Level-spacing distribution of a fractal matrix

We diagonalize numerically a Fibonacci matrix with fractal Hilbert space structure of dimension $d_{f}=1.8316...$ We show that the density of states is logarithmically normal while the corresponding level-statistics can be described as critical since the nearest-neighbor distribution function approaches the intermediate semi-Poisson curve. We find that the eigenvector amplitudes of this matrix are also critical lying between extended and localized.Comment: 6 pages, Latex file, 4 postscript files, published in Phys. Lett. A289 pp 183-7 (2001

Freed by interaction kinetic states in the Harper model

We study the problem of two interacting particles in a one-dimensional quasiperiodic lattice of the Harper model. We show that a short or long range interaction between particles leads to emergence of delocalized pairs in the non-interacting localized phase. The properties of these Freed by Interaction Kinetic States (FIKS) are analyzed numerically including the advanced Arnoldi method. We find that the number of sites populated by FIKS pairs grows algebraically with the system size with the maximal exponent $b=1$, up to a largest lattice size $N=10946$ reached in our numerical simulations, thus corresponding to a complete delocalization of pairs. For delocalized FIKS pairs the spectral properties of such quasiperiodic operators represent a deep mathematical problem. We argue that FIKS pairs can be detected in the framework of recent cold atom experiments [M.~Schreiber {\it et al.} Science {\bf 349}, 842 (2015)] by a simple setup modification. We also discuss possible implications of FIKS pairs for electron transport in the regime of charge-density wave and high $T_c$ superconductivity.Comment: 26 pages, 21 pdf and png figures, additional data and high quality figures are available at http://www.quantware.ups-tlse.fr/QWLIB/fikspairs/ , parts of sections 2 and 3 moved to appendices, manuscript accepted for EPJ

Ethical Consumerism and the Designated Supplier Program: International Labor Rights Fund Position Statement

This document is part of a digital collection provided by the Martin P. Catherwood Library, ILR School, Cornell University, pertaining to the effects of globalization on the workplace worldwide. Special emphasis is placed on labor rights, working conditions, labor market changes, and union organizing.ILRF_Ethical_Consumerism_and_the_Designated_Supplier_Program__International_Labor_Rights_Fund_Position_Statement.pdf: 66 downloads, before Oct. 1, 2020

Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems

Incommensurate structures can be described by the Frenkel Kontorova model. Aubry has shown that, at a critical value K_c of the coupling of the harmonic chain to an incommensurate periodic potential, the system displays the analyticity breaking transition between a sliding and pinned state. The ground state equations coincide with the standard map in non-linear dynamics, with smooth or chaotic orbits below and above K_c respectively. For the standard map, Greene and MacKay have calculated the value K_c=.971635. Conversely, evaluations based on the analyticity breaking of the modulation function have been performed for high commensurate approximants. Here we show how the modulation function of the infinite system can be calculated without using approximants but by Taylor expansions of increasing order. This approach leads to a value K_c'=.97978, implying the existence of a golden invariant circle up to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation provided; Revised version, accepted for publication in Europhysics Letter

Delocalization and Heisenberg's uncertainty relation

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Harper model with its quasiperiodic potential shows a transition from extended to localized states. The difference between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for the delocalization of a quantum particle.Comment: 7 pages, 2 figures, EPL class include

Design citeria for applications with non-manifest loops

In the design process of high-throughput applications, design choices concerning the type of processor architecture and appropriate scheduling mechanism, have to be made. Take a reed-solomon decoder as an example, the amount of clock cycles consumed in decoding a code is dependent on the amount of errors within that code. Since this is not known in advance, and the environment in which the code is transmitted can cause a variable amount of errors within that code, a processor architecture which employs a static scheduling scheme, has to assume the worst case amount of clock cycles in order to cope with the worst case situation and provide correct results. On the other hand a processor that employs a dynamic scheduling scheme, can gain wasted clock cycles, by scheduling the exact amount of clock cycles that are needed and not the amount of clock cycles needed for the worst case situation. Since processor architectures that employ dynamic scheduling schemes have more overhead, designers have to make their choice beforehand. In this paper we address the problem of making the correct choice of whether to use a static or dynamic scheduling scheme. The strategy is to determine whether the application possess non-manifest behavior\ud and weigh out this dynamic behavior against static scheduling solutions which were quite common in the past. We provide criteria for choosing the correct scheduling architecture for a high throughput application based upon the environmental and algorithm-specification constraints. Keywords¿ Non-manifest loop scheduling, variable latency functional units, dynamic hardware scheduling, self\ud scheduling hardware units, optimized data-flow machine architecture

Scheduling and Allocation of Non-Manifest Loops on Hardware Graph-Models

We address the problem of scheduling non-manifest data dependant periodic loops for high throughput DSP-applications based on a streaming data model. In contrast to manifest loops, non-manifest data dependant loops are loops where the number of iterations needed in order to perform a calculation is data dependant and hence not known at compile time. For the case of manifest loops, static scheduling techniques have been devised which produce near optimal schedules. Due to the lack of exact run-time execution knowledge of non-manifest loops, these static scheduling techniques are not suitable for tackling scheduling problems of DSP-algorithms with non-manifest loops embedded in them. We consider the case where (a) a-priori knowledge of the data distribution, and (b) worst case execution time of the non-manifest loop are known and a constraint on the total execution time has been given. Under these conditions dynamic schedules of the non-manifest data dependant loops within the DSP-algorithm are possible. We show how to construct hardware which dynamically schedules these non-manifest loops. The sliding window execution, which is the execution of a non-manifest loop when the data streams through it, of the constructed hardware will guarantee real time performance for the worst case situation. This is the situation when each non-manifest loop requires its maximum number of iterations

Breakdown of Lindstedt Expansion for Chaotic Maps

In a previous paper of one of us [Europhys. Lett. 59 (2002), 330--336] the validity of Greene's method for determining the critical constant of the standard map (SM) was questioned on the basis of some numerical findings. Here we come back to that analysis and we provide an interpretation of the numerical results by showing that no contradiction is found with respect to Greene's method. We show that the previous results based on the expansion in Lindstedt series do correspond to the transition value but for a different map: the semi-standard map (SSM). Moreover, we study the expansion obtained from the SM and SSM by suppressing the small divisors. The first case turns out to be related to Kepler's equation after a proper transformation of variables. In both cases we give an analytical solution for the radius of convergence, that represents the singularity in the complex plane closest to the origin. Also here, the radius of convergence of the SM's analogue turns out to be lower than the one of the SSM. However, despite the absence of small denominators these two radii are lower than the ones of the true maps for golden mean winding numbers. Finally, the analyticity domain and, in particular, the critical constant for the two maps without small divisors are studied analytically and numerically. The analyticity domain appears to be an perfect circle for the SSM analogue, while it is stretched along the real axis for the SM analogue yielding a critical constant that is larger than its radius of convergence.Comment: 12 pages, 3 figure

Multifractality of correlated two-particle bound states in quasiperiodic chains

We consider the quasiperiodic Aubry-Andr\'e chain in the insulating regime with localised single-particle states. Adding local interaction leads to the emergence of extended correlated two-particle bound states. We analyse the nature of these states including their multifractality properties. We use a projected Green function method to compute numerically participation numbers of eigenstates and analyse their dependence on the energy and the system size. We then perform a scaling analysis. We observe multifractality of correlated extended two-particle bound states, which we confirm independently through exact diagonalisation.Comment: 7 pages, 8 figure