Robert Sims

Assistant 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) 621-5186
Office: 610 Mathematics

Course for Spring 2010:

Math 523 B

Courses for Fall 2009:

Math 523 A

Math 125

Course for Spring 2009:

Math 413/513

Course for Fall 2008:

Math 124

Education:

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

Employment:

2008-present: 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:

I recently helped organize a school in Tucson on analytical methods in mathematical physics. See below for details.

Entropy and the Quantum March 2009

Publications:

  1. Localization in one dimensional random media: A scattering theoretic approach. (with Gunter Stolz) Comm. Math. Phys. 213, 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 , 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 , 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 , no. 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 , 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 , 1073-1098 (2009).
  21. Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems. (with Hillel Raz) J. Stat. Phys. 137 , 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) Journal of Mathematical Analysis and Applications 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) Accepted for publication in Reviews in Mathematical Physics arXiv:0909.2249.