Abel KleinProfessor, Mathematics |
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Research Interests |
Mathematical Physics: Random Schrödinger operators | |
| URL | www.math.uci.edu/faculty/aklein.html | |
| Appointments |
1982-present: Professor, Department of Mathematics, UC Irvine. 1996-1999: Chair, Department of Mathematics, UC Irvine. 1977-1982: Associate Profesor, Department of Mathematics, UC Irvine. 1974-1977: Assistant Professor, Department of Mathematics, UC Irvine. 1972-1974: Instructor, Princeton University. 1971-1972: Adjunct Assistant Professor, UCLA. |
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Research Abstract |
The main subject of Klein's research is the study of phenomena that occur in disordered systems. Impurities can change dramatically the properties of certain materials. The best known examples are transistors, which are made of certain materials whose properties are modified by impurities. Such materials are modeled by disordered systems. Random Schrödinger operators describe an electron moving in a medium with random impurities. In the widely accepted picture, in three or more dimensions there exists a transition from an insulator region, characterized by localized states, to a very different metallic region, characterized by extended states, while in one or two dimensions there are only localized states and no metal-insulator transition. Klein's reseacrch aims to further the mathematical understanding of this picture. |
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| Publications | (with H. von Dreifus) A new proof of localization in the Anderson tight binding model, Communications in Mathematical Physics 124, 285-299 (1989). | |
| Extended states in the Anderson model on the Bethe lattice, Advances in Mathematics 133, 163-184 (1998). | ||
| Spreading of wave packets in the Anderson model on the Bethe lattice, Communications in Mathematical Physics 177, 755-773 (1996). | ||
| Bootstrap multiscale analysis and localization in random media, Communications in Mathematical Physics 222, 415-448 (2001). | ||
| (with F. Germinet) Explicit finite volume criteria for localization in continuous random media and applications, Geometric and Functional Analysis 13, 1201-1238 (2003). | ||
| (with F. Germinet) A characterization of the Anderson metal-insulator transport transition, Duke Mathematical Journal 124, 309-351 (2004). | ||
| (with F. Germinet) New characterizations of the region of complete localization for random Schrodinger operators, Journal of Statistical Physics 122, 73-94 (2006). | ||
| (with S. Molchanov) Simplicity of eigenvalues in the Anderson model, Journal of Statistical Physics 122, 95-99 (2006). | ||
| Multiscale analysis and localization of random operators, in Random Schrodinger operators: methods, results, and perspectives, F. Klopp, ed., Panoramas et Synthèses 25, 121-159 (2008). | ||
| (with F. Germinet and B. Mandy) Delocalization for random Landau Hamiltonians with unbounded random variables, in Spectral and Scattering Theory for Quantum Magnetic Systems, Contemporary Mathematics 500, 87-100 (2009) | ||
| (with F. Germinet and J. Schenker) Quantization of the Hall conductance and delocalization in ergodic Landau Hamiltonians, Reviews in Mathematical Physics 21, 1045-1080 (2009). | ||
| (with J.-M. Combes and F. Germinet) Poisson statistics for eigenvalues of continuum random Schrodinger operators, Analysis & PDE, to appear. | ||
| (with F. Germinet) Random Schrödinger operators: Localization and delocalization, and all that, in New Trends in Mathematical Physics, V. Sidoravicius, ed., Springer 2009, pp. 371-388. | ||
| (with J.-M. Combes and F. Germinet) Generalized eigenvalue-counting for the Anderson model, Journal of Statistical Physics 135, 201-216 (2009). | ||
| (with M. Aizenman, F. Germinet and S. Warzel) On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Probability Theory and Related Fields 143, 219-238 (2009). | ||
| (with P. Mueller) The conductivity measure for the Anderson model, Journal of Mathematical Physics, Analysis, Geometry 4, 128-150 (2008). | ||
| (with F. Germinet) Localization for a continuum Cantor-Anderson Hamiltonian, in Adventures in Mathematical Physics, Contemporary Mathematics 447, 103-112 (2007). | ||
| (with A. Figotin, F. Germinet and P. Mueller) Persistence of Anderson localization in Schrodinger operators with decaying random potentials, Arkiv för Matematik 44, 1-16 (2007). | ||
| (with F. Germinet and P. Hislop) Localization at low energies for attractive Poisson random Schrodinger operators, in Probability and Mathematical Physics, 153-165, CRM Proc. Lecture Notes, 42, Amer. Math. Soc., Providence, RI, 2007 | ||
| (with F. Germinet and P. Hislop) Localization for Schrodinger operators with Poisson random potential, Journal of the European Mathematical Society 9, 577-607 (2007) | ||
| (with O. Lenoble and P. Mueller) On Mott's formula for the ac-conductivity in the Anderson model, Annals of Mathematics 166, 549-577 (2007). | ||
| (with F. Germinet and J. Schenker) Dynamical delocalization in random Landau Hamiltonians, Annals of Mathematics 166, 215-244 (2007). | ||
| (with J.-M. Bouclet, F. Germinet and J. Schenker) Linear response theory for magnetic Schrodinger operators in disordered media, Journal of Functional Analysis 226, 301-372 (2005). | ||
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(with A. Figotin) Localization of electromagnetic and acoustic waves in random m edia. Lattice models, Journal of Statistical Physics 76, 985-1003 (1994). |
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(with H. von Dreifus and J. F. Perez) Taming Griffiths' singularities: Infinite differentiability of quenched correlation functions, Communications in Mathemati cal Physics 170, 21-39 (1995). |
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Absolutely continuous spectrum in the Anderson model on the Bethe lattice, Mathem atical Research Letters 1, 399-407 (1994). |
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The Anderson metal-insulator transition on the Bethe lattice, in: XIth Internat ional Congress of Mathematical Physics, D. Iagolnitzer, ed., pp. 383-391, Interna tional Press, Boston 1995. |
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Absolutely continuous spectrum in random Schrodinger operators, Proceedings of Sy mposia in Pure Mathematics 59, 139-147 (1996) |
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| (with A. Figotin) Localized Classical Waves Created by Defects, Journal of Statistical Physics 86, 165-177 (1997). | ||
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(with A. Figotin) Localization of Classical Waves II: Electromagnetic Waves, Communications in Mathematical Physics 184, 411-441 (1997). |
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| (with S. Masooman) Taming Griffiths' singularities in long range random Ising models, Communications in Mathematical Physics 189, 497-512 (1997). | ||
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(with A. Figotin) Midgap Defect Modes in Dielectric and Acoustic Media, SIAM Journal on Applied Mathematics 58, 1748-1773 (1998). |
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(with A. Figotin) Localization of Light in Inhomogeneous Dielectrics, Journal of the Optical Society of America A 15, 1423-1435 (1998) (Feature Issue on Mathematics and Modeling in Modern Optics) |
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| Grant | NSF DMS-0457474 | |
| Link to this profile | http://www.faculty.uci.edu/profile.cfm?faculty_id=2060 | |
| Last updated | 11/20/2009 | |