Department of Mathematics

University of Arizona

- 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

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

University of Alabama at Birmingham

Advisor: Gunter Stolz

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

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.

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.

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

Arizona School of Analysis and Mathematical Physics 2012

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.

- Localization in one dimensional random
media: A scattering theoretic approach. (with Gunter Stolz)
*Comm. Math. Phys.***213**, issue 3, 575-597 (2000). - 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). - Localization for one dimensional models of disordered media. Ph.D. Thesis, University of Alabama at Birmingham, (2001).
- Localization for one dimensional, continuum, Bernoulli-Anderson models. (with David Damanik and Gunter Stolz)
*Duke Math. J.***114**, Number 1, 59-100 (2002). - An extended variational principle for the SK spin glass model. (with Michael Aizenman and Shannon Starr)
*Phys. Rev. B.***68**, 214403, (2003). - Localization for discrete, one dimensional random word models. (with David Damanik and Gunter Stolz)
*J. Funct. Anal.***208**, no.2, 423-445 (2004). - 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). - 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). - 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). - Lieb-Robinson bounds and the exponential clustering theorem. (with Bruno Nachtergaele)
*Comm. Math. Phys.***265**, issue 1, 119--130 (2006). - 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). - Absence of reflection as a function of the coupling constant. (with Rowan Killip)
*J. Math. Phys.***47**, 062102 (2006). - Propagation of correlations in quantum lattice systems. (with Bruno Nachtergaele and Yoshiko Ogata)
*J. Stat. Phys.***124**, issue 1, 1--13 (2006). - Reflectionless Sturm-Liouville equations.
*Journal of Computational and Applied Mathematics.***208**, 207--225 (2007). - 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). - A multi-dimensional Lieb-Schultz-Mattis theorem. (with Bruno Nachtergaele)
*Comm. Math. Phys.***276**, issue 2, 437--472 (2007). - 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). - 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). - 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). - 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). - Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems. (with Hillel Raz)
*J. Stat. Phys.***137**, issue 1, 79-108 (2009). - 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). - 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). - 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). - 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). - 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.
- 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).
- 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). - Dynamical localization in disordered quantum spin systems. (with Eman Hamza and Gunter Stolz)
*Comm. Math. Phys.***315**, issue 1, 215 -- 239 (2012). - Dispersive estimates for harmonic oscillator systems. (with Vita Borovyk)
*J. Math. Phys.***53**, 013302 (2012). - Lieb-Robinson bounds for the Toda Lattice. (with Umar Islambekov and Gerald Teschl)
*J. Stat. Phys.***148**, issue 3, 440 -- 479 (2012). - Quantum harmonic oscillator systems with disorder. (with Bruno Nachtergaele and Gunter Stolz)
*J. Stat. Phys.***149**, issue 6, 969 -- 1012 (2012). - An Area Law for the Bipartite Entanglement of Disordered Oscillator Systems. (with Bruno Nachtergaele and Gunter Stolz)
*J. Math. Phys.***54**, 042110 (2013). - Many-Body Localization: Concepts and Simple Models. (with Gunter Stolz)
*Markov Processes Relat. Fields***21**, issue 3, 791 -- 822 (2015). - On the dynamics of lattice systems with unbounded on-site terms in the Hamiltonian. (with Bruno Nachtergaele) arXiv:1410.8174
- Decay of determinantal and pfaffian correlation functionals in one-dimensional lattices. (with Simone Warzel)
*Comm. Math. Phys.***347**, issue 3, 903-931 (2016). - Entanglement Dynamics of Disordered Quantum XY Chains. (with Houssam Abdul -- Rahman, Bruno Nachtergaele, and Gunter Stolz)
*Lett. Math. Phys.***106**, 649 -- 674 (2016). - 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). - 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). - 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). - 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). - 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). - On the Regime of Localized Excitations for Disordered Oscillator systems. (with Houssam Abdul -- Rahman and Gunter Stolz)
*Lett. Math. Phys.***110**, 1159 -- 1189 (2020). - Lieb-Robinson bounds and strongly continuous dynamics for a class of
many-body fermion systems in R
^{d}. (with Martin Gebert, Bruno Nachtergaele, and Jake Reschke)*Ann. Henri Poincare***21**, 3609 -- 3637 (2020). - 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). - 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).