Gunter Stolz

Gunter Stolz
Professor

Professor (P), Mathematics , College of Arts and Sciences

Selected Publications

Academic Article

Year	Title	Altmetric
2018	Manifestations of dynamical localization in the disordered XXZ spin chain. Communications in Mathematical Physics. 361:1083-1113. 2018
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 Theoretical. 51. 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	Localization for Random Block Operators Related to the XY Spin Chain 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 2014
2014	The infinite XXZ quantum spin chain revisited: Structure of low lying spectral bands and gaps 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 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 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 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 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 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 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 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” 1997
1997	Spectral theory for slowly oscillating potentials .2. Schrodinger operators (vol 183, pg 275, 1997) 1997
1997	Spectral theory for slowly oscillating potentials II. Schrödinger operators 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 1995
1995	One-dimensional Schrödinger operators with local point interactions 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	NOTE TO THE PAPER BY P. D. HISLOP AND S. NAKAMURA: STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS 1993
1993	APPROXIMATION OF ISOLATED EIGENVALUES OF ORDINARY DIFFERENTIAL-OPERATORS 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. 1991
1989	Expansions in generalized eigenfunctions of selfadjoint operators. Mathematische Zeitschrift. 202:397-408. 1989

Book

Year	Title	Altmetric
2007	Operator Theory, Analysis and Mathematical Physics 2007

Chapter

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	LOCALIZATION FOR THE RANDOM DISPLACEMENT MODEL. 169-175. 2011
2011	An introduction to the mathematics of Anderson localization. 71-108. 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