sturm-Liouville operators
.
Journal of Mathematical Analysis and Applications
. 169:210-228.
1992
1991
On the absolutely continuous spectrum of perturbed periodic Sturm-Liouville operators.
.
Journal für die reine und angewandte Mathematik
. 1991:1-24.
1991
1989
Expansions in generalized eigenfunctions of selfadjoint operators
.
Mathematische Zeitschrift
. 202:397-408.
1989
Book
Filter
Year
Title
Altmetric
2007
Operator theory, analysis and mathematical physics
. Ed. 174.
2007
Chapter
Filter
Year
Title
Altmetric
2012
Understanding the random displacement model: From ground state properties to localization
. 183-219.
2012
2012
Understanding the random displacement model: from ground state properties to localization
. 183-219.
2012
2011
An introduction to the mathematics of Anderson localization
. 71-108.
2011
2011
Localization for the random displacement model
. 169-175.
2011
2006
Fractional moment methods for Anderson localization in the continuum
. 619-625.
2006
2002
Lyapunov exponents in continuum Bernoulli-Anderson models
. 121-130.
2002
1999
Monotonicity versus non-monotonicity in random operators
. 365-371.
1999
1997
Band edge localization in randomly perturbed crystals
. 184-191.
1997
1997
Sturm-Liouville problems with an infinite number of interior singularities
. 211-249.
1997
1995
Localization for the Poisson model
. 375-380.
1995
1994
Results in the spectral theory of Schrödinger operators with wide potential barriers
. 27-32.
1994
1990
Expansions in generalized eigenfunctions of Schrödinger operators with singular potentials
. 353-372.
1990
Research
Principal Investigator On
Localization Properties of Interacting Disordered Quantum Systems
awarded by
NSF - National Science Foundation
2011 - 2015
Random Schrodinger Operators
awarded by
NSF - National Science Foundation
2007 - 2011
Investigator On
CBMS Conference: Quantum Spin Systems
awarded by
NSF - National Science Foundation
2014 - 2015
Teaching
Teaching Activities
MA798 - Non-Diss Research/Comp Prep (Fall Term 2019)
2019
MA799 - Dissertation Research (Fall Term 2019)
2019
MA798 - Non-Diss Research/Comp Prep (Summer Term 2019)
2019
MA799 - Dissertation Research (Summer Term 2019)
2019
EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2019)
2019
MA747 - Linear Ops in Hilbert Space (Spring Term 2019)
2019
MA798 - Non-Diss Research/Comp Prep (Spring Term 2019)
2019
MA799 - Dissertation Research (Spring Term 2019)
2019
MA798 - Non-Diss Research/Comp Prep (Fall Term 2018)
2018
MA698 - M Lev Non-Thesis Res (Summer Term 2018)
2018
MA798 - Non-Diss Research/Comp Prep (Summer Term 2018)
2018
EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2018)
2018
MA798 - Non-Diss Research/Comp Prep (Spring Term 2018)
2018
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2017)
2017
MA485 - Probability (Fall Term 2017)
2017
MA585 - Intro to Probability (Fall Term 2017)
2017
MA798 - Non-Diss Research/Comp Prep (Fall Term 2017)
2017
MA798 - Non-Diss Research/Comp Prep (Summer Term 2017)
2017
MA646 - Real Analysis II (Spring Term 2017)
2017
MA798 - Non-Diss Research/Comp Prep (Spring Term 2017)
2017
MA645 - Real Analysis I (Fall Term 2016)
2016
MA698 - M Lev Non-Thesis Res (Summer Term 2016)
2016
MA799 - Dissertation Research (Summer Term 2016)
2016
MA485 - Probability (Spring Term 2016)
2016
MA585 - Intro to Probability (Spring Term 2016)
2016
MA646 - Real Analysis II (Spring Term 2016)
2016
MA698 - M Lev Non-Thesis Res (Spring Term 2016)
2016
MA799 - Dissertation Research (Spring Term 2016)
2016
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2015)
2015
MA631 - Linear Algebra (Fall Term 2015)
2015
MA698 - M Lev Non-Thesis Res (Fall Term 2015)
2015
MA799 - Dissertation Research (Fall Term 2015)
2015
MA799 - Dissertation Research (Summer Term 2015)
2015
EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2015)
2015
MA693 - Special Topics in Mathematics (Spring Term 2015)
2015
MA798 - Non-Diss Research/Comp Prep (Spring Term 2015)
2015
MA799 - Dissertation Research (Spring Term 2015)
2015
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2014)
2014
MA648 - Complex Analysis (Fall Term 2014)
2014
MA798 - Non-Diss Research/Comp Prep (Fall Term 2014)
2014
MA799 - Dissertation Research (Fall Term 2014)
2014
MA798 - Non-Diss Research/Comp Prep (Summer Term 2014)
2014
MA799 - Dissertation Research (Summer Term 2014)
2014
EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2014)
2014
MA646 - Real Analysis II (Spring Term 2014)
2014
MA798 - Non-Diss Research/Comp Prep (Spring Term 2014)
2014
MA799 - Dissertation Research (Spring Term 2014)
2014
MA645 - Real Analysis I (Fall Term 2013)
2013
MA693 - Special Topics in Mathematics (Fall Term 2013)
2013
MA798 - Non-Diss Research/Comp Prep (Fall Term 2013)
2013
MA798 - Non-Diss Research/Comp Prep (Summer Term 2013)
2013
EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2013)
2013
MA792 - Special Topics in Mathematics (Spring Term 2013)
2013
MA798 - Non-Diss Research/Comp Prep (Spring Term 2013)
2013
MA799 - Dissertation Research (Spring Term 2013)
2013
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2012)
2012
MA485 - Probability (Fall Term 2012)
2012
MA585 - Intro to Probability (Fall Term 2012)
2012
MA698 - M Lev Non-Thesis Res (Fall Term 2012)
2012
MA793 - Special Topics in Mathematics (Fall Term 2012)
2012
MA798 - Non-Diss Research/Comp Prep (Fall Term 2012)
2012
MA799 - Dissertation Research (Fall Term 2012)
2012
MA798 - Non-Diss Research/Comp Prep (Summer Term 2012)
2012
MA799 - Dissertation Research (Summer Term 2012)
2012
MA692 - Special Topics in Mathematics (Spring Term 2012)
2012
MA792 - Special Topics in Mathematics (Spring Term 2012)
2012
MA798 - Non-Diss Research/Comp Prep (Spring Term 2012)
2012
MA798 - Non-Diss Research/Comp Prep (Fall Term 2011)
2011
MA698 - M Lev Non-Thesis Res (Summer Term 2011)
2011
MA798 - Non-Diss Research/Comp Prep (Summer Term 2011)
2011
MA798 - Non-Diss Research/Comp Prep (Summer Term 2011)
2011
MA693 - Special Topics in Mathematics (Spring Term 2011)
2011
MA793 - Special Topics in Mathematics (Spring Term 2011)
2011
MA794 - Special Topics in Mathematics (Spring Term 2011)
2011
MA798 - Non-Diss Research/Comp Prep (Spring Term 2011)
2011
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2010)
2010
MA631 - Algebra II (Fall Term 2010)
2010
MA693 - Special Topics in Mathematics (Fall Term 2010)
2010
MA793 - Special Topics in Mathematics (Fall Term 2010)
2010
MA798 - Non-Diss Research/Comp Prep (Fall Term 2010)
2010
MA698 - M Lev Non-Thesis Res (Summer Term 2010)
2010
MA799 - Dissertation Research (Summer Term 2010)
2010
MA646 - Real Analysis II (Spring Term 2010)
2010
MA691 - Mathematics Seminar (Spring Term 2010)
2010
MA799 - Dissertation Research (Spring Term 2010)
2010
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2009)
2009
MA645 - Real Analysis I (Fall Term 2009)
2009
MA799 - Dissertation Research (Fall Term 2009)
2009
MA799 - Dissertation Research (Summer Term 2009)
2009
EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2009)
2009
MA799 - Dissertation Research (Spring Term 2009)
2009
EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2008)
2008
MA798 - Non-Diss Research/Comp Prep (Fall Term 2008)
2008
MA798 - Non-Diss Research/Comp Prep (Summer Term 2008)
2008
MA798 - Non-Diss Research/Comp Prep (Spring Term 2008)
2008
MA125 - Calculus I (Fall Term 2007)
2007
MA125 - Calculus I (Fall Term 2007)
2007
MA693 - Special Topics in Mathematics (Fall Term 2007)
2007
MA793 - Special Topics in Mathematics (Fall Term 2007)
2007
MA798 - Non-Diss Research/Comp Prep (Fall Term 2007)
2007
MA799 - Dissertation Research (Fall Term 2007)
2007
Background
Education And Training
Doctor of Philosophy Level Degree in Mathematics,
Goethe University Frankfurt am Main
1989
Contact
Full Name
Gunter
Stolz