Statement of Bruce H. Simon Before the Commission on the Future of Worker-Management Relations

Testimony_Simon_022494.pdf: 204 downloads, before Oct. 1, 2020

Effect of Landau Level Mixing on Braiding Statistics

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of abelian and nonabelian quantum Hall states. While path dependent geometric phases can perturb the abelian part of the statistics, we find that the nonabelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.Comment: 4 page

Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State

We perform numerical studies to determine if the fractional quantum Hall state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space approach we find that for realistic interactions, including Landau-level mixing, the ground state remains fully polarized and the AntiPfaffian is strongly favored.Comment: Main change is that the Anti-Pfaffian is favored instead of the Pfaffian (caused by a sign error in the commutation relation of the dynamical momenta). 4-plus pages, 3 figure

Spin-singlet Gaffnian wave function for fractional quantum Hall systems

We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The "spin dressed squeezing algorithm", and the "generalized Pauli principle".Comment: 15 pages, 2 figures. Version 3 fixes a typographical error in the Hamiltonian, Eq 3. Version 2 incorporates referee and editorial suggestions. The original title "Putting a Spin on the Gaffnian" was deemed to be too inappropriate for PR

Risk and return of publicly held versus privately owned banks

The author divides bank holding companies (BHCs) into four size classes, then categorizes each class according to public or private ownership. He compares the performance and risk across bank size classes between 1986 and 2000 and in five-year windows therein. For the largest BHCs, returns on assets and operating costs do not depend on ownership, but for the smaller BHCs, returns on assets are lower and operating costs are higher for those that are publicly owned. Small public BHCs also hold more capital than do small private ones.Corporate governance ; Bank holding companies ; Bank stocks ; Bank management

Five seconds or sixty? Presentation time in expert memory

The template theory presented in Gobet and Simon (1996a, 1998) is based on the EPAM theory (Feigenbaum & Simon, 1984; Richman et al., 1995), including the numerical parameters that have been estimated in tests of the latter; and it therefore offers precise predictions for the timing of cognitive processes during the presentation and recall of chess positions. This paper describes the behavior of CHREST, a computer implementation of the template theory, in a task when the presentation time is systematically varied from one second to sixty seconds, on the recall of both game and random positions, and compares the model to human data. As predicted by the model, strong players are better than weak players with both types of positions. Their superiority with random positions is especially clear with long presentation times, but is also present after brief presentation times, although smaller in absolute value. CHREST accounts for the data, both qualitatively and quantitatively. Strong players’ superiority with random positions is explained by the large number of chunks they hold in LTM. Strong players’ high recall percentage with short presentation times is explained by the presence of templates, a special class of chunks. The model is compared to other theories of chess skill, which either cannot account for the superiority of Masters with random positions (models based on high-level descriptions and on levels of processing) or predict too strong a performance of Masters with random positions (long-term working memory)

Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size

We show that all the bands of the Hofstadter model on the torus have an exactly flat dispersion and Berry curvature when a special system size is chosen. This result holds for any hopping and Chern number. Our analysis therefore provides a simple rule for choosing a particularly advantageous system size when designing a Hofstadter system whose size is controllable, like a qubit lattice or an optical cavity array. The density operators projected onto the flat bands obey exactly the Girvin-MacDonald-Platzman algebra, like for Landau levels in the continuum in the case of $C=1$, or obey its straightforward generalization in the case of $C>1$. This allows a mapping between density-density interaction Hamiltonians for particles in the Hofstatder model and in a continuum Landau level. By using the well-known pseudopotential construction in the latter case, we obtain fractional Chern insulator phases, the lattice counterpart of fractional quantum Hall phases, that are exact zero-energy ground states of the Hofstadter model with certain interactions. Finally, the addition of a harmonic trapping potential is shown to lead to an appealingly symmetric description in which a new Hofstadter model appears in momentum space.Comment: 15 pages, 8 figures; Published versio