A. R. Bishop

University of Massachusetts Amherst, Amherst Center, MA, United States

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Publications (806)1859.45 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios of instability development are exhibited through direct simulations.
  • 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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    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 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 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
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    ABSTRACT: We present a theoretical study on the relation between the size of the rare earth ions, often known as chemical pressure, and the stability of the coherent Jahn-Teller distortions in undoped perovskite manganites. Using a Keating model expressed in terms of atomic scale symmetry modes, we show that there exists a coupling between the uniform shear distortion and the staggered buckling distortion within the Jahn-Teller energy term. It is found that this coupling provides a mechanism by which the coherent Jahn-Teller distortion is more stabilized by smaller rare earth ions. We analyze the appearance of the uniform shear distortion below the Jahn-Teller ordering temperature, estimate the Jahn-Teller ordering temperature and its variation between NdMnO3 and LaMnO3, and obtain the relations between distortions. We find good agreement between theoretical results and experimental data.
    Physical review. B, Condensed matter 08/2012; 86(18). · 3.66 Impact Factor
  • T. F. Seman, K. H. Ahn, T. Lookman, A. R. Bishop
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    ABSTRACT: We present a detailed study of a model for strain-induced metal-insulator phase coexistence in perovskite manganites. Both nanoscale and mesoscale inhomogeneities are self-consistently described using atomic scale modes and their associated constraint equations. We also examine the stability of domain configurations against uniform and nonuniform modifications of domain walls. Our results show that the long range interactions between strain fields and the complex energy landscape with multiple metastable states play essential roles in stabilizing metal-insulator phase coexistence, as observed in perovskite manganites. We elaborate on the modes, constraint equations, energies, and energy gradients that form the basis of our simulation results.
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    ABSTRACT: Exotic vortex states with long range attraction and short range repulsion have recently been proposed to arise in superconducting hybrid structures and multi-band superconductors. 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 completely phase separates. 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. We show that a signature of the exotic vortex interactions under transport measurements is a robust double peak feature in the differential conductivity curves.
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    ABSTRACT: We study the dynamics of the discrete nonlinear Schrödinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather. PACS. 63.70.+h Statistical mechanics of lattice vibrations and displacive phase transitions - 63.20.Pw Localized modes - 63.20.Ry Anharmonic lattice modes
    Physics of Condensed Matter 04/2012; 15(1):169-175. · 1.28 Impact Factor
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    I.martin, G.ortiz, A. V.balatsky, A. R.bishop
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    ABSTRACT: We present a minimal model for cuprate superconductors. At the unrestricted mean-field level, the model produces homogeneous superconductivity at large doping, striped superconductivity in the underdoped regime and various antiferromagnetic phases at low doping and for high temperatures. On the underdoped side, the superconductor is intrinsically inhomogeneous and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. The model is applied to calculate experimentally measurable ARPES spectra.
    International Journal of Modern Physics B 01/2012; 14(29n31). · 0.46 Impact Factor
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    ABSTRACT: In this paper we review a number of recent developments in the study of the Discrete Nonlinear Schrödinger (DNLS) equation. Results concerning ground and excited states, their construction, stability and bifurcations are presented in one and two spatial dimensions. Combinations of such steady states lead to the study of coherent structure bound states. A special case of such structures are the so-called twisted modes and their two-dimensional discrete vortex generalization. The ideas on such multi-coherent structures and their interactions are also useful in treating finite system effects through the image method. The statistical mechanics of the system is also analyzed and the partition function calculated in one spatial dimension using the transfer integral method. Finally, a number of open problems and future directions in the field are proposed.
    International Journal of Modern Physics B 01/2012; 15(21). · 0.46 Impact Factor

Publication Stats

11k Citations
1,859.45 Total Impact Points


  • 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
  • 1970–2012
    • Los Alamos National Laboratory
      • • Theoretical Division
      • • Center for Nonlinear Studies
      Los Alamos, CA, 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
  • 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
  • 2004
    • Boston University
      • Department of Physics
      Boston, Massachusetts, United States
  • 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 Bologna
      Bolonia, Emilia-Romagna, Italy
    • University of California, Riverside
      Riverside, California, United States
  • 1997
    • The University of Western Ontario
      • Department of Applied Mathematics
      London, Ontario, Canada
    • Fudan University
      Shanghai, Shanghai Shi, China
  • 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