Penn Arts & Sciences

The University of Pennsylvania School of Arts and Sciences forms the foundation of the scholarly excellence that has established Penn as one of the world's leading research universities. We teach students across all 12 Penn schools, and our academic departments span the reach from anthropology and biology to sociology and South Asian studies.

Members of the Penn Arts & Sciences faculty are leaders in creating new knowledge in their disciplines and are engaged in nearly every area of interdisciplinary innovation. They are regularly recognized with academia's highest honors, including membership in prestigious societies like the National Academy of Sciences, the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the American Philosophical Society, as well as significant prizes such as MacArthur and Guggenheim Fellowships.

The educational experience offered by Penn Arts & Sciences is likewise recognized for its excellence. The School's three educational divisions fulfill different missions, united by a broader commitment to providing our students with an unrivaled education in the liberal arts. The College of Arts and Sciences is the academic home of the majority of Penn undergraduates and provides 60 percent of the courses taken by students in Penn's undergraduate professional schools. The Graduate Division offers doctoral training to over 1,300 candidates in more than 30 graduate programs. And the College of Liberal and Professional Studies provides a range of educational opportunities for lifelong learners and working professionals.

 

 

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Author: Aharony, Amnon ×

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  • Publication
    Series Study of Random Animals in General Dimensions
    (1988-09-01) Adler, Joan; Meir, Yigal; Harris, A. Brooks; Aharony, Amnon; Duarté, José A. M. S
    We construct general-dimension series for the random animal problem up to 15th order. These represent an improvement of five terms in four dimensions and above and one term in three dimensions. These series are analyzed, together with existing series in two dimensions, and series for the related Yang-Lee edge problem, to obtain accurate estimates of critical parameters, in particular, the correction to scaling exponent. There appears to be excellent agreement between the two models for both dominant and correction exponents.
  • Publication
    Localization and Quantum Percolation
    (1982-08-16) Shapir, Yonathan; Aharony, Amnon; Harris, A. Brooks
    Electronic wave functions are studied on dilute lattices, at dimensionalities 1⩽d⩽8. Generalized average inverse participation ratios are expanded in powers of the bond concentration, p. Dlog Padé approximants indicate that these ratios diverge as (pq−p)-γq, signaling the appearance of extended states for p>pq. These Anderson transitions occur above classical percolation. No divergence is detected at d=2. These results are consistent with the existence of localized states at the center of the band.
  • Publication
    Vibrational Excitations in Percolation: Localization and Multifractality
    (1992-11-30) Bunde, Armin; Roman, H. Eduardo; Russ, Stefanie; Aharony, Amnon; Harris, A. Brooks
    We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes ψi in terms of the chemical (minimal) path, we show theoretically that the ψ’s are characterized by a logarithmically broad distribution, and display multifractal features as a function of the Euclidean distance. The moments of ψi exhibit novel crossover phenomena. Our numerical simulations of fractons exhibit a nontrivial distribution of localization lengths, even when the chemical distance is fixed. These results are explained via a generalization of the theory.
  • Publication
    Evidence for Two Exponent Scaling in the Random Field Ising Model
    (1993-09-06) Gofman, Michael; Adler, Joan; Aharony, Amnon; Harris, A. Brooks; Schwartz, Moshe
    Novel methods were used to generate and analyze new 15 term high temperature series for both the (connected) susceptibility χ and the structure factor (disconnected susceptibility) χd for the random field Ising model with dimensionless coupling K=J/kT, in general dimension d. For both the bimodal and the Gaussian field distributions, with mean square field J2g, we find that (χd-χ)/K2gχ2=1 as T→Tc(g), for a range of [h2]=J2g and d=3,4,5. This confirms the exponent relation γ¯=2γ (where χd~t−γ¯, χ~t−γ, t=T-Tc) providing that random field exponents are determined by two (and not three) independent exponents. We also present new accurate values for γ.
  • Publication
    Was Superlocalization Observed in Carbon-Black–Polymer Composites?
    (1993-06-28) Aharony, Amnon; Harris, A. Brooks; Entin-Wohlman, Ora
    A Comment on the Letter by van der Putten, Phys. Rev. Lett. 69, 494 (1992).
  • Publication
    Spin Structures of Tetragonal Lamellar Copper Oxides
    (1994-06-06) Yildirim, Taner; Harris, A. Brooks; Entin-Wohlman, Ora; Aharony, Amnon
    The spin Hamiltonian of tetragonal lamellar antiferromagnets is shown to contain several novel anisotropies. Symmetry allows bond-dependent anisotropic exchange interactions, which lead to (a) interplane mean-field coupling and (b) an in-plane anisotropy which vanishes classically but arises from quantum zero point energy (QZPE). A similar QZPE involving the interplane isotropic interaction prefers collinear spins. Adding also diploar anisotropy, the competition between all these effects explains for the first time the spin structures of many cuprates.
  • Publication
    Symmetry, Spin-Orbit Interactions, and Spin Anisotropies
    (1994-11-21) Yildirim, Taner; Harris, A. Brooks; Entin-Wohlman, Ora; Aharony, Amnon
    The origins of anisotropy in the effective spin Hamiltonian, describing the ground manifold of Hubbard models with spin-orbit interactions, are critically discussed. For tetragonal symmetry, we show exactly that spin anisotropy can arise only if one includes both spin-orbit and Coulomb exchange interactions. For lower symmetries, additional anisotropies arise from terms which were hitherto neglected. Our analytic results are supported by numerical solutions for single bond clusters. These results can explain the easy plane anisotropy in the antiferromagnetic cuprates.
  • Publication
    Localization Length Exponent in Quantum Percolation
    (1995-03-13) Chang, Iksoo; Lev, Zvi; Harris, A. Brooks; Adler, Joan; Aharony, Amnon
    Connecting perfect one-dimensional leads to sites i and j on the quantum percolation (QP) model, we calculate the transmission coefficient Tij(E) at an energy E near the band center and the averages of ΣijTij, Σijr2ijTij, and Σijr4ijTij to tenth order in the concentration p. In three dimensions, all three series diverge at pq=0.36+0.01−0.02, with exponents γ=0.82+0.10−0.15, γ+2ν, and γ+4ν. We find ν=0.38±0.07, differing from “usual” Anderson localization and violating the bound ν≥2/d of Chayes et al. [Phys. Rev. Lett. 57, 2999 (1986)]. Thus, QP belongs to a new universality class.
  • Publication
    Yildirim et al. Reply
    (1995-04-03) Yildirim, Taner; Harris, A. Brooks; Entin-Wohlman, Ora; Aharony, Amnon
    A Reply to the Comment by S. Skanthakumar, J. W. Lynn, and I. W. Sumarlin, Phys. Rev. Lett. 74, 2842 (1995).
  • Publication
    Absence of Self-Averaging and Universal Fluctuations in Random Systems Near Critical Points
    (1996-10-28) Aharony, Amnon; Harris, A. Brooks
    The distributions P(X) of singular thermodynamic quantities, on an ensemble of d-dimensional quenched random samples of linear size L near a critical point, are analyzed using the renormalization group. For L much larger than the correlation length ξ, we recover strong self-averaging (SA): P(X) approaches a Gaussian with relative squared width RX~(L/ξ)−d. For L≪ξ we show weak SA (RX decays with a small power of L) or no SA [P(X) approaches a non-Gaussian, with universal L-independent relative cumulants], when the randomness is irrelevant or relevant, respectively.