A. R. Bishop

Los Alamos National Laboratory, Los Alamos, California, United States

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Publications (901)2072.18 Total impact

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    ABSTRACT: A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to $\ln N$, which is much less than the time (proportional to $N^2$) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms.
    Quantum Information Processing 02/2014; 13:371–389. · 1.75 Impact Factor
  • K. H. Ahn, T. F. Seman, T. Lookman, A. R. Bishop
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    ABSTRACT: We analyze the essential role played by complex energy landscapes in the nanometer- to micron-scale inhomogeneities observed in perovskite manganites using a model expressed in terms of symmetrized atomic-scale lattice distortion modes. We also examine the stability of large metal and insulator domains in the absence of defects. Our results demonstrate that an intrinsic mechanism, which involves long-range interactions between strain fields, the Peierls-Nabarro energy barrier, and complex energy landscapes with multiple metastable states, rather than an extrinsic mechanism such as chemical randomness, is responsible for the inhomogeneity in perovskite manganites.
    Physical Review B 10/2013; 88(14). · 3.66 Impact Factor
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    ABSTRACT: We study the stable states of the wave equation with d-spatial and 1-time dimensions and with space-time periodic potential. The dispersed stable states spectrum of such -periodic wave equation is due to the incommensurability of the speed of light and the ratio of space and time periods. A Bloch-Floquet analysis leads to a -cube as a reduced Brillouin zone, but because of the speed incommensurability the stable states in this cube may form a spectrum of sets with a reduced dimensionality. For electromagnetic waves in photonic crystals the medium may amplify some waves with lengths fitting the crystal lattice. The energy from the external field can be pumped to the waves via the dipole moment oscillations.
    EPL (Europhysics Letters) 09/2013; 103(5):50001. · 2.26 Impact Factor
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    ABSTRACT: Exotic vortex states with long range attraction and short range repulsion have recently been proposed to arise in certain superconducting hybrid structures such as type-I/type-II layered systems as well as multi-band superconductors. In previous work it has been shown that such systems can form clump or phase separated states, but little is known about how they behave in the presence of pinning and under an applied drive. Using large scale simulations we examine the static and dynamic properties of such vortex states interacting with random and periodic pinning. In the absence of pinning this system does not form patterns but instead undergoes complete phase separation. When pinning is present there is a transition from inhomogeneous to homogeneous vortex configurations similar to a wetting phenomenon. Under an applied drive, a dynamical dewetting process can occur from a strongly pinned homogeneous state into pattern forming states, such as moving stripes that are aligned with the direction of drive or moving labyrinth or clump phases. We show that a signature of the exotic vortex interactions observable with transport measurements is a robust double peak feature in the differential resistance curves. Our results should be valuable for determining whether such vortex interactions are occurring in these systems and also for addressing the general problem of systems with competing interactions in the presence of random and periodic pinning.
    Journal of Physics Condensed Matter 08/2013; 25(34):345703. · 2.22 Impact Factor
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    ABSTRACT: Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is highly hardware-specific, which could become an obstacle when using heterogeneous systems. Also, it is as yet unclear how the wide single instruction multiple data (SIMD) units in current multi- and many-core processors should be used most efficiently if there is no structure in the sparsity pattern of the matrix. We suggest SELL-C-sigma, a variant of Sliced ELLPACK, as a SIMD-friendly data format which combines long-standing ideas from General Purpose Graphics Processing Units (GPGPUs) and vector computer programming. We discuss the advantages of SELL-C-sigma compared to established formats like Compressed Row Storage (CRS) and ELLPACK, and show its suitability on a variety of hardware platforms (Intel Sandy Bridge, Intel Xeon Phi and Nvidia Tesla K20) for a wide range of test matrices from different application areas. Using appropriate performance models we develop deep insight into the data transfer properties of the SELL-C-sigma spMVM kernel. SELL-C-sigma comes with two tuning parameters whose performance impact across the range of test matrices is studied and for which reasonable choices are proposed. This leads to a hardware-independent ("catch-all") sparse matrix format, which achieves very high efficiency for all test matrices across all hardware platforms.
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    Jian-Huang She, A R Bishop
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    ABSTRACT: We study the RKKY interaction in non-Fermi-liquid metals. We find that the RKKY interaction mediated by some non-Fermi-liquid metals can be of much longer range than for a Fermi liquid. The oscillatory nature of the RKKY interaction thus becomes more important in such non-Fermi liquids, and gives rise to enhanced frustration when the spins form a lattice. Frustration suppresses the magnetic ordering temperature of the lattice spin system. Furthermore, we find that the spin system with a longer range RKKY interaction can be described by the Brazovskii model, where the ordering wave vector lies on a higher dimensional manifold. Strong fluctuations in such a model lead to a first-order phase transition and/or glassy phase. This may explain some recent experiments where glassy behavior was observed in stoichiometric heavy fermion material close to a ferromagnetic quantum critical point.
    Physical Review Letters 07/2013; 111(1):017001. · 7.73 Impact Factor
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    ABSTRACT: We address the question of the origin of the recently discovered chiral property of the charge-density-wave phase in 1$T$-TiSe$_2$ which so far lacks a microscopic understanding. We argue that the lattice degrees of freedom seems to be crucial for this novel phenomenon. We motivate a theoretical model that takes into account one valence and three conduction bands, a strongly screened Coulomb interaction between the electrons, as well as the coupling of the electrons to a transverse optical phonon mode. The Falicov-Kimball model extended in this way possesses a charge-density-wave state at low temperatures, which is accompanied by a periodic lattice distortion. The charge ordering is driven by a lattice deformation and electron-hole pairing (excitonic) instability in combination. We show that both electron-phonon interaction and phonon-phonon interaction must be taken into account at least up to quartic order in the lattice displacement to achieve a stable chiral charge order. The chiral property is exhibited in the ionic displacements. Furthermore, we provide the ground-state phase diagram of the model and give an estimate of the electron-electron and electron-phonon interaction constants for 1$T$-TiSe$_2$.
    Physical Review B. 04/2013; 88(7).
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    ABSTRACT: We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the sink, with noise acting between the donor and acceptor. The noise is considered classically (as an external random force), and it is described by an ensemble of two-level systems (random fluctuators). Each fluctuator has two independent parameters, an amplitude and a switching rate. We represent the noise by a set of fluctuators with fitting parameters (boundaries of switching rates), which allows us to build a desired spectral density of noise in a wide range of frequencies. We analyze the quantum dynamics and the efficiency of the ET as a function of (i) the energy gap between the donor and acceptor, (ii) the strength of the interaction with the continuum, and (iii) noise parameters. As an example, numerical results are presented for the ET through the active pathway in a quinone-type photosystem II RC.
    Fortschritte der Physik 04/2013; 61(2-3):95 - 110. · 0.98 Impact Factor
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    ABSTRACT: We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation with an external time-independent force of the form f(x)=rexp(−iKx). Here the solitons travel with an oscillating velocity and all other characteristics of the solitons (amplitude, width, momentum, and phase) also oscillate. This behavior was predicted by a collective variable theory and confirmed by simulations. However, the reason for these oscillations remains unclear. Moreover, the spectrum of the oscillations exhibits a second strong peak, in addition to the intrinsic soliton peak. We show that the additional frequency belongs to a certain extended linear mode (which we refer to as a phonon for short) close to the lower band edge of the phonon continuum. Initially the soliton is at rest. When it starts to move it is deformed, begins to oscillate, and excites the above phonon mode such that the total momentum in a certain moving frame is conserved. In this frame the phonon does not move. However, not only does the soliton move in the homogeneous, time-periodic field of the phonon, but it also oscillates.
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 03/2013; 87(3).
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    ABSTRACT: High-temperature superconducting copper oxides display a variety of both long-range and local lattice anomalies which are related to the onset of the pseudogap phase and / or the onset of superconductivity. Here we show that these anomalies demonstrate polaron formation where specifically the local character of the polarons plays an important role. We predict that unconventional isotope effects will appear in both the long-wavelength and local lattice effects.
    EPL (Europhysics Letters) 03/2013; 101(4):47004. · 2.26 Impact Factor
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    ABSTRACT: Inelastic electron tunneling spectroscopy is a powerful spectroscopy that allows one to investigate the nature of local excitations and energy transfer in the system of interest. We study inelastic electron tunneling spectroscopy for topological insulators and investigate the role of inelastic scattering on the Dirac node states on the surface of topological insulators. Local inelastic scattering is shown to significantly modify the Dirac node spectrum. In the weak coupling limit, peaks and steps are induced in second derivative d^{2}I/dV^{2}. In the strong coupling limit, the local negative-U centers are formed at impurity sites, and the Dirac cone structure is fully destroyed locally. At intermediate coupling, resonance peaks emerge. We map out the evolution of the resonance peaks from weak to strong coupling, which interpolate nicely between the two limits. There is a sudden qualitative change of behavior at intermediate coupling, indicating the possible existence of a local quantum phase transition. We also find that, even for a simple local phonon mode, the inherent coupling of spin and orbital degrees in topological insulators leads to the spin-polarized texture in inelastic Friedel oscillations induced by the local mode.
    Physical Review Letters 01/2013; 110(2):026802. · 7.73 Impact Factor
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    ABSTRACT: We report that terahertz (THz) irradiation of mouse mesenchymal stem cells (mMSCs) with a single-frequency (SF) 2.52 THz laser or pulsed broadband (centered at 10 THz) source results in irradiation specific heterogenic changes in gene expression. The THz effect depends on irradiation parameters such as the duration and type of THz source, and on the degree of stem cell differentiation. Our microarray survey and RT-PCR experiments demonstrate that prolonged broadband THz irradiation drives mMSCs toward differentiation, while 2-hour irradiation (regardless of THz sources) affects genes transcriptionally active in pluripotent stem cells. The strictly controlled experimental environment indicates minimal temperature changes and the absence of any discernable response to heat shock and cellular stress genes imply a non-thermal response. Computer simulations of the core promoters of two pluripotency markers reveal association between gene upregulation and propensity for DNA breathing. We propose that THz radiation has potential for non-contact control of cellular gene expression.
    Scientific Reports 01/2013; 3:1184. · 5.08 Impact Factor
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    ABSTRACT: Physicochemical properties of DNA, such as shape, affect protein-DNA recognition. However, the properties of DNA that are most relevant for predicting the binding sites of particular transcription factors (TFs) or classes of TFs have yet to be fully understood. Here, using a model that accurately captures the melting behavior and breathing dynamics (spontaneous local openings of the double helix) of double-stranded DNA, we simulated the dynamics of known binding sites of the TF and nucleoid-associated protein Fis in Escherichia coli. Our study involves simulations of breathing dynamics, analysis of large published in vitro and genomic datasets, and targeted experimental tests of our predictions. Our simulation results and available in vitro binding data indicate a strong correlation between DNA breathing dynamics and Fis binding. Indeed, we can define an average DNA breathing profile that is characteristic of Fis binding sites. This profile is significantly enriched among the identified in vivo E. coli Fis binding sites. To test our understanding of how Fis binding is influenced by DNA breathing dynamics, we designed base-pair substitutions, mismatch, and methylation modifications of DNA regions that are known to interact (or not interact) with Fis. The goal in each case was to make the local DNA breathing dynamics either closer to or farther from the breathing profile characteristic of a strong Fis binding site. For the modified DNA segments, we found that Fis-DNA binding, as assessed by gel-shift assay, changed in accordance with our expectations. We conclude that Fis binding is associated with DNA breathing dynamics, which in turn may be regulated by various nucleotide modifications.
    PLoS Computational Biology 01/2013; 9(1):e1002881. · 4.87 Impact Factor
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    ABSTRACT: X-ray pair distribution function (pdf) and U L 3 extended x-ray absorption fine structure (EXAFS) and neutron pdf measurements that give identical results for UO 2 show U(VI)-oxo moieties with x rays for mixed valence U 4 O 9 and U 3 O 7 , in contrast to the neutron data that indicate only U(V) sites with no short U-O bonds as well as other differences. In addition, although the EXAFS spectra of UO 2 are essentially identical at 30, 100, and 200 K, those of the UO 2+x compounds exhibit different nearest-neighbor U-O distributions at each temperature. Further tunneling polaron-type behavior is found in the broadening of the features of the O K-edge x-ray absorption spectra (XAS) of the UO 2+x compounds. Raman spectra of powders also show a large increase in scattering cross section with increasing O content that would originate in a change in the electronic structure that increases the overall polarizability. The XAS and Raman also show that U 4 O 9 does not behave as a linear combination of the UO 2 and U 3 O 7 fluorite endpoints. The properties induced by mobile rather than static charged quasiparticles were explored by optical pumping of the metal-to-metal charge-transfer transition. The temperature dependence of 4.71 eV pump–1.57 eV probe reflectivity on UO 2 that initially populates the U 6d-dominated portion of the upper Hubbard band (UHB) shows a sharp 28-μsec lifetime peak at 25 K that may be associated with the fluctuations of its antiferromagnetic transition. Pumping at 3.14 eV into the 5f -dominated portion of the UHB shows an analogous 2.8-μsec peak but also a plateau bracketing this peak that ends in a cusp at 50–60 K and an abrupt change in the hardening rate of a novel 12–15 GHz phonon that is the signature for the quasiparticle quantum phase. The different results for the different excitation channels indicate a highly specific nonthermal relaxation mechanism. These results constitute the first observation of a distinct phase of photoinduced quasiparticles that is sufficiently coupled to the lattice to undergo a gap-opening transition. When the intragap state is probed with a terahertz time domain spectroscopy (TTDS) measurement 33 psec after a 3.14 excitation pulse, it shows increased absorption in the 0.5–1.1 THz range with a decrease in temperature from ∼30 to 10 K instead of the expected decrease, a result consistent with the presence of a condensate. These results are too extreme to originate in the dynamical, nonadiabatic, coupled charge-transfer–phonon/tunneling polaron scenario previously used for doped Mott-Hubbard insulators with intermediate electron-phonon coupling and therefore indicate novel physics. One possibility that could cause all of these behaviors is that a collective, dynamical, charge transfer-coupled Peierls distortion involving the 2 U(V) ↔ U(IV) + U(VI)-oxo excitation occurs coherently over an entire domain to cause the atoms in this domain to condense into a system with Bose-Einstein or Bose-Einstein-Hubbard properties.
    Physical Review B 01/2013; 88:115135. · 3.66 Impact Factor
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    ABSTRACT: In the living cell, the double-stranded DNA molecule experiences thermal motions that induce spontaneous openings and re-closings of the double helix known as “DNA breathing,” or “DNA transient bubbles” (Englander et al., 1980). The propensity for breathing is interconnected with DNA local stability and flexibility (Vafabakhsh & Ha, 2012), which play a key role in DNA biological function (Bishop et al., 2012). Here, we investigate the relationship between the DNA local propensity for breathing and binding of two transcription factors (TFs): (i) the human TF YY1, (see e.g. Usheva & Shenk, 1996), and (ii) the nucleoid-associated protein Fis in Escherichia coli (see e.g. Finkel & Johnson, 1992). Using a mesoscopic nonlinear model of double-stranded DNA (Peyrard & Bishop, 1989) that can be augmented for rational design of DNA breathing (Alexandrov et al., 2010), we have simulated the dynamics of known Fis- and YY1-binding sites, analyzed published in vitro and genomic data-sets, and conducted targeted experimental tests of our predictions (Alexandrov et al., 2012; Nowak-Lovato et al., in press). We found a strong correlation between the propensity for breathing (at the binding sites) and YY1/Fis binding. We identified a breathing profile that is characteristic for a strong Fis-binding site that is significantly enriched among the identified in vivo E. coli Fis-binding sites. To test our understanding of how Fis binding is influenced by the breathing, we designed base-pair substitutions, mismatch, and O6-Guanine methylation modifications of nucleotides, in sequences that are known to interact (or not interact) with Fis, seeking to make the breathing either closer to or farther from the breathing profile of a strong Fis-binding site. For the modified DNA segments, we found that Fis-DNA binding, as assessed by EMSA, changed in accordance with our expectations. Further, by using site-specific chromatin immunopecipitations, BIOBASE data, and simulations, we also found a specific breathing profile at the binding cites of YY1 in vivo. Our finding suggests that the genomic-flanking sequence variations and SNPs presence may exert long-range effects on DNA breathing and predetermine YY1 binding in cells.
    Journal of biomolecular structure & dynamics 01/2013; 31. · 4.99 Impact Factor
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    ABSTRACT: We study the effects of the anharmonic strand-separation dynamics of double-stranded DNA on the infrared spectra of the intramolecular base-pairing hydrogen bonds. Using the extended Peyrard-Bishop-Dauxois model for the DNA breathing dynamics coupled with the Lippincott-Schroeder potential for N-H⋯N and N-H⋯O hydrogen bonding, we identify a high-frequency (∼96 THz) feature in the infrared spectra. We show that this sharp peak arises as a result of the anharmonic base-pair breathing dynamics of DNA. In addition, we study the effects of friction on the infrared spectra. For higher temperatures (∼300 K), where the anharmonicity of DNA dynamics is pronounced, the high-frequency peak is always present irrespective of the friction strength.
    Physical Review E 12/2012; 86(6-1):061913. · 2.31 Impact Factor
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    ABSTRACT: We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its nondimensionalized Hamiltonian form and its linear spectrum is examined in a range of temperatures. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises. The effect of breathers on properties such as nonlinear dielectric response is discussed.
    Physical Review E 12/2012; 86(6-2):066601. · 2.31 Impact Factor
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    ABSTRACT: There are many examples of particle assemblies where the particles have competing repulsive and attractive interactions. In solid state systems, it has recently been proposed that exotic vortex states in type-I and type-II superconducting hybrids and type-1.5 superconductors fall into this category. In soft matter systems, competing interactions can arise for charged colloids with short range attraction or with multiple length scale interactions. Systems with competing interactions have been shown to exhibit a wide variety of patterns including stripes, labyrinths, bubbles, and crystalline phases. Although there has been considerable work analyzing these phases for different relative interaction strengths, there is little work on understanding what happens when such systems are driven over a periodic substrate. Such substrates for collective assemblies of particles could be created lithographically or using optical trap arrays and would introduce a new length scale into the system. Here we examine how a system with competing interactions behaves when interacting with a square periodic substrate. We find a novel wetting-dewetting phenomena similar to that of liquids on surfaces. In the presence of a strong substrate, the pattern formation normally found for particles with competing interactions is lost and the particles completely cover the substrate homogeneously. Under an applied drive, such a wetted system undergoes a transition to a partially dewetted state with anisotropic transport and structural features.
    Proc SPIE 10/2012;
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    ABSTRACT: EuTiO3 (ETO) has recently experienced a significant revival of interest because of its possible multiferroic properties, which are currently the focus of much research. Unfortunately, ETO is an unlikely candidate for enlarged multifunctionality since the mode softening—typical of ferroelectrics—remains incomplete, and the antiferromagnetic properties appear only at 5.5 K. However, a strong coupling between lattice and Eu spins exists and this leads to the appearance of a magnon–phonon-hybrid mode at elevated temperatures as evidenced by EPR, muon spin relaxation experiments and model predictions based on a coupled spin-polarizability Hamiltonian. This novel finding supports the notion of strong magneto-dielectric effects being realized in ETO and opens up new strategies in material design and technological applications.
    New Journal of Physics 09/2012; 14(9):093013. · 4.06 Impact Factor
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    ABSTRACT: Recently there has been renewed interest in understanding vortex patterns in superconductors and Bose–Einstein condensates, where the repulsive vortex–vortex interactions have an additional intermediate or long range attractive component. These states can arise in low-κ materials and may occur in multi-band superconductors. A combination of repulsive and attractive pairwise interactions can also occur in certain types of Bose–Einstein condensates and in magnetic superconductors. We show that when the pairwise interaction includes a long range attractive term, the ground state consists of a single vortex cluster. In the presence of pinning there is a well defined transition to a fragmented state as a function of pinning strength and density. We also demonstrate that in systems with intermediate range attraction and long range repulsion, ordered stripe and bubble phases occur.
    Physica C Superconductivity 09/2012; 479:15–18. · 0.72 Impact Factor

Publication Stats

11k Citations
2,072.18 Total Impact Points


  • 1970–2014
    • Los Alamos National Laboratory
      • • Theoretical Division
      • • Center for Nonlinear Studies
      Los Alamos, California, United States
  • 2004–2013
    • Beth Israel Deaconess Medical Center
      • Department of Medicine
      Boston, MA, United States
    • Boston University
      • Department of Physics
      Boston, Massachusetts, United States
  • 2002–2012
    • University of Massachusetts Amherst
      • Department of Mathematics and Statistics
      Amherst Center, MA, United States
    • Princeton University
      • Program in Applied and Computational Mathematics
      Princeton, NJ, United States
  • 1985–2011
    • University of Bayreuth
      • Institute of Physics
      Bayreuth, Bavaria, Germany
  • 2010
    • Universidad de Sevilla
      • Departamento de Física Aplicada I
      Sevilla, Andalusia, Spain
    • National Chiao Tung University
      Hsin-chu-hsien, Taiwan, Taiwan
  • 2009
    • Academy of Sciences of the Czech Republic
      • Fyzikální ústav
      Praha, Hlavni mesto Praha, Czech Republic
  • 2007
    • McGill University
      • Department of Physics
      Montréal, Quebec, Canada
    • Max Planck Institute for Solid State Research
      Stuttgart, Baden-Württemberg, Germany
  • 2006
    • Université Paris-Sud 11
      Orsay, Île-de-France, France
    • Università degli Studi di Trento
      Trient, Trentino-Alto Adige, Italy
  • 2005–2006
    • University of Zaragoza
      • Departamento de Física de la Materia Condensada
      Zaragoza, Aragon, Spain
    • Max Planck Institute for the Physics of Complex Systems
      Dresden, Saxony, Germany
    • University of Jyväskylä
      • Department of Physics
      Jyväskylä, Western Finland, Finland
    • Center for Research and Advanced Studies of the National Polytechnic Institute
      • Departamento de Física Aplicada
      Mexico City, The Federal District, Mexico
  • 2003–2005
    • City University of New York - York College
      New York City, New York, United States
    • Università degli Studi di Modena e Reggio Emilia
      Modène, Emilia-Romagna, Italy
  • 2001–2002
    • University of New Mexico
      • Department of Physics & Astronomy
      Albuquerque, NM, United States
    • Institute of Physics of the National Academy of Science of Ukraine
      Kievo, Kyiv City, Ukraine
  • 2000–2001
    • Rutgers, The State University of New Jersey
      • Department Physics and Astronomy
      New Brunswick, NJ, United States
    • Xerox Research Center Webster
      Webster, New York, United States
    • Centro Atómico Bariloche
      San Carlos de Bariloche, Río Negro, Argentina
    • University of California, Riverside
      Riverside, California, United States
    • University of Bologna
      Bolonia, Emilia-Romagna, Italy
  • 1998
    • University of California, Santa Barbara
      Santa Barbara, California, United States
  • 1997
    • Fudan University
      Shanghai, Shanghai Shi, China
    • The University of Western Ontario
      • Department of Applied Mathematics
      London, Ontario, Canada
  • 1989
    • Argonne National Laboratory
      • Division of Materials Science
      Lemont, Illinois, United States
    • Johns Hopkins University
      Baltimore, Maryland, United States
  • 1984
    • University of Florida
      • Department of Physics
      Gainesville, FL, United States
  • 1980–1983
    • University of Southern California
      Los Angeles, California, United States
  • 1982
    • Stanford University
      Palo Alto, California, United States
  • 1978–1980
    • Queen Mary, University of London
      Londinium, England, United Kingdom
  • 1976–1978
    • Cornell University
      • Laboratory of Atomic and Solid State Physics
      Ithaca, NY, United States