Robert Sims

Associate Professor
Department of Mathematics
University of Arizona

Contact Information:


Paper mail:
Department of Mathematics
University of Arizona
617 N. Santa Rita Avenue
Tucson, AZ 85721
USA
E-mail: rsims@math.arizona.edu
Phone: + (520) 626-1990
Fax: + (520) 621-8322
Office: 610 Mathematics


Courses for Spring 2014:

Math 413/513

Math 254


Course for Spring 2013:

Math 464


Courses for Fall 2012:

Math 129

Math 541


Course for Spring 2012:

Math 413


Course for Fall 2011:

Math 254


Course for Spring 2011:

Math 528 B


Courses for Fall 2010:

Math 528 A

Math 129


Course for Spring 2010:

Math 523 B


Education:

Ph.D., Applied Mathematics, 2001
University of Alabama at Birmingham
Advisor: Gunter Stolz

Employment:

2013-present: Associate Professor, University of Arizona
2008-2013: Assistant Professor, University of Arizona
2007-2008: Senior Postdoc, University of Vienna
2005-2007: Visiting Research Assistant Professor, University of California, Davis
2002-2005: NSF Postdoctoral Fellow, Princeton University
2001-2002: Visiting Research Assistant Professor, University of California, Irvine

Research Interests:

My research interests lie in the area of analysis with specific emphasis on problems related to mathematical physics. Primarily, my research has focused on particle dynamics, both classical and quantum, in systems which arise naturally in the context of statistical mechanics. The questions I have considered address issues concerning three main topics: the evolution of a quantum particle in disordered media, the ground state properties of spin glass models, and the effects of interactions in multi-particle quantum spin systems.

Entropy and the Quantum:

In 2009, Daniel Ueltschi and I organized a school in Tucson on analytical methods in mathematical physics. See below for details.

Entropy and the Quantum March 2009

Lecture notes for our school just appeared. You can find a description of them here.

E & Q Lecture Notes

Arizona School of Analysis with Applications:

Since the first school was so much fun, Daniel and I have agreed to host a Second. See below for details

Arizona School of Analysis with Applications 2010

Our lecture notes for the second school just appeared. See link below.

E & Q II Lecture Notes

Arizona School of Analysis and Mathematical Physics:

With Günter Stolz, we are organizing a third Arizona School. See below for details

Arizona School of Analysis and Mathematical Physics 2012


Publications:

  1. Localization in one dimensional random media: A scattering theoretic approach. (with Gunter Stolz) Comm. Math. Phys. 213, issue 3, 575-597 (2000).
  2. Lyapunov exponents in continuum Bernoulli-Anderson models. (with David Damanik and Gunter Stolz) Operator methods in ordinary and partial differential equations. Birkhauser, Basel (Stockholm, 2000) Oper. Theory Adv. Appl. 132 , 121-130 (2002).
  3. Localization for one dimensional models of disordered media. Ph.D. Thesis, University of Alabama at Birmingham, (2001).
  4. Localization for one dimensional, continuum, Bernoulli-Anderson models. (with David Damanik and Gunter Stolz) Duke Math. J. 114 , Number 1, 59-100 (2002).
  5. An extended variational principle for the SK spin glass model. (with Michael Aizenman and Shannon Starr) Phys. Rev. B. 68 , 214403, (2003).
  6. Localization for discrete, one dimensional random word models. (with David Damanik and Gunter Stolz) J. Funct. Anal. 208 , no.2, 423-445 (2004).
  7. Stability of the absolutely continuous spectrum of random Schrodinger operators on tree graphs. (with Michael Aizenman and Simone Warzel) Probab. Theory Relat. Fields 136 , no.3, 363--394 (2006).
  8. Absolutely continuous spectra of quantum tree graphs with weak disorder. (with Michael Aizenman and Simone Warzel) Comm. Math. Phys. 264 , issue 2, 371--389 (2006).
  9. Fluctuation based proof of the stability of ac spectra of random operators on tree graphs . (with Michael Aizenman and Simone Warzel) Recent advances in differential equations and mathematical physics (Birmingham, AL, 2005), 1--14, Contemp. Math. 412 , Amer. Math. Soc., Providence, RI, 2006. Also published in: Quantum Graphs and Their Applications (Snowbird, UT, 2005), 1--14, Contemp. Math. 415 , Amer. Math. Soc., Providence, RI, (2006).
  10. Lieb-Robinson bounds and the exponential clustering theorem. (with Bruno Nachtergaele) Comm. Math. Phys. 265 , issue 1, 119--130 (2006).
  11. Recent progress in quantum spin systems. (with Bruno Nachtergaele) Markov Processes and Related Fields (J.T. Lewis special edition) , 13 , no.2, 315--329 (2007).
  12. Absence of reflection as a function of the coupling constant. (with Rowan Killip) J. Math. Phys. 47 , 062102 (2006).
  13. Propagation of correlations in quantum lattice systems. (with Bruno Nachtergaele and Yoshiko Ogata) J. Stat. Phys. 124 , issue 1, 1--13 (2006).
  14. Reflectionless Sturm-Liouville equations. Journal of Computational and Applied Mathematics. 208 , 207--225 (2007).
  15. Mean-field spin glass models from the cavity--ROSt perspective. (with Michael Aizenman and Shannon Starr) Prospects in Mathematical Physics (Lisbon, Portugal 2003), 1--30, Contemp. Math. , 437 Amer. Math. Soc., Providence, RI, (2007).
  16. A multi-dimensional Lieb-Schultz-Mattis theorem. (with Bruno Nachtergaele) Comm. Math. Phys. 276 , issue 2, 437--472 (2007).
  17. Isolated eigenvalues of the ferromagnetic spin-J XXZ chain with kink boundary conditions. (with Jaideep Mulherkar, Bruno Nachtergaele, and Shannon Starr) J. Stat. Mech. , P01016 (2008).
  18. On the absolutely continuous spectrum of Sturm-Liouville operators with applications to radial quantum trees. (with Michael Schmied and Gerald Teschl) Operators and Matrices 2 , No. 3, 417-434 (2008).
  19. Locality estimates for quantum spin systems. (with Bruno Nachtergaele) New trends in mathematical physics. Selected contributions of the XVth international congress on mathematical physics. 591-614 Springer (2009).
  20. Lieb-Robinson bounds for harmonic and anharmonic lattice systems. (with Bruno Nachtergaele, Hillel Raz, and Benjamin Schlein) Comm. Math. Phys. 286 , issue 3, 1073-1098 (2009).
  21. Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems. (with Hillel Raz) J. Stat. Phys. 137 , issue 1, 79-108 (2009).
  22. Approximating the ground state of gapped quantum spin systems. (with Eman Hamza, Spyridon Michalakis, and Bruno Nachtergaele) J. Math. Phys. Special Issue: Integrable quantum systems and solvable statistical mechanics models. 50 , 095213 (2009).
  23. A note on fractional moments for the one-dimensional continuum Anderson model. (with Eman Hamza and Gunter Stolz) J. Math. Anal. Appl. 365 , issue 2, 435 - 446 (2010).
  24. On the existence of the dynamics for anharmonic quantum oscillator systems. (with Bruno Nachtergaele, Benjamin Schlein, Shannon Starr, and Valentin Zagrebnov) Rev. Math. Phys. 22 , issue 2, 207-231 (2010).
  25. Lieb-Robinson bounds in quantum many-body physics. (with Bruno Nachtergaele) Entropy and the Quantum (Tucson, AZ, 2009), 141 -- 176, Contemp. Math. 529 , Amer. Math. Soc., Providence, RI, (2010).
  26. Much ado about something: why Lieb-Robinson bounds are useful. (with Bruno Nachtergaele) In the News Bulletin for the International Association of Mathematical Physics, October 2010.
  27. Lieb-Robinson bounds and quasi-locality for the dynamics of many-body quantum systems. Mathematical Results in Quantum Physics. Proceedings of the QMath 11 Conference in Hradec Kralove, Czech Republic 2010, 95 -- 106, Edited by Pavel Exner. World Scientific, Hackensack, NJ (2011).
  28. Automorphic equivalence within gapped phases of quantum lattice systems. (with Sven Bachmann, Spyridon Michalakis, and Bruno Nachtergaele) Comm. Math. Phys. 309 , issue 3, 835-871 (2012).
  29. Dynamical localization in disordered quantum spin systems. (with Eman Hamza and Gunter Stolz) Comm. Math. Phys. 315 , issue 1, 215 -- 239 (2012).
  30. Dispersive estimates for harmonic oscillator systems. (with Vita Borovyk) J. Math. Phys. 53 , 013302 (2012).
  31. Lieb-Robinson bounds for the Toda Lattice. (with Umar Islambekov and Gerald Teschl) J. Stat. Phys. 148 , issue 3, 440 -- 479 (2012).
  32. Quantum harmonic oscillator systems with disorder. (with Bruno Nachtergaele and Gunter Stolz) J. Stat. Phys. 149 , issue 6, 969 -- 1012 (2012).
  33. An Area Law for the Bipartite Entanglement of Disordered Oscillator Systems. (with Bruno Nachtergaele and Gunter Stolz) J. Math. Phys. 54 , 042110 (2013).
  34. Many-Body Localization: Concepts and Simple Models. (with Gunter Stolz) arXiv:1312.0577