Robert J Sims
 Professor
 Member of the Graduate Faculty
 Professor, Applied Mathematics  GIDP
Contact
 (520) 6261990
 Environment and Natural Res. 2, Rm. S346
 Tucson, AZ 85719
 rsims@math.arizona.edu
Awards
 Simons Fellows in Mathematics
 Simons Foundation, Fall 2014
Interests
No activities entered.
Courses
202425 Courses

Dissertation
MATH 920 (Fall 2024)
202324 Courses

Calculus II
MATH 129 (Spring 2024) 
Dissertation
MATH 920 (Spring 2024) 
Independent Study
MATH 599 (Spring 2024) 
Dissertation
MATH 920 (Fall 2023)
202223 Courses

Anls Ord Diff Equations
MATH 355 (Spring 2023) 
Calculus II
MATH 129 (Spring 2023) 
Dissertation
MATH 920 (Spring 2023) 
Independent Study
MATH 599 (Spring 2023) 
Anls Ord Diff Equations
MATH 355 (Fall 2022) 
Calculus II
MATH 129 (Fall 2022) 
Dissertation
MATH 920 (Fall 2022)
202122 Courses

Intro Ord Diff Equations
MATH 254 (Summer I 2022) 
Anls Ord Diff Equations
MATH 355 (Spring 2022) 
Independent Study
MATH 599 (Spring 2022) 
Complex Analysis
MATH 520A (Fall 2021) 
Independent Study
MATH 499 (Fall 2021) 
Independent Study
MATH 599 (Fall 2021)
202021 Courses

Intro Ord Diff Equations
MATH 254 (Summer I 2021) 
Independent Study
MATH 499 (Spring 2021) 
Independent Study
MATH 599 (Spring 2021) 
Independent Study
PHYS 499 (Spring 2021) 
Real Analysis
MATH 523B (Spring 2021) 
Thesis
MATH 910 (Spring 2021) 
Calculus II
MATH 129 (Fall 2020) 
Independent Study
MATH 599 (Fall 2020) 
Independent Study
PHYS 499 (Fall 2020) 
Real Analysis
MATH 523A (Fall 2020)
201920 Courses

Banach + Hilbert Spaces
MATH 528B (Spring 2020) 
Directed Research
PHYS 492 (Spring 2020) 
Independent Study
MATH 599 (Spring 2020) 
Topics in Undergrad Math
MATH 396T (Spring 2020) 
Independent Study
MATH 599 (Fall 2019) 
Real Analy One Variable
MATH 425A (Fall 2019) 
Real Analy One Variable
MATH 525A (Fall 2019) 
Thesis
MATH 910 (Fall 2019)
201819 Courses

Anls Ord Diff Equations
MATH 355 (Spring 2019) 
Calculus II
MATH 129 (Spring 2019) 
Independent Study
MATH 599 (Spring 2019) 
Honors Thesis
MATH 498H (Fall 2018) 
Intro Math Physics
MATH 541 (Fall 2018) 
Intro Math Physics
PHYS 541 (Fall 2018)
201718 Courses

Calculus II
MATH 129 (Spring 2018) 
Real Analysis
MATH 523B (Spring 2018) 
Independent Study
MATH 599 (Fall 2017) 
Real Analysis
MATH 523A (Fall 2017)
201617 Courses

Calculus II
MATH 129 (Spring 2017) 
Real Analysis
MATH 523B (Spring 2017)
201516 Courses

Theory of Probability
MATH 464 (Spring 2016)
Scholarly Contributions
Books
 Sims, R. J., Young, A., & AbdulRahman, H. (2020). Analytic Trends in Mathematical Physics. AMS.More infoThis volume of Contemporary Mathematics contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5–9, 2018, at the University of Arizona.
 Ueltschi, D., & Sims, R. J. (2011). Entropy and the Quantum II. American Mathematical Society. doi:10.1090/CONM/552
 Ueltschi, D., & Sims, R. J. (2010). Entropy and the Quantum. American Mathematical Society. doi:10.1090/CONM/529
Journals/Publications
 Nachtergaele, B., Sims, R., & Young, A. (2022). QuasiLocality Bounds for Quantum Lattice Systems. Part II. Perturbations of FrustrationFree Spin Models with Gapped Ground States. Annales Henri Poincare. doi:https://doi.org/10.1007/s00023021010865More infoWe study the stability with respect to a broad class of perturbations ofgapped ground state phases of quantum spin systems defined by frustrationfreeHamiltonians. The core result of this work is a proof using theBravyiHastingsMichalakis (BHM) strategy that under a condition of LocalTopological Quantum Order, the bulk gap is stable under perturbations thatdecay at long distances faster than a stretched exponential. Compared toprevious work we expand the class of frustrationfree quantum spin models thatcan be handled to include models with more general boundary conditions, andmodels with discrete symmetry breaking. Detailed estimates allow us toformulate sufficient conditions for the validity of positive lower bounds forthe gap that are uniform in the system size and that are explicit to somedegree. We provide a survey of the BHM strategy following the approach ofMichalakis and Zwolak, with alterations introduced to accommodate more generalthan just periodic boundary conditions and more general lattices. We expressthe fundamental condition known as LTQO by means of the notion ofindistinguishability radius, which we introduce. Using the uniformfinitevolume results we then proceed to study the thermodynamic limit. Wefirst study the case of a unique limiting ground state and then also considermodels with spontaneous breaking of a discrete symmetry. In the latter case,LTQO cannot hold for all local observables. However, for perturbations thatpreserve the symmetry, we show stability of the gap and the structure of thebroken symmetry phases. We prove that the GNS Hamiltonian associated with eachpure state has a nonzero spectral gap above the ground state.[Journal_ref: ]
 Young, A., Sims, R., & Nachtergaele, B. (2021). QuasiLocality Bounds for Quantum Lattice Systems. Part II. Perturbations of FrustrationFree Spin Models with Gapped Ground States. Annales Henri Poincaré, 23(2), 393511. doi:10.1007/s00023021010865More infoAbstractWe study the stability with respect to a broad class of perturbations of gapped groundstate phases of quantum spin systems defined by frustrationfree Hamiltonians. The core result of this work is a proof using the Bravyi–Hastings–Michalakis (BHM) strategy that under a condition of local topological quantum order (LTQO), the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work, we expand the class of frustrationfree quantum spin models that can be handled to include models with more general boundary conditions, and models with discrete symmetry breaking. Detailed estimates allow us to formulate sufficient conditions for the validity of positive lower bounds for the gap that are uniform in the system size and that are explicit to some degree. We provide a survey of the BHM strategy following the approach of Michalakis and Zwolak, with alterations introduced to accommodate more general than just periodic boundary conditions and more general lattices. We express the fundamental condition known as LTQO by means of an indistinguishability radius, which we introduce. Using the uniform finitevolume results, we then proceed to study the thermodynamic limit. We first study the case of a unique limiting ground state and then also consider models with spontaneous breaking of a discrete symmetry. In the latter case, LTQO cannot hold for all local observables. However, for perturbations that preserve the symmetry, we show stability of the gap and the structure of the broken symmetry phases. We prove that the GNS Hamiltonian associated with each pure state has a nonzero spectral gap above the ground state.
 AbdulRahman, H., Sims, R., & Stolz, G. (2020). On the Regime of Localized Excitations for Disordered Oscillator Systems. Letters in Mathematical Physics, 110, 11591189. doi:https://doi.org/10.1007/s11005020012562More infoWe study quantum oscillator lattice systems with disorder, in arbitrarydimension, requiring only partial localization of the associated effectiveoneparticle Hamiltonian. This leads to a manybody localized regime of excitedstates with arbitrarily large energy density. We prove zerovelocityLiebRobinson bounds for the dynamics of Weyl operators as well as for positionand momentum operators restricted to this regime. Dynamical localization isalso shown in the form of quasilocality of the time evolution of local Weyloperators and through exponential clustering of the dynamic correlations ofstates with localized excitations.[Journal_ref: ]
 Sims, R. J. (2019). LiebRobinson bounds and strongly continuous dynamics for a class of manybody fermion systems in $\mathbb{R}^d$. Ann. Henri Poincare, 21, 36093637. doi:https://doi.org/10.1007/s00023020009595More infoWe introduce a class of UVregularized twobody interactions for fermions in$\mathbb{R}^d$ and prove a LiebRobinson estimate for the dynamics of thisclass of manybody systems. As a step toward this result, we also prove apropagation bound of LiebRobinson type for Schr\"odinger operators. We applythe propagation bound to prove the existence of infinitevolume dynamics as astrongly continuous group of automorphisms on the CAR algebra.[Journal_ref: ]
 Sims, R., Reschke, J., Nachtergaele, B., & Gebert, M. (2020). Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of ManyBody Fermion Systems in $${\mathbb {R}}^d$$. Annales Henri Poincaré. doi:10.1007/s00023020009595
 Sims, R., Reschke, J., Nachtergaele, B., & Gebert, M. (2020). Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of ManyBody Fermion Systems in $${\mathbb {R}}^d$$Rd. Annales Henri Poincaré, 21(11), 36093637. doi:10.1007/s00023020009595More infoWe introduce a class of UVregularized twobody interactions for fermions in $${\mathbb {R}}^d$$ and prove a Lieb–Robinson estimate for the dynamics of this class of manybody systems. As a step toward this result, we also prove a propagation bound of Lieb–Robinson type for Schrodinger operators. We apply the propagation bound to prove the existence of infinitevolume dynamics as a strongly continuous group of automorphisms on the CAR algebra.
 Sims, R., Nachtergaele, B., & Young, A. (2019). Quasilocality bounds for quantum lattice systems. I. LiebRobinson bounds, quasilocal maps, and spectral flow automorphisms. Journal of Mathematical Physics, 60(6), 061101. doi:10.1063/1.5095769
 Warzel, S., & Sims, R. (2018). Correction to: Decay of Determinantal and Pfaffian Correlation Functionals in OneDimensional Lattices. Communications in Mathematical Physics, 361(2), 825826. doi:10.1007/s0022001831713
 Sims, R. J., AbdulRahman, H., Nachtergaele, B., & Stolz, G. (2017). Localization Properties of the Disordered XY Spin Chain. Annalen der Physik, 529(7), 17. doi:10.1002/andp.201600280
 Sims, R., Abdul‐Rahman, H., Nachtergaele, B., & Stolz, G. (2017). Localization properties of the disordered XY spin chain: A review of mathematical results with an eye toward many‐body localization. Annalen der Physik, 529(7), 1600280. doi:10.1002/andp.201600280
 Sims, R. J., & Warzel, S. (2016). Decay of determinantal and pfaffian correlation functionals in onedimensional lattices. Comm. Math. Phys., 347(3), 903931. doi:10.1007/s0022001626120
 Sims, R. J., AbdulRahman, H., Nachtergaele, B., & Stolz, G. (2016). Entanglement Dynamics of Disordered Quantum XY Chains. Letters in Mathematical Physics, 106(5), 649674. doi:10.1007/s1100501608359
 Nachtergaele, B., Sims, R., & Stolz, G. (2013). An area law for the bipartite entanglement of disordered oscillator systems. Journal of Mathematical Physics, 54(4).More infoAbstract: We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are satisfied for some standard models that are almost surely gapless in the thermodynamic limit. © 2013 AIP Publishing LLC.
 Bachmann, S., Michalakis, S., Nachtergaele, B., & Sims, R. (2012). Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems. Communications in Mathematical Physics, 309(3), 835871.More infoAbstract: Gapped ground states of quantum spin systems have been referred to in the physics literature as being 'in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on s ∈ [0, 1], such that for each s, H(s) has a nonvanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an sdependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasiadiabatic evolution' technique, of which we give a proof extended to infinitedimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasilocal structure and prove that the flow, which we call the spectral flow, connecting the gapped ground states in the same phase, satisfies a LiebRobinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a cocycle of automorphisms of the algebra of quasilocal observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models H(s), 0 ≤ s ≤ 1. © 2011 The Author(s).
 Borovyk, V., & Sims, R. (2012). Dispersive estimates for harmonic oscillator systems. Journal of Mathematical Physics, 53(1).More infoAbstract: We consider a large class of harmonic systems, each defined as a quasifree dynamics on the Weyl algebra over l 2(Z 2). In contrast to recently obtained, shorttime locality estimates, known as LiebRobinson bounds, we prove a number of longtime dispersive estimates for these models. © 2012 American Institute of Physics.
 Hamza, E., Sims, R., & Stolz, G. (2012). Dynamical Localization in Disordered Quantum Spin Systems. Communications in Mathematical Physics, 315(1), 215239.More infoAbstract: We say that a quantum spin system is dynamically localized if the timeevolution of local observables satisfies a zerovelocity LiebRobinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective oneparticle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized. © 2012 SpringerVerlag.
 Islambekov, U., Sims, R., & Teschl, G. (2012). LiebRobinson Bounds for the Toda Lattice. Journal of Statistical Physics, 148(3), 440479.More infoAbstract: We establish locality estimates, known as LiebRobinson bounds, for the Toda lattice. In contrast to harmonic models, the LiebRobinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kacvan Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems. © 2012 Springer Science+Business Media, LLC.
 Nachtergaele, B., Sims, R., & Stolz, G. (2012). Quantum Harmonic Oscillator Systems with Disorder. Journal of Statistical Physics, 149(6), 9691012.More infoAbstract: We study manybody properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zerovelocity LiebRobinson bound, is formulated in terms of the decay of the eigenfunction correlators for an effective oneparticle Hamiltonian. We show how stateoftheart techniques for proving Anderson localization can be used to prove that these properties hold in a number of standard models. We also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of oneparticle eigenfunction correlators. In particular, we show that static correlations decay exponentially fast if the corresponding effective oneparticle Hamiltonian exhibits localization at low energies, regardless of whether there is a gap in the spectrum above the ground state or not. Our results apply to finite as well as to infinite oscillator systems. The eigenfunction correlators that appear are more general than those previously studied in the literature. In particular, we must allow for functions of the Hamiltonian that have a singularity at the bottom of the spectrum. We prove exponential bounds for such correlators for some of the standard models. © 2012 Springer Science+Business Media New York.
 Hamza, E., Sims, R., & Stolz, G. (2010). A note on fractional moments for the onedimensional continuum Anderson model. Journal of Mathematical Analysis and Applications, 365(2), 435446.More infoAbstract: We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the onedimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any singlesite distribution with bounded, compactly supported density. © 2009 Elsevier Inc. All rights reserved.
 Nachtergaele, B., Schlein, B., Sims, R., Starr, S., & Zagrebnov, V. (2010). On the existence of the dynamics for anharmonic quantum oscillator systems. Reviews in Mathematical Physics, 22(2), 207231.More infoAbstract: We construct a W*dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved LiebRobinson bounds for such systems on finite lattices [19]. © 2010 2010 by the authors.
 Zagrebnov, V. A., Starr, S., Sims, R., Schlein, B., & Nachtergaele, B. (2010). ON THE EXISTENCE OF THE DYNAMICS FOR ANHARMONIC QUANTUM OSCILLATOR SYSTEMS. Reviews in Mathematical Physics, 22(2), 207231. doi:10.1142/s0129055x1000393xMore infoWe construct a W^*dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved LiebRobinson bounds for such systems on finite lattices.
 Hamza, E., Michalakis, S., Nachtergaele, B., & Sims, R. (2009). Approximating the ground state of gapped quantum spin systems. Journal of Mathematical Physics, 50(9).More infoAbstract: We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Zd. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset XV the ground state projector can be approximated by the product of two projections, one supported on X and one supported on Xc, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. This result generalizes to multidimensional models, a result of Hastings that was an important part of his proof of an area law in one dimension ["An area law for one dimensional quantum systems," J. Stat. Mech.: Theory Exp. 2007, 08024]. © 2009 American Institute of Physics.
 Nachtergaele, B., Raz, H., Schlein, B., & Sims, R. (2009). Liebrobinson bounds for harmonic and anharmonic lattice systems. Communications in Mathematical Physics, 286(3), 10731098.More infoAbstract: We prove LiebRobinson bounds for systems defined on infinite dimensional Hilbert spaces and described by unbounded Hamiltonians. In particular, we consider harmonic and certain anharmonic lattice systems. © 2008 The Author(s).
 Raz, H., & Sims, R. (2009). Estimating the LiebRobinson velocity for classical anharmonic lattice systems. Journal of Statistical Physics, 137(1), 79108.More infoAbstract: We estimate the LiebRobsinon velocity, also known as the group velocity, for a system of harmonic oscillators and a variety of anharmonic perturbations with mainly shortrange interactions. Such bounds demonstrate a quasilocality of the dynamics in the sense that the support of the time evolution of a local observable remains essentially local. Our anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition. © Springer Science+Business Media, LLC 2009.
 Mulherkar, J., Nachtergaele, B., Sims, R., & Starr, S. (2008). Isolated eigenvalues of the ferromagnetic spinJXXZ chain with kink boundary conditions. Journal of Statistical Mechanics: Theory and Experiment, 2008(1).More infoAbstract: We investigate the lowlying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum. © IOP Publishing Ltd.
 Teschl, G., Sims, R., & Schmied, M. (2008). ON THE ABSOLUTELY CONTINUOUS SPECTRUM OF STURMLIOUVILLE OPERATORS WITH APPLICATIONS TO RADIAL QUANTUM TREES. Operators and Matrices, 417434. doi:10.7153/oam0225More infoWe consider standard subordinacy theory for general SturmLiouville operators and give criteria when boundedness of solutions implies that no sub ordinate solutions exist. As applications, we prove a Weidmanntype result for general SturmLiouville operators and investigate the absolutely continu ous spectrum of radially symmetric quantum trees.
 Nachtergaele, B., & Sims, R. (2007). A multidimensional LiebSchultzMattis theorem. Communications in Mathematical Physics, 276(2), 437472.More infoAbstract: For a large class of finiterange quantum spin models with halfinteger spins, we prove that uniqueness of the ground state implies the existence of a lowlying excited state. For systems of linear size L, with arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C log L)/L. This result can be regarded as a multidimensional LiebSchultzMattis theorem [14] and provides a rigorous proof of the main result in [8]. © SpringerVerlag 2007.
 Sims, R. (2007). Reflectionless SturmLiouville equations. Journal of Computational and Applied Mathematics, 208(1 SPEC. ISS.), 207225.More infoAbstract: We consider compactly supported perturbations of periodic SturmLiouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, we also provide the proofs of several basic estimates, e.g., bounds and asymptotics for the relevant mfunctions. © 2006 Elsevier B.V. All rights reserved.
 Aizenman, M., Sims, R., & Warzel, S. (2006). Absolutely continuous spectra of quantum tree graphs with weak disorder. Communications in Mathematical Physics, 264(2), 371389.More infoAbstract: We consider the Laplacian on a rooted metric tree graph with branching number K≥2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the WeylTitchmarsh function to trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
 Aizenman, M., Sims, R., & Warzel, S. (2006). Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Probability Theory and Related Fields, 136(3), 363394.More infoAbstract: The subject of this work is random Schrödinger operators on regular rooted tree graphs [script T sign] with stochastically homogeneous disorder. The operators are of the form H λ (ω)=T+U+λ V(ω) acting in l2(script T sign), with T the adjacency matrix, U a radially periodic potential, and V(ω) a random potential. This includes the only class of homogeneously random operators for which it was proven that the spectrum of H λ (ω) exhibits an absolutely continuous (ac) component; a results established by A. Klein for weak disorder in case U=0 and V(ω) given by iid random variables on script T sign. Our main contribution is a new method for establishing the persistence of ac spectrum under weak disorder. The method yields the continuity of the ac spectral density of H λ (ω) at λ=0. The latter is shown to converge in the L 1sense over closed Borel sets in which H 0 has no singular spectrum. The analysis extends to random potentials whose values at different sites need not be independent, assuming only that their joint distribution is weakly correlated across different tree branches.
 Killip, R., & Sims, R. (2006). Absence of reflection as a function of the coupling constant. Journal of Mathematical Physics, 47(6).More infoAbstract: We consider solutions of the onedimensional equation  u″+(Q+λV)u=0 where Q:ℝ→ℝ is locally integrable, V:ℝ→ℝ is integrable with supp(V) ⊂[0, 1], and λ ∈ ℝ is a coupling constant. Given a family of solutions {u λ}λ∈ℝ which satisfy u λ(x) = u0(x) for all x
 Nachtergaele, B., & Sims, R. (2006). LiebRobinson bounds and the exponential clustering theorem. Communications in Mathematical Physics, 265(1), 119130.More infoAbstract: We give a LiebRobinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a nonvanishing spectral gap implies exponential clustering in the ground state of such systems.
 Nachtergaele, B., Ogata, Y., & Sims, R. (2006). Propagation of correlations in quantum lattice systems. Journal of Statistical Physics, 124(1), 113.More infoAbstract: We provide a simple proof of the LiebRobinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics. © 2006 Springer Science+Business Media, Inc.
 Damanik, D., Sims, R., & Stolz, G. (2004). Localization for discrete onedimensional random word models. Journal of Functional Analysis, 208(2), 423445.More infoAbstract: We consider Schrödinger operators in ℓ2(ℤ) whose potentials are obtained by randomly concatenating words from an underlying set W according to some probability measure ν on W. Our assumptions allow us to consider models with local correlations, such as the random dimer model or, more generally, random polymer models, We prove spectral localization and, away from a finite set of exceptional energies, dynamical localization for such models. These results are obtained by employing scattering theoretic methods together with Furstenberg's theorem to verify the necessary input to perform a multiscale analysis. © 2003 Elsevier Inc. All rights reserved.
 Aizenman, M., Sims, R., & Starr, S. L. (2003). Extended variational principle for the SherringtonKirkpatrick spinglass model. Physical Review B  Condensed Matter and Materials Physics, 68(21), 21440312144034.More infoAbstract: The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the SherringtonKirkpatrick (SK) spinglass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound as well as the actual value are expressed through an optimization procedure for which ultrametric/hierarchal structures form only a subset of the variational class. The validity of Parisi's ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.
 Damanik, D., Sims, R., & Stolz, G. (2002). Localization for onedimensional, continuum, BernoulliAnderson models. Duke Mathematical Journal, 114(1), 59100.More infoAbstract: We use scattering theoretic methods to prove strong dynamical and exponential localization for onedimensional, continuum, Andersontype models with singular distributions; in particular, the case of a Bernoulli distribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools are the reflection and transmission coefficients for compactly supported singlesite perturbations of a periodic background which we use to verify the necessary hypotheses of multiscale analysis. We show that nonreflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.
 Stolz, G., Sims, R., & Damanik, D. (2002). LOCALIZATION FOR ONE DIMENSIONAL, CONTINUUM, BERNOULLIANDERSON MODELS. Duke Mathematical Journal, 114(1), 59100. doi:10.1215/s0012709402114148More infoWe use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Andersontype models with singular distributions; in particular the case of a Bernoulli dis tribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multiscale analysis. We show that nonreflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.
 Sims, R., & Stolz, G. (2000). Localization in one dimensional random media: A scattering theoretic approach. Communications in Mathematical Physics, 213(3), 575597.More infoAbstract: We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, nonreflectionless single sites lead to localization.
 Coorpender, S. J., Sims, R., Finkel, D., Smirnova, A. B., Kyzar, J., Tawhid, M., Bouton, C. E., & Smith, R. C. (1999). Modeling and optimization issues concerning a circular piezoelectric actuator design. American Society of Mechanical Engineers, Aerospace Division (Publication) AD, 59, 199204.More infoAbstract: An electromechanical model for a circular piezoelectric actuator is developed. A critical challenge in certain applications employing piezoceramic actuators is to maximize the displacement provided by the actuator while minimizing it power consumption. This problem is addressed here by developing an electromechanical model which can be used to optimize the volume displacement to admittance ratio for various circular actuator designs. The model includes multiple layers with independent radii which can be varied to optimize performance. The piezoceramic, bonding, plating, and mounting materials can be varied to accommodate various design criteria. An advantage of the model lies in the property that for a variety of material configurations, analytic solutions can be obtained. Numerical examples demonstrating the properties of the model are presented.
Proceedings Publications
 Sims, R. J. (2018, May). Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches. In Contemporary Mathematics, 717, 3147.More infoWe prove spatial decay estimates on disorderaveraged positionmomentumcorrelations in a gapless class of random oscillator models. First, we prove adecay estimate on dynamic correlations for general eigenstates with a boundthat depends on the magnitude of the maximally excited mode. Then, we considerthe situation of a quantum quench. We prove that the full timeevolution of aninitially chosen (uncorrelated) product state has disorderaveragedcorrelations which decay exponentially in space, uniformly in time.[Journal_ref: ]
 Sims, R. (2011). LIEBROBINSON BOUNDS AND QUASILOCALITY FOR THE DYNAMICS OF MANYBODY QUANTUM SYSTEMS. In Mathematical Results in Quantum Physics, 95106.More infoWe review a recently proven LiebRobinson bound for general, manybody quantum systems with bounded interactions. Several basic examples are discussed as well as the connection between commutator estimates and quasilocality.