Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.Comment: Some clarifications were added in the introduction and an extra appendix was adde

Enacting Productive Dialogue: Addressing the Challenge that Non-Human Cognition Poses to Collaborations Between Enactivism and Heideggerian Phenomenology

This chapter uses one particular proposal for interdisciplinary collaboration – in this case, between early Heideggerian phenomenology and enactivist cognitive science – as an example of how such partnerships may confront and negotiate tensions between the perspectives they bring together. The discussion begins by summarising some of the intersections that render Heideggerian and enactivist thought promising interlocutors for each other. It then moves on to explore how Heideggerian enactivism could respond to the challenge of reconciling the significant differences in the ways that each discourse seeks to apply the structures it claims to uncover

Transient rectification of Brownian diffusion with asymmetric initial distribution

In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum

On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schroedinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schroedinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon, Simon, and Souillard.Comment: (1 figure

Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations

Multiconfiguration electron density function for the ATSP2K-package

A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation of its expectation value is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique. The natural orbitals are evaluated from the diagonalization of the density matrix

Exchange-assisted tunneling in the classical limit

The exchange interaction and correlations may produce a power-law decay instead of the usual exponential decrease of the wave function under potential barrier. The exchange-assisted tunneling vanishes in the classical limit, however, the dependence on the Planck constant h is different from that for a conventional single-particle tunneling

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur

Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI

Wavefunctions of complex lanthanide atoms NdI, PmI and SmI, obtained via multi-configuration Dirac-Fock method, are analyzed for density of states in terms of partial densities, strength functions ($F_k(E)$), number of principal components ($\xi_2(E)$) and occupancies (\lan n_\alpha \ran^E) of single particle orbits using embedded Gaussian orthogonal ensemble of one plus two-body random matrix ensembles [EGOE(1+2)]. It is seen that density of states are in general multi-modal, $F_k(E)$'s exhibit variations as function of the basis states energy and $\xi_2(E)$'s show structures arising from localized states. The sources of these departures from EGOE(1+2) are investigated by examining the partial densities, correlations between $F_k(E)$, $\xi_2(E)$ and \lan n_\alpha \ran^E and also by studying the structure of the Hamiltonian matrices. These studies point out the operation of EGOE(1+2) but at the same time suggest that weak admixing between well separated configurations should be incorporated into EGOE(1+2) for more quantitative description of chaos and localization in NdI, PmI and SmI.Comment: There are 9 figure

“Go get a job right after you take a bath”: Occupy Wall Street as Matter Out of Place

Anthropological studies of purity reveal how notions of cleanliness influence political and social life. During its 2011 Zuccotti Park occupation in Lower Manhattan, Occupy Wall Street (OWS) contested spatial and symbolic manifestations of neoliberalism by re-inserting Otherness into sanitized and privatized space. But the demonstration provoked reactions from politicians and news media that entwined discourses of cleanliness and productivity (such as Newt Gingrich’s riposte to the protestors: “Go get a job right after you take a bath”). This ethnographic study argues that such representations had spatial and political effects. In particular, our account illuminates the plural agency of Occupiers, where resistance to depictions of dirt and idleness existed alongside the use of such discourses to discipline each other. We trace a discursive legacy of these events as notions of productivity and cleanliness have circulated within activist responses to 2012’s Superstorm Sandy and the 2014 Flood Wall Street mobilization.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1111/anti.1222