Robert Sims

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: S346 ENR2

Course for Spring 2022:

Math 355 Section 001

Course for Fall 2021:

Math 520 Section 001

Course for Spring 2021:

Math 523B Section 001

Courses for Fall 2020:

Math 129 Section 010

Math 523A Section 001

Courses for Spring 2020:

Math 396T Section

Math 528B Section

Courses for Fall 2019:

Math 425 Section 002

Courses for Spring 2019:

Math 355 Section

Math 129 Section

Course for Fall 2018:

Math 541 Section 001 (also listed as PHYS 541 Section 001)

Courses for Spring 2018:

Math 523B Section 001

Math 129 Section 011

Course for Fall 2017:

Math 523A Section 001

Courses for Spring 2017:

Math 523B Section 001

Math 129 Section 007

On Paternity Leave for Fall 2016:

Course for Spring 2016:

Math 464

Courses for Fall 2015:

Math 129 Section 006

Math 129 Section 007

On Sabbatical for Spring 2015:

On Sabbatical for Fall 2014:

Courses for Spring 2014:

Math 413/513

Math 254

Education:

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

Employment:

2021-present: Professor, University of Arizona
2013-2021: 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 2012:

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

Arizona School of Analysis and Mathematical Physics 2012

The Arizona School of Analysis and Mathematical Physics 2018:

With Houssam Abdul-Rahman and Amanda Young, we are organizing a fourth Arizona School. See below for details

Arizona School of Analysis and Mathematical Physics 2018

A proceedings volume for this school may be found here.

2018 AZ School Proceedings

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) Markov Processes Relat. Fields 21 , issue 3, 791 -- 822 (2015).
  35. On the dynamics of lattice systems with unbounded on-site terms in the Hamiltonian. (with Bruno Nachtergaele) arXiv:1410.8174
  36. Decay of determinantal and pfaffian correlation functionals in one-dimensional lattices. (with Simone Warzel) Comm. Math. Phys. 347 , issue 3, 903-931 (2016).
  37. Entanglement Dynamics of Disordered Quantum XY Chains. (with Houssam Abdul -- Rahman, Bruno Nachtergaele, and Gunter Stolz) Lett. Math. Phys. 106 , 649 -- 674 (2016).
  38. Localization properties of the disordered XY spin chain. A review of mathematical results with an eye toward Many-Body Localization. (with Houssam Abdul -- Rahman, Bruno Nachtergaele, and Gunter Stolz) Annalen der Physik 1600280 (2017).
  39. Correction to: Decay of determinantal and pfaffian correlation functionals in one-dimensional lattices. (with Simone Warzel) Comm. Math. Phys. 361 , issue 2, 825-826 (2018).
  40. Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches. (with Houssam Abdul -- Rahman and Gunter Stolz) Mathematical Problems in Quantum Physics (Atlanta, GA, 2016), 31 -- 47, Contemp. Math. 717 , Amer. Math. Soc., Providence, RI, (2018).
  41. Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems. (with Bruno Nachtergaele and Amanda Young) Mathematical Problems in Quantum Physics (Atlanta, GA, 2016), 93 -- 115, Contemp. Math. 717 , Amer. Math. Soc., Providence, RI, (2018).
  42. Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms. (with Bruno Nachtergaele and Amanda Young) J. Math. Phys. 60 , issue 6, 061101 (2019).
  43. On the Regime of Localized Excitations for Disordered Oscillator systems. (with Houssam Abdul -- Rahman and Gunter Stolz) Lett. Math. Phys. 110 , 1159 -- 1189 (2020).
  44. Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in Rd. (with Martin Gebert, Bruno Nachtergaele, and Jake Reschke) Ann. Henri Poincare 21 , 3609 -- 3637 (2020).
  45. Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States. (with Bruno Nachtergaele and Amanda Young) Ann. Henri Poincare 23 , 393 -- 511 (2022).
  46. Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems. (with Bruno Nachtergaele and Amanda Young) Lett. Math. Phys. 114 , no. 24, (2024).